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Pratik Uygulama Örnekler17
Power Electronics
1 Introduction
19.1.1 Overview
This Chapter lists a series of experiments, with
explanatory material, suitable for exploring power
electronics in depth. Four sets of experiments are
included: a set of rectifier experiments that includes a
laboratory orientation sequence, a set of dc-dc converter
experiments, inverter experiments, and component
experiments. An additional set, directed toward a dc-dc
converter design project, is included as well. The Chapter
in many ways stands alone as a Laboratory Manual; its
inclusion here in the text helps provide a complete
context for work in power electronics.
RATINGS. Before applying power, check that the voltage,
current, and power levels you expect to see do not violate
any ratings. What is the power expected in a given
resistor or other component? Does the device have
polarity, and is it connected in the proper direction?
HEAT. Small parts can become hot enough to cause
burns with as little as one watt applied to them. Even
large resistors will become hot if five watts or so are
applied.
CAREFUL WORKMANSHIP. Check and recheck all
connections before applying power. Plan ahead: consider
the effects of a circuit change before trying it. Use the
right wires and connectors for the job, and keep the
experiment area neat. Avoid manipulating circuits or
making
changes
with
power
applied.
LIVE PARTS. Most semiconductor devices have an
electrical connection to the case. Assume that anything
touching the case is part of the circuit and is connected.
Avoid tools and other metallic objects around live circuits.
Keep beverage containers away from the work area.
19.1.2 Safety information
The experiments discussed here are designed for
relatively low power levels of about 100 W and below.
They therefore can be performed with a minimum
investment in special instrumentation and equipment, and
safety concerns are minimized. However, the risks are
not negligible, and it is important to make proper
preparations and use due care in performing the work.
Safe lab practice is the responsibility of the experimenter.
It is not possible to perform completely benign power
electronics experiments; damaged components or
expensive repairs will be necessary if basic safety rules
are not addressed.
It is especially important to be careful when working with
spinning motors, and parts which become hot from power
dissipation. Even if rugged equipment is chosen, many
instruments can be damaged when driven beyond
ratings. Please follow the safety precautions listed to
avoid injury, discomfort, and lost lab time.
GROUND. Be aware of which connections are grounded,
and which are not. The most common cause of
equipment damage is unintended shorts to ground.
Remember that most oscilloscopes are designed to
measure voltage relative to ground, not between two
Neckties and loose clothing should not be worn
when working with motors. Be sure motors are not free
to move about or come in contact with circuitry.
The most common cause of trouble in power conversion
experiments is improper grounding practice. Any circuit
can have only one reference node, and the circuit is
altered if a probe or tool introduces an external
connection. Ratings and polarities are also common
problems. Electrolytic capacitors, for example, often burn
or even explode if connected in reverse. Small resistors
do not tolerate excess power levels very long. Neatness
is an issue as well. A messy, convoluted circuit is
extremely hard to debug. In power electronics, small
inductances of wires make a significant difference. A
neat, tight package in general operates much better than
a layout with long looping wires.
19.1.3 Equipment assumptions
For the purposes of the experiments discussed here, the
following minimum equipment is assumed:
1. Oscilloscope (digital preferred), two channels, 60 MHz
bandwidth.
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2. Function generator, 10 Hz to 2 MHz, sine and square
waves.
3. True RMS multimeters.
4. Power supply, 0-24 V, 0-5 A or better.
5. Power supply, +12 V, 0-0.5 A (for control functions).
6. Access to standard ac mains power.
7. FET and SCR control circuits as discussed in Chapter
18, along with transformers described there.
8. Leads, connectors, various parts, and a breadboard
system for circuit prototypes.
The following additional equipment is very helpful, and is
recommended:
1. Magnetic current probe, 0-20 MHz.
2. Digital wattmeter.
3. Power supply, 0-50 V, 0-10 A.
4. Isolation amplifier for oscilloscope channels.
5. Temperature probe for multimeter.
6. Access to three-phase mains.
7. A semiconductor curve tracer.
Be sure to be aware of ground connections or other
considerations of the instruments. Many power supplies
have ground connections that should be removed before
using the equipment with a power converter.
List of equipment used, especially if unusual items are
involved.
All experiment data. Be sure to include units and scale
settings. It is generally good practice to record data in its
most primitive form to avoid errors. Scaling or other
calculations
can
be
done
later.
The date, and the names and signatures of the
experimenters.
It is usually permissible to include calculations,
observations, and even speculations in a notebook,
provided these are clearly marked and kept apart from
experimental data and actual lab work. A bound book
with permanent, pre-printed page numbers is a good
selection for use as a notebook. Loose sheets often get
lost or spoiled, and spiral books offer the temptation to
tear out unwanted information. Notebook errors should be
crossed out (not obliterated). A notebook should be kept
in ink, consistent with its function as a permanent record.
Keeping a complete lab notebook sometimes seems
inconvenient, but in the long run saves a tremendous
amount of time and effort.
19.1.4 Keeping a laboratory notebook
19.2 Experiment
Equipment.
A proper laboratory notebook is a crucial tool for work in
any experimental environment. A notebook used in a
research lab, a development area, or on the factory floor
is probably the most valuable piece of gear in the
engineer's arsenal. The purpose of the notebook is to
provide a complete record of practical work. This should
help avoid duplication of effort. Human memory is not
perfect, but a notebook is a permanent record. In
industrial practice, the notebook is usually the employer's
property. Many companies have specific rules about
notebook format and content. The suggestions here are
provided for general guidance, and are not meant to
conflict with requirements in various areas of practice. In
general, a notebook should include:
Diagrams of all circuits used in the lab. The important
factors are to be able to reproduce a setup and check for
possible errors.
Procedures and actions. The idea is to provide enough
information so that the experiment could be repeated.
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--
Demonstration
of
Special
19.2.1 Introduction
This experiment tests some of the special equipment
discussed in Chapter 18. It also provides practice with the
general equipment of an electronics lab in preparation for
the full sequence of experimental work. As discussed in
Chapter 18, three special equipment items are proposed
to support the full range of power electronics experiments
in a standard laboratory:
A low-voltage ac mains supply, from a transformer bank,
for experiments with rectifiers and other circuits. The
suggested arrangement supports both single-phase and
three-phase power input. A circuit diagram for the
combination was provided in Figure 18.4.
A self-contained SCR control unit. The suggested design
contains three silicon controlled rectifiers (SCRs) and
time delay circuits to produce turn-on control signals. The
anodes
and
cathodes
are
isolated.
Pratik devreler / N. Abut
An isolated power FET control box. The FET provides
switch action for almost any type of dc-dc converter. A
complete pulse-width modulation block creates a PWM
switching function, with adjustable frequency and duty
ratio. As in the SCR circuit, this means that the terminals
of the FET can be connected to any voltage level up to
the device ratings.
The function of these circuits is to support tests of useful
power converters. The internal operation is important and
well worth exploring. The circuits will be considered as
"blue boxes" rather than black boxes, meaning that their
function is not hidden away.
1N4004 diodes for full-wave output (anodes to phase A
and B output, cathodes in common to load). See Figure
19.2
.
2.
Con
nect
a
load
of approximately 50 from the common cathode to ground.
What resistor power rating is needed?
3. Observe the resistor voltage waveform. Observe diode
current and comment. Measure the resistor RMS voltage,
RMS current, power, and average voltage. What is the
relevance of each?
4. Remove the diodes, and substitute SCRs labelled A
and B from the SCR unit. Set up the SCR box for twophase operation. Use a 25 load in this case. What should
the power rating be?
5. Turn the phase delay control to the lowest setting.
Double check all connections, then turn the power on.
19.2.2 Demonstration circuits
For this demonstration, both the SCR and the FET will be
used in simple converter circuits. The SCR set will be
used in a controlled full-wave rectifier circuit, while the
FET unit will be used to form a basic dc-dc converter.
These circuits are typical power electronics applications,
not too far removed from simple commercial products.
There are two major ways to form a full-wave rectifier.
One is the rectifier bridge circuit, which converts a single
ac voltage source into a full-wave rectified waveform. The
second involves a center-tapped transformer as a "twophase" ac source. This second form requires a more
expensive transformer, but needs only two rectifiers. Both
are shown in Figure 19.1. As shown in the Figure, SCRs
can be substituted for the diodes in a full-wave rectifier.
The SCRs are operated half a cycle apart, with an
adjustable phase angle delay.
19.2.3 Procedure
Part 1 -- Rectifiers and the SCR box
6. Observe the voltage waveform across the resistor.
Notice how the waveform changes with changes in the
control setting. Again measure RMS voltage, RMS
current, power, and average voltage, and consider the
relevance of each.
Part 2 -- Dc-dc conversion and the FET box
The FET unit will be used in a simple circuit which
converts a dc voltage to a lower level with minimal power
loss. In essence, the output is presented with a rapid
switching of the input. The average output level (the dc
portion) is lower than the input since the switch cannot be
on more than 100% of the time.
1. Set up the FET control box as shown in Figure 19.3.
2. Observe the drain-to-source voltage. Turn the unit on.
Adjust the output for 50% duty ratio and about 50 kHz.
3. Connect a voltage source of 20 to 30 V to the input.
Observe the output waveform and average voltage.
Adjust the duty ratio and notice the change. Adjust the
1. Connect the transformer set to single-phase input to
provide both positive and negative outputs. Connect two
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frequency and notice the change. Explain the results.
off state.
Part 3 -- Power semiconductor devices and the curve
tracer
3. Check your connections. Apply power to the socket
and observe the diode waveform. Notice that the typical
model of a constant 0.7 V drop has limited accuracy. A
better model would also include a resistor to model the
upward slope of the curve. What resistance and forward
voltage provide the most accurate model for your
device?
Power semiconductors are important to the field of power
electronics. The curve tracer is a helpful measuring
instrument to characterize these devices. Recall the
characteristic curves for diodes, bipolar transistors
(BJTs), and FETs. Examples are given below. The diode
shows exponential V-I behavior. Transistors show a
family of curves, dependent on the base or gate input
operation. For switching operation, only a small portion of
these curves is relevant. (Which portion would it be?)
4. A BJT is to be tested on the curve tracer. Let us
assume that the device is a generic, unknown part. To be
conservative, limit current to 0.1 A, power to 0.5 W, and
voltage to 20 V. Connect the part with the socket off.
5. Double check connections. Allow base current of 0.1
mA per step to be applied. Turn on the socket. Adjust as
necessary to observe the curves. Keep power levels
below 0.5 W in any case if a small device is being tested.
Which portions of the curves are useful for switching
action? How much base current will be needed if the
device is to be used to switch 0.5 A?
The curve tracer is an instrument intended to measure
these device curves directly. The BJT, for example, is
characterized by a certain collector-emitter voltage,
collector current, and base current. Recall that the BJT is
basically a current-controlled current source. To measure
BJT curves, the curve tracer applies a specified range of
collector-emitter voltage and collector current values.
Several discrete base current values are then applied in
steps, and the results are displayed on an oscilloscope.
The FET is a voltage-controlled current source. The drain
and source terminals function very much like those of the
BJT collector and emitter. The gate must have a voltage
applied relative to the source, rather than a current. In the
procedure below, four classes of devices will be tested on
the curve tracer.
1. A rectifier diode (1N4004) is to be tested on the curve
tracer. Since the defining characteristics are forward
voltage and current, the device should be connected as if
its anode were a collector and cathode were an emitter.
2. With the curve tracer
socket off, set up the unit
for limits of about 1 A and
1 W. The 1N4004 can
handle up to 400 V in its
30
6. A power FET is to be tested on the curve tracer. This
power part should be limited to 5 A, 1 W, and 50 V.
Connect the part with power off. The drain terminal
should be connected as the collector, source should be
connected as emitter, and gate should be connected as
base.
7. Double check your connection. We want to vary gatesource voltage from approximately zero to about ten
volts.
8. When ready, apply power to the socket and observe
the curves which result. Which portions are relevant for
switch action? As with the diode, a resistance is often
used to model the slope of the curves. What value of
resistance provides a good model when the gate-source
voltage
is
10
V?
9. The SCR can be thought of as a diode with an extra
gate terminal. When sufficient gate current flows, the
device operates as a diode. Without it, the device is off.
For the SCR here, limits of 10 A, 2 W, and 100 V are
appropriate. To test it, associate the anode with a BJT
collector, the cathode with an emitter, and the gate with a
base.
Pratik devreler / N. Abut
3. Which portion of the curve tracer device characteristics
would you expect to use in a switching application? What
would the curve tracer display if a current-controlled ideal
switch were to be measured?
10. Double check connections. The gate current can be
made as high as 0.2 A without damage, but try values
around 50 mA to best see the device curves.
11. Consider what curves are expected (e.g. diode when
on), then apply power. Are the results what you
anticipated? Is there a family of curves, as for the
transistors?
19.3 Experiment -- Basic Rectifier Circuits
19.3.1 Introduction
The objective of this experiment is to provide additional
practice with power electronics measurement techniques.
These will be studied in the context of simple controlled
and uncontrolled rectifier circuits.
19.2.4 Study questions
In each experiment, a set of questions to guide further
study and reports will be provided.
1. In dc output converters, what is the relevance of RMS
output voltage? What about average voltage? (Hint:
consider the effects on loads which are purely resistive,
and on loads which consist of a large inductor in series
with a resistor.)
2. For the simple dc-dc converter tested in Part 1 of the
above procedures, explain how to predict the average
value of output voltage from the input voltage, the
switching frequency, and the switch duty ratio (the
fraction of the time during which the switch is on).
Properties of simple R-C, R-L, and R-L-C circuits are
studied in introductory circuit analysis courses. Properties
of "D-C" circuits (diode-capacitor circuits) are less well
known. Similarly, D-L, D-L-C, and various D-R-x circuits
are not widely studied. The behavior of these circuits
provides a practical look at power electronic converters,
both from the standpoint of energy conversion
applications and from the standpoint of laboratory
measurements. This is the focus of the Basic Rectifier
Circuits experiment. The operation of the SCR will be
examined briefly as well. An R-C timing circuit for
adjusting the phase delay of an SCR will be constructed
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Elektrik Devreleri
and tested.
19.3.2 Basic theory
Consider the simple half-wave rectifier shown in Figure
19.5. The state of the diode depends on the input voltage
polarity -- and also on the load. With no information about
the load, it is not possible to predict either the load current
or voltage. With a resistive load, the load voltage is zero
whenever the diode is off. One simple way to find the
circuit action (even though we already know what the
circuit does), is to take a trial method approach as in
Chapter 2. Since an off diode cannot block forward
voltage, the diode will be on if and only if the input voltage
is positive. The current is given in Figure 19.6. All
currents and voltages in a diode circuit must be
consistent with the restrictions imposed by the diodes.
Even a complicated diode circuit combination can be
understood quickly with the trial method.
Now, look at the inductive load of Figure 19.7. Assume
that the inductor is large. If current is initially flowing in the
inductor, the diode is on. Inductor voltage VL will be
positive or negative, depending on the input voltage and
the inductor current.
Since there is current flow, the diode will stay on for some
time regardless of the Vin value. If VL = L(di/dt) is
negative, the inductor current will fall, possibly even to
zero. The diode must stay on until the current reaches
zero.
Capacitive loads act much differently. Consider the
capacitor of Figure 19.8, fully charged and supplying
energy to the resistor. As long as Vin < Vout, the diode will
be off. When Vin becomes larger than Vout, the diode must
turn on. But then a large forward current C(dv/dt) will flow
until Vinbecomes less than Vout. Brief, large current spikes
are a feature of Diode-Capacitor circuits. Such currents
are typical of the simple dc power supplies in most cheap
electronic equipment.
Consider the half-wave resistive circuit of Figure 19.9.
Turn-on of the SCR can be delayed to alter the
waveshape. The turn-on delay is traditionally measured in
degrees relative to a full diode waveform.
The action of this control is not hard to determine for a
known load, since the input waveform is simply being
switched on and off.
19.3.3 Measurement issues
In power electronics, measurement interpretation is an
important ingredient of obtaining data and coming to
conclusions about circuit behavior. Like any electronics
laboratory, we will use voltage waveforms from an
oscilloscope, and voltage and current magnitudes
obtained from meters. Some important additional
measurements include current waveforms and phase
angles. Many of the waveforms are not sinusoidal, so the
actual wave shape is important information.
For average and RMS measurements, a typical
laboratory multimeter such as the Fluke model 8010A
provides a useful basis for discussion. It displays the
average value of the input whenever it is set for dc. When
set to ac, this meter directs the input through a capacitor,
and computes the RMS value of the ac portion which
Diodes offer no control means, and a switch capable of
blocking forward voltage is needed to add a control
function. The SCR is one provides this function.
Nevertheless, it fulfills the necessary forward-conducting
bidirectional blocking characteristic. The SCR is called
a latching device, because the on-state is self-sustaining.
Once a turn-on command is applied, the SCR will remain
on until the forward current is removed. This means that
the device is exactly equivalent to a diode once on.
passes
32
through.
Some
of
the
important
meter
Pratik devreler / N. Abut
specifications are given in Table 19.1. Many power
converter waveforms contain both dc and ac. The "full
RMS" value might be useful in this case. With most
multimeters, even "true RMS" units, such as the 8010A,
the RMS values for ac and dc portions must be measured
separately and combined to give the correct result.
Power itself is important. There are growing numbers of
manufacturers offering digital power meters appropriate
for complicated waveforms. One type, which will be used
here as an example, is represented by the Valhalla
Scientific model 2101 voltage-current-power meter. This
instrument samples the incoming voltage and current
waveforms, and computes RMS values as well as the
average power. The current is measured by sensing the
voltage across a fixed 0.01 resistor. A meter configured in
this way need not distinguish between dc and ac
waveforms, and can provide accurate power readings
over a wide frequency range. A functional symbol is
shown in Figure 19.10. The voltage is sensed across the
input. The output connection forces the current to flow
through the sensing resistor. An input signal at 0 Hz or 40
Hz-10 kHz will give a true RMS display.
Low-impedance sense resistors can be used for
complete current waveforms, but they can introduce
grounding problems in a circuit. Industrial laboratories
specializing in power electronics make extensive use of
Hall-effect current probes that sense the magnetic fields
around conductors. One major drawback is that the
probes have an internal dc offset which might drift as the
temperature changes.
One important detail in making this measurement is to
make sure both oscilloscope traces are triggered
simultaneously. The "chop" mode of the scope is useful
for this purpose.
19.3.4 Procedure
Part One -- The Diode
In this first part, a waveform generator is used as the
power source so that higher frequencies and small
components can be used for testing. Please use care in
connecting and operating this instrument. It is not
designed to supply high current.
1. Obtain a toroidal or audio transformer. One alternative
is a 60 turn primary and a 60 turn secondary on a
Ferroxcube 500XT400-3C8 ferrite toroid core.
2. Construct the circuit shown in Figure 19.12. Diodes
should be standard 1N4148 rectifiers, or similar.
3. Be careful with ground connections. Set the waveform
generator for approximately 1 kHz output at about 10 V
peak. Observe Voutwith the scope.
4. Sketch the output waveform under "no load" conditions
(the scope probe gives a slight load).
Timing is critical in the operation of most power
converters. Since switches are the only means of control,
the exact moment when a switch operates is a key piece
of information. The SCR provides a typical example.
Consider the waveforms in Figure 19.11. A sinusoidal
waveform (perhaps the input voltage to a rectifier) serves
as a timing reference. It is straightforward to measure the
time shift between this wave's zero crossing and the turnon rise of the switched signal below it. The example in the
Figure shows two 60 Hz waveforms. The time delay d can
be measured directly from the graph as about 1.25 ms.
Since a full 360 degree period lasts 16.667 ms, an
angle d can be calculated from d as
5. Load the bridge with a 500 resistor (compute the
necessary power rating first). Observe and sketch the
output voltage waveform. Use a current probe or place a
10 resistor in series with the transformer output to
observe the current out of the transformer. Sketch the
current waveform.
6. Connect an inductor (a reasonable value is about 2550 mH) in series with the resistor. Observe and sketch
the resistor voltage waveform and the current into the
bridge. Measure the average resistor voltage with a
multimeter.
7. Remove the R-L load. Instead, attach a 47 resistor in
series with an 0.1 µF capacitor. Place a 10 k resistor
across the capacitor terminals. Observe and sketch the
capacitor voltage waveform and the bridge input current
waveform. Also measure the average capacitor voltage.
33
Elektrik Devreleri
19.4 Experiment -- Single-phase Rectifiers
Part 2 -- The SCR
In Section 19.2, we saw a simple controlled rectifier
example, and the waveforms which result. The gate
control was described as a pulse. In this Section, an R-C
delay circuit for operating an SCR will be examined. It is
similar to the circuit used in commercial lamp dimmers.
1. Construct the circuit shown in Figure 19.14. The input
source is taken from the 25 V transformer set.
2. Use a resistor substitution box or other variable resistor
for Rc. Observe the Vg and Vload waveforms for Rc values
of 0, 200, 400, 600, 800, and 1000 . Sketch the two
waveforms for two or three values of Rc. Measure the
turn-on delay by comparing Vg or the gate current with
Vload with the oscilloscope set for line triggering. Also, use
a multimeter to measure the average value of Vload in all
cases.
19.4.1 Introduction
This experiment examines the properties of single-phase
controlled rectifiers. Converter concepts such as source
conversion and switch types will be illustrated. Popular
applications such as battery chargers and dc motor drives
will be tested. In Section 19.3, you had a chance to
become familiar with the basic action of the SCR, and
also studied a number of non-resistive rectifier load
circuits. Now, the SCR boxes described in Chapter 18 will
be used to study controlled-rectifier action in more depth.
19.3.5 Study questions
1. For part 1, what waveforms would you expect for R, RL, and R-C loads? Hint: think in terms of simple filtering.
2. Compare the actual waveforms with those expected.
Compute the actual circuit time constants, and discuss
how they might affect the waveforms.
3. The R-L and R-C cases of part 1 represent different
output filter arrangements for a rectifier circuit. Discuss
the circumstances under which each of these will be
effective and appropriate.
19.4.2 Basic theory
In a switched converter network, KVL will not allow us to
connect the utility ac voltage source directly to a dc
volt
age
sour
ce,
so a
dc
4. Comment on how the diode forward voltage drop
(about 1V) affects the waveforms.
5. From part 2 data, tabulate and plot the average load
voltage vs. the value of Rc.
6. Compute the SCR gate circuit R-C time constants. Is
the
turn-on
delay
governed
by
R-C?
34
current source is needed. Consider some of the loads
studied in Section 19.3. A resistive load is a crude
example of current conversion: the incoming voltage
produces a proportional resistor current. This is a far cry
from an ideal current source, but it does result in a
conversion function. An inductive load is a better
conversion example: the inductor voltage VL = L(di/dt)
resists any change in current. If L is very large, any
reasonable voltage will not alter the inductor current,
and a current source is realized. A capacitive load has
the opposite behavior. The capacitor current iC =
C(dv/dt) responds whenever an attempt is made to
Pratik devreler / N. Abut
change the capacitor voltage. If C is very large, no
amount of current will change the voltage, and a voltage
source is realized. Many electrical loads, especially
motors, are inductive. As a result, most circuits behave in
such a way that current does not change much over very
short periods of time. In power electronics practice, this
behavior, along with the desired source conversion
function, means that most loads are treated as "shortterm" current sources.
The basic single-phase controlled rectifier is shown in
Figure 19.15. If the load is inductive, there is a KCL
problem: the switch cannot be turned off. To see that this
is so, observe what happens to L(di/dt) when an attempt
is made to turn the switch off. The current must approach
zero almost instantaneously. The value of L(di/dt) is a
huge negative voltage. In practice, this voltage will likely
exceed the blocking capabilities of the switch, which will
be damaged. A simple solution is to provide a second
switch across the load, as shown in Figure 19.16. In
simple ac-dc converters, this switch can be a diode, or it
can be a second bidirectional-blocking forwardconducting device.
with the battery for current conversion. A resistor can be
used with a loss in efficiency. Alternatively, an inductor
can be used, as in the circuit of Figure 19.18. Analysis of
this circuit is not trivial. The controlled switch is on
whenever Vin is positive. When it is on, the output current
is given by
When the controlled switch is off, inductor current is
If L is large, the current is approximately constant. These
differential equations can be solved to give actual values
of current. Charging current is controlled by the resistor
value and also by the phase delay used to operate the
SCR.
The form of circuit expected for single-phase conversion
appears in Figure 19.19. The switches are implemented
with an SCR and a diode. In this case, the output voltage
is Vinwhenever the SCR is on, and zero when it is off. The
SCR turns off automatically when Vin 0. The voltage
waveform is familiar: a half-wave rectified waveform,
possibly with a delayed turn-on, as in Figure 19.20. The
voltage has an average value given by
Two typical loads for ac-dc converters are the dc motor
and the rechargeable battery. The dc motor has an
inductive model, as shown in Figure 19.17. The motor
looks rather like a voltage source, but its windings provide
a significant series inductance. A battery is intended as a
good dc voltage source. To provide the desired energy
conversion function, something must be placed in series
35
Elektrik Devreleri
where is the angle of delay before the SCR is turned on.
This integral gives
3. Repeat #2 for delays of approximately 30°, 60°, 90°,
120°, and 150°. Sketch just one or two typical waveforms,
rather than the whole series.
Since the output is a dc current source, average power
exists only at dc, and is simply Iout·Vout(ave).
4. Place an inductor, for example 25 mH, in series with
the resistor, as shown in Figure 19.22. Observe the
resistor voltage waveform. Repeat #2 and #3 above for
this new circuit, and also record the average and rms
values of Vload.
Part 2 -- A battery load
1. Connect a rechargeable battery in the circuit of Figure
19.23.
2. Measure battery currents Iout(ave) and Iout(rms). Do this for,
and record the phase delay angle value, at least four
different SCR delay angles. Observe and sketch the
resistor current waveform at one intermediate SCR delay
angle.
3. Measure the input power from the ac source.
19.4.3 Procedure
19.4.4 Study questions
Part 1: Ideal R-L load
1. For the simple loads of Part 1, tabulate and plot
Vout(ave) and Vout(rms) vs. the SCR phase delay angles.
Compute a theoretical result, and compare it to the data.
Do these agree?
1. Connect phase "A" of the nominal 25 V supply, the
SCR labelled "A" in the SCR box, and a resistive load, as
shown in Figure 19.21. Estimate the required resistor
power rating. Record the RMS value of the source
voltage.
2. For the battery load in Part 2, tabulate and plot
Iout(ave) and Iout(RMS) vs. the SCR phase delay angle. Again
consider whether your results are consistent with
theoretical expectations.
3. Why is the "flyback" diode included in these circuits?
4. Compute the efficiency of the battery charger studied
here.
5. Comment on how the diode and SCR forward voltage
drops affect your results.
2. Set the SCR turn-on for zero delay (i.e. set it to act as
a diode). Observe the output and load voltage waveforms
(see the figure). Measure the following output parameters
and sketch the voltage waveform: Vout(ave), Vout(rms).
36
Pratik devreler / N. Abut
19.5 Experiment -- Polyphase rectifiers
arisen. In communication systems, a "quadrature" voltage
source is a set of two signals, spaced by 90-- a sine and
a cosine. Quadrature sources were used in many early
power systems, and gave rise to an unfortunate use of
the term "two-phase" for such a source. We will use the
term two-phase to refer to a set of two voltages 180 apart
rather than to a quadrature set. In this experiment, the
SCR boxes will be used to study controlled-rectifier action
19.5.1 Introduction
This experiment will examine the properties of ac-dc
converters with polyphase input voltage sources. The
midpoint converter will be the focus of this experiment,
and will be tested with inductive loads including a dc
motor. In the preceding experiment, the circuits had a
single SCR in a half-wave rectifier configuration. A
flyback diode was needed to provide a current path when
the SCR turned off. The simple half-wave circuit
transferred energy to the load no more than half of the
time. The half-wave circuit seems ineffective. Polyphase
sources offer a much better alternative.
with two and
three-phase
sources.
19.5.2
theory
Basic
When multiple input sources are available for ac-dc
converters, it is natural to use all of them. The circuit of
Figure 19.24 shows the most general such converter -an m-phase to dc converter. The experiment here
considers a simplified version of this converter -- the one
in which there is a common neutral connection between
input and output. This is called a midpoint converter, and
appears in Figure 19.25.
A three-phase source, the most common polyphase type,
has three voltages equal in amplitude and 120 apart. The
definition of polyphase sources also applies to the "twophase" case -- two voltages, each 180 apart. While this is
consistent, a confusing historical nomenclature has
In the midpoint converter, the KVL and KCL restrictions
require that no more than one switch may be on at any
time, and one switch must be on if the load current is not
zero. This implies that qi 1. If the load is a current source,
qi = 1. We want to operate the switches so that the dc
value is maximized and the unwanted ac components are
minimized. It can be shown that if the switching frequency
is chosen to equal in, the best choice of switching
functions is to follow the polyphase input: each switch is
on 1/m of the time, and switching functions are spaced
360/m apart. The dc output component can be controlled
by adjusting the phase of the switching functions. The
output voltage is given by
This gives a complicated series, in the form
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Elektrik Devreleri
The dc component appears in the n=1 term, and is given
by
This, in turn, can be simplified to give
Notice that Vout(ave) depends on , where is defined as the
delay angle between any voltage and the switching
function associated with it. The result is a controlled
rectifier.
3. Set the SCR turn-on for zero delay (i.e. set it to act as
a diode). Observe the output voltage waveform. Measure
Vout(ave) and Vout(rms), and sketch the waveform.
4. Repeat #3 for delays of approximately 30°, 60°, 90°,
and 120°. Sketch just one typical waveform, rather than
the whole series.
5. Repeat #3 with a dc motor as the converter load,
except set the delay at about 90° initially. Observe and
sketch the motor current and voltage waveforms with no
motor shaft load.
6. Add a moderate shaft load, and observe how the
current and voltage waveforms change. Record your
observations.
19.5.3 Procedure
19.5.4 Study questions
Part 1: Two-phase converter
1. Set up the 25 V 60 Hz supply for two-phase output.
Remember to connect the output neutral.
1. For each of the load and source combinations, tabulate
and plot Vout(ave) and Vout(rms) vs. the SCR phase delay
angle. What would you expect in theory? How well do
your results agree with the theory?
2. For one phase delay angle (pick 60, for instance), plot
Vout(ave) and Vout(rms) vs. the number of input phases (you
have data for one, two, and three). What do you expect to
happen when more phases are used?
2. Connect the SCRs labelled "A" and "B" in the SCR box
with a resistive load, as shown in Figure 19.26. Estimate
the required resistor power rating, and abide by it. Set the
SCR box for two-phase control.
3. Set the SCR turn-on for zero delay (i.e. set it to act as
a diode). Observe the output voltage waveform. Record
Vout(rms) and Vout(ave)and sketch the output voltage
waveform.
4. Repeat #3 for delays of approximately 30°, 60°, 90°,
120°, and a delay close to 180°. Sketch just one typical
waveform, rather than the whole series.
Part 2 -- Three-phase converter
1. Connect the 25 V 60 Hz supply and SCR box for threephase operation.
2. Apply 120/208 V 3 power to the three-phase setup.
38
3. Why is the flyback diode not included in these circuits?
4. A bridge converter implements the full switch matrix of
Fig. 19. . How would Vout(ave) be affected by the use of a
bridge rather than a midpoint converter?
19.6 Experiment -- One-Quadrant Dc-Dc Conversion
19.6.1 Introduction
In this experiment, some common one-quadrant dc-dc
converters will be implemented and tested. The main tool
of the experiment is the FET switch control unit. The
circuitry provides direct adjustment of the switching
function frequency and duty ratio. The FET box can be
used to generate any of the four common dc-dc onequadrant converters (buck, boost, buck-boost, or boostbuck). In this experiment, we will set up two of these
circuits and characterize their operation. The converters
we will build are similar to commercial applications, with
fast switching functions and switching frequencies as high
Pratik devreler / N. Abut
as 200 kHz.
19.6.2 Basic theory
Dc-dc converters can be depicted as providing energy
transfer between two ideal sources. In practice, one of
the sources is almost always implemented as an
electrical energy storage element. For example, the buck
converter stores energy in an inductor when the
controlling switch is on, and discharges that
energy through the load when the controlling
switch is off. An objective is to keep energy flow
into the load nearly constant as the switches
operate. Since most converters apply nearly
constant voltages or currents to the storage
elements,
much
of
the
analysis
is
straightforward.
boost and boost-buck) are shown as two matrices
connected together. In each of these circuits, practical
current sources are formed with inductors. Output voltage
sources are formed with capacitors. The average values,
governed by the switching function duty ratios, are of
interest. For example, the buck converter below has
Vout = q1Vin,
which is just
The average value of this series is simply D1Vin.
Unwanted Fourier components appear at the switching
frequency fswitchand its multiples. The largest unwanted
component is
The general dc-dc converter is shown in Figure 19.28.
The four major one-quadrant converters are shown in
Figure 19.29. Notice that the indirect converters (buck-
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Elektrik Devreleri
19.6.3 Procedure
Part 1: Buck converter
1. Set up the FET control box as a buck dc-dc converter.
Be sure to provide the capacitor shown across the input
power supply. The capacitor should be placed as close to
the FET box as possible so that the inductance of the
wires to the FET will be very low.
2. Set the power supply current limit for about 3 A, and
the voltage to 12 V. Set the duty ratio to about 50%.
Observe the load voltage, Vload, and the output voltage
Vout.
3. Turn on the FET box and the input power supply.
4. Set fswitch to about 100 kHz. Notice that Vout allows easy
measurement of fswitch.
5. Confirm that the duty ratio is close to 50%. Sketch the
Vout and Vload waveforms.
In general, as switching frequencies increase, the values
of dv/dt and di/dt values also increase, and smaller
inductors and capacitors can be used without sacrifice in
performance.
6. Use the oscilloscope to measure the peak-to-peak
ripple on Vload at duty ratios of 10%, 50%, and 90%. The
ripple measurement can be performed by setting the
oscilloscope input coupling to "ac," and expanding the
voltage scale.
7. Measure average values of Vload and Iin at duty ratios of
10%, 30%, 50%, 70%, and 90%. Use your multimeter for
Vload(ave). Record the input and output RMS voltage and
current as well as the power.
8. Change fswitch to 5 kHz. Try to measure the waveform
time constant during the voltage fall. Recall that this will
be the time for Vload to fall from its peak value to 36.8% of
that
value.
Part 2 -- Buck-boost converter
1. Set up the FET control box as a buck-boost dc-dc
converter, as shown in Figure 19.32.
2. Set the power supply current limit for about 3 A, and
the voltage to 12 V. Set the duty ratio to zero. Connect
oscilloscope leads across the load resistor and across
the inductor.
40
Pratik devreler / N. Abut
3. Turn on the FET box and the input power supply. Set
fswitch to about 100 kHz.
4. Confirm that the duty ratio is set to about 50%. Sketch
the inductor voltage waveform. Use the current probe to
sketch the inductor current waveform. Observe and
sketch the load voltage waveform.
5. Measure average and RMS values of Vload and Iin at
duty ratios of 20%, 40%, 50%, 60%, and 70%. Record
power readings as well.The output voltage becomes
high quickly with D>60%, so be careful.
3. Estimate the average input and
output
power
from
the average readings of Vload and Iin for
each operating condition. Compare
these results to the wattmeter readings.
Calculate efficiency, PoutPin, from the
wattmeter readings.
4. Estimate the inductor value from the
measurements of fall time in the buck
converter. Use this value to compute an
expected load voltage ripple at 100 kHz. How do your
results compare with the data? If the inductor value were
to double, how would this affect the behavior of these
circuits?
19.6.4 Study questions
1. Tabulate your data in an organized fashion. Compare
the RMS readings from the wattmeters with the various
average readings. Do they agree?
2. Compute and tabulate ratios of Vload(ave)Vin for these
converters for your data. Are the results consistent with
duty ratio settings?
19.7 Dc-Dc Converters for Motor
Drives
41
Elektrik Devreleri
19.7.1 Introduction
This experiment will examine the operation of dc-dc
converters in the context of motor drives. Motor drives
are the most common application of multi-quadrant dc-dc
converters. Dc power supplies are almost always based
on one-quadrant circuits: the output power is intended to
be positive at all times, and there is rarely a need to
handle negative output current. Some special-purpose
laboratory supplies are designed to handle multi-quadrant
output, but often do not have efficiency as a high priority.
Large dc motor drives have energy considerations
beyond those we have seen so far: the rotating kinetic
energy of a large motor is quite considerable, and in a
braking situation, this energy must be removed. The
energy can be converted to heat and lost, as it is in
gasoline engine vehicles, or it can be directed back to the
energy source for recovery. This regeneration energy can
be controlled only with multi-quadrant circuits.
19.7.2 Basic Theory
The equivalent circuit of a dc motor is repeated in Figure
19.33. Rotation of the motor produces a back EMF, equal
to kif, where k is some constant, is the motor shaft speed
in rad/s, and if is the "field exciting current" or some other
variable representing the magnetic field strength inside
the motor. If a voltage Vt is applied to the motor terminals,
a current (Vt Vg)/Ra will flow in the steady state. This
current sends power into the motor, which is converted to
mechanical energy. The input power accelerates the
motor until the electrical input power exactly balances any
mechanical input into a shaft load.
The power input, and hence the operating speed, of a dc
motor can be controlled easily by altering the value of Vt.
Since the actual output power is into some mechanical
load, with its associated inertia, will not change much
over short time periods, and Vg will be nearly constant.
The average electrical power into the motor will be
determined by the average value of Vt, even if the
inductance is low. For example, a simple buck converter
could be used to control Vt, as in Figure 19.34. The
output can vary from 0 to 100% of the input dc source
voltage, and thus speed can be altered from near 0 to
near rated speed.
42
If if is held approximately constant, as it is in separately
excited motors or motors with permanent magnets, the
input power is a very direct function of converter duty
ratio, and speed control is made easy. In fact, many
converters have feedback systems built in for this
purpose. Consider the unit of Figure 19.35 in which the
transistor duty ratio depends on a low-power input
voltage. This voltage could be generated as shown in the
figure, with some reference signal being compared to
information from a tachometer. In this unit, the duty ratio
automatically increases if the motor speed drops. This
results in additional input power and is intended to keep
running speed nearly constant. The operating speed can
be changed easily by adjusting the reference voltage, and
will be held constant at the desired value.
In the case of a very high power motor drive, a
considerable amount of energy is represented even
during a speed decrease. An excellent example is the
braking of an electric vehicle -- an operation which must
occur often in any transportation application. In
mechanical systems, the braking energy is converted to
heat, dissipated, and lost. This is not an acceptable
situation in battery-powered electrical units, and causes
substantial wear and tear even when batteries are not an
issue. Multi-quadrant dc converters can be used to
convert the braking energy back into electrical form. The
energy can be dissipated just as it would be by
mechanical brakes, or it can be returned to the energy
source. The dissipation version is called dynamic
braking and is often used for very rapid deceleration of
electric
motors.
The
recovery
version
is
called regenerative braking, or just regeneration, since it
uses the motor as a generator during deceleration.
Pratik devreler / N. Abut
A motor could be attached to both a
buck and a boost converter, with the
buck converter operating (with Ia > 0)
during "motoring," and the boost
converter operating (with Ia< 0) during
regeneration. Such a unit is called a class-C chopper,
and is widely used for dc motor drives.
The buck converter is sometimes called a
class-A chopper when used as a motor drive.
As we have seen, this converter makes a useful, simple
motor control. When braking, the controlling switch turns
off, and only the diode conducts. If inductance is low, the
output current quickly goes to zero, and the motor coasts
to a stop. If inductance is high, the braking energy is
dissipated in Ra. Figure 19.36 shows some typical
waveforms.
A boost converter can be used to return generated
energy from a motor to a source, provided that the source
voltage Vt is less than Vg. Such a converter, shown in
Figure 19.37, can provide regenerative or dissipative
braking. It is sometimes referred to as a class-B chopper.
To operate a class-C chopper, the
boost converter active switch is shut off,
and the buck converter is used to
accelerate and provide running power
to the motor. When regeneration is
desired, the buck converter is shut off
until Ia becomes negative. At that point,
the boost converter can begin
operating, and will transfer energy from
the motor back to the source. In effect,
43
Elektrik Devreleri
the buck and boost converters operate independently.
Figure 19.40.
19.7.3 Procedure
Part 1: Class-A motor drive
1. Obtain a small dc motor. Use your multimeter to
measure Ra for it.
2. Set up the FET control box as a buck dc-dc converter,
with a dc motor as the output load. Be sure to provide the
capacitor and resistor shown across the input power
supply. The resistor is intended take up any regenerated
energy.
3. Set the power supply current limit for about 5.0 A, and
the voltage to 24 V (depending on the motor ratings). Set
the duty ratio dial to zero. Connect an oscilloscope lead
The general dc voltage to dc current converter
shown in Figure 19.39 is not especially useful
for dc motor control, since the inductance value
is usually too low for useful regeneration. The
converter cannot provide negative steady-state
voltage to the motor, and so is no more useful
than the class-C chopper above. It is called a
class-D chopper. In many applications, it is
necessary to reverse the motor direction, while
maintaining both motoring and regeneration.
Two class-C choppers, one for each motor
Vt polarity, can be assembled for this purpose.
The resulting class-E chopper is shown in
across the motor. Set up the current
probe to measure the motor armature
current.
44
Pratik devreler / N. Abut
4. Turn on the FET box and the input power supply. Set
fswitch to about 20 kHz (a period of 50 µs). Monitor and
record the power supply current and voltage levels and
shut down if anything unexpected appears.
5. Sketch the motor terminal voltage waveform and
current waveform with a duty ratio setting of about 50%. If
there are intervals during which Ia = 0, take special care
to record the value of voltage during such intervals.
Measure the peak-to-peak ripple on Ia.
6. Observe and sketch the motor voltage and current
waveforms, and measure the motor average voltage and
current, at: (a) the lowest duty ratio for which the motor
runs steadily, and (b) a duty ratio of about 90%. In each
case, observe qualitatively the effects of shaft load on the
current waveform.
7. Change fswitch to 2 kHz. Measure the time constant of
Vt during its fall. This will allow you to estimate La later.
Part 2 -- Class-C chopper circuit
1. The two active switches of the class-C chopper
operate separately, but they must act in complement. In
this part of the experiment, it will be necessary to use
special care to insure proper switch operation.
2. Use two FET control boxes. One, designated
the master unit, will determine the switching functions of
both portions of the class-C chopper. The second,
designated the slave unit, will function only as requested
by the master unit. The FET box design in Chapter 18
has a switch to select this function: up for master and
down for slave. Connect the control terminal on the
master unit to the control terminal on the slave unit.
Adjust the slave duty ratio to the 100 % position. The
frequency controls should be in approximately the same
position.
3. Wire the circuit shown in Figure 19.42. The 0.2 resistor
will help prevent damage if the switching functions are not
operating exactly in complement.
4. Operate the master unit as a buck converter. Observe
operation at approximately 50% duty ratio, as in part 1.
Sketch the motor voltage and current waveforms, and
record the average motor voltage and current. Measure
the peak-to-peak ripple on Ia.
5. Increase the duty ratio to near the maximum amount,
then drop the duty ratio abruptly in an attempt to observe
converter action during regeneration. You may need to
repeat this step, or spin the shaft externally by hand or
with another motor to observe regeneration behavior
(we've used an electric drill in the past). Make note of
your observations. Try to obtain a situation in which
Iareverses.
19.7.4 Study questions
1. During intervals when Ia = 0, the
motor voltage is not necessarily zero.
Interpret its value during such intervals.
(Hint: Since Ia = 0, this is an opencircuit voltage.)
2. Compute average power into the
motor for each operating condition.
3. Estimate the motor series inductance
value from the buck converter data. Use this to estimate
the voltage ripple at 20 kHz. Does this match your
measurements?
4. Is the average motor voltage determined by the duty
ratio?
45
Elektrik Devreleri
5. Why is the class-A chopper incapable of regeneration?
What will happen in such a converter if Vt is suddenly
lowered?
19.8 Dc-Ac Conversion -- Voltage-Sourced Inverters
19.8.1 Introduction
This experiment examines inverter circuits. Inverters, or
dc-ac converters, are used for generation of backup ac
power, for ac motor drives, and for switching amplifiers.
Commercial inverters are also used in alternate energy
applications such as the demonstration photovoltaic and
battery power plants. Various simple types of inverters
will be studied in this experiment. Emphasis will be placed
on phase control techniques and on simple switching
functions. Inverters can be classified according to the
properties of the dc source. Those with a dc current
source are often used for sending energy into an ac
power system. Dc regeneration and HVDC transmission
are two examples. Such inverters are really the same as
ac-dc converters with ac voltage inputs. In effect, the only
difference between rectifiers and inverters when dc
current sources are involved is the direction of any
unidirectional switches used in the circuits. The ac-dc/dcac converters with dc current sources almost always
involve a utility ac voltage supply, and have well-defined
values of phase. Any switching function can be altered in
phase relative to this fixed reference frame, resulting in
variation of input and output power levels.
46
Ac-dc/dc-ac converters which involve dc voltage sources
are, in practice, quite different from the current-sourced
versions. Such converters imply an ac current source -rare in practice. Normally, the "ac current source" simply
reflects some electrical load, such as a circuit or a motor,
which requires ac power. These loads rarely define a
phase reference -- the phase is determined by
impedance characteristics, and will always lead or lag the
input voltage by a definite amount.
The voltage sourced inverters, then, provide a window
into the complexities of true, independent inversion -conversion of a dc source into some ac source. Inversion
is important in three basic applications:
1. Transfer of energy from some dc source into an ac
power system. Such uses include alternate energy source
conversion and dc motor regeneration.
2. Backup ac power. Since most electrical equipment is
intended for ac power from a utility, switching power
converters which produce ac from storage batteries have
long been important.
3. Ac motor drives. Induction motors, synchronous
motors, and so-called brushless dc motors require ac
power at variable frequency. Today, this is often achieved
by converting power from some dc source.
Pratik devreler / N. Abut
the input voltage. Changing the phase of the input voltage
19.8.2 Basic Theory
The most general dc-ac converter (with single
phase ac) is shown in Figure 19.43. It has at
most four switches. The switching functions are
constrained by KVL and KCL, as usual. They
also must have a Fourier component at the ac
source frequency, to ensure nonzero power
flow. An important practical consideration is that most real
ac sources cannot tolerate a dc component. This further
constrains the functions. A reasonable choice is to
operate the switches with a duty ratio of 50 % to bring
about the highest symmetry and hence avoid any dc
component on the ac source. A general converter of the
dc voltage source type is shown in Figure 19.44. As in the
case of the two-quadrant buck converter, Vout can be
either Vin, -Vin, or 0, depending on the switch combination.
Notice the switch types to be used in this converter. In
general, current can flow in either direction, although
there is only one voltage polarity.
Consider the induction motor equivalent circuit, shown in
Figure 19.45. This circuit requires ac power, and is an
inductive load. For the purposes of KCL a current source
is an appropriate model over short times. Nonetheless,
the phase of this current source is linked to the phase of
will change the current phase so as not to alter power.
Because of the ac current source
phase behavior, dc-ac converters are
harder to study than dc-dc converters.
Properties of the load are important to
converter operation. A half-bridge converter with R-L load
is shown in Figure 19.46. KVL and KCL require the two
switching functions to act in complement, so that q1 + q2 =
1. The practical requirement of no dc component in
Vout requires D1 = D2 = ½. Vout is a simple square wave at
the desired frequency, and has a value of Vout = (2D1 1)Vin. This generates the Fourier series
Output current and power depend on the load, in a
manner which is actually easy to calculate. Consider that
47
Elektrik Devreleri
Vout = RIout+L(dIout/dt). In steady state, Iout is periodic at the
same frequency as Vout, and has a Fourier series
1. Set up two FET control boxes in a master-slave
configuration, to form a half-bridge inverter. Be sure to
include the capacitors and resistors shown with the power
supply input. Refer to Figure 19.48.
This series can be differentiated easily. Let X n =
nL. Then we can solve for Iout term by term,
obtaining
This is equivalent to finding each component of
Ioutseparately in terms of the corresponding
component of Vout. It is easy to automate such a
procedure on any computer. Sample waveforms
are given in Figure 19.47. Some loads of this
type will be tested in this experiment.
2. Set the power supply current limit, if there is one, for
about 2.0 A, and the voltage to zero. Set the master and
slave duty ratio dials for 50 %. Connect oscilloscope
leads and wattmeters across the load resistor and across
the converter output, as shown in Figure 19.48.
3. Turn on the FET boxes and the input power supply. Set
fswitch to 10 kHz. Set the supply to 24 V.
19.8.3 Procedure
Part 1: Voltage-sourced inverter, R-L and R-L-C loads
48
4. Measure the output average voltage. Adjust the duty
ratio and fine-tune the input supplies to get 50% duty and
zero average output.Small average offsets can swing the
current to the power supply current limits.
Pratik devreler / N. Abut
5. Sketch the load resistor voltage and the output voltage
waveforms. Record the RMS voltage, current, and power
from the wattmeter. Measure the average input current
from the supply.
6. Compute the series capacitance needed for resonance
with the inductor at the switching frequency. Add this
capacitor in series with the inductor. Adjust the frequency
as needed to obtain near-resonant operation.
7. Sketch the resistor voltage waveform with the R-L-C
load. Record the RMS value of the load resistor voltage,
the output power, and the average input current from the
supplies.
Part 2 -- Isolated converter with ac link (half-bridge
forward converter)
1. Set fswitch to 50 kHz. Wire a toroidal transformer into the
circuit, as shown in Figure 19.49.
2. Measure the average output voltage of this circuit.
Sketch the waveform.
3. Place a 1 µF capacitor across the output terminals.
Again measure the average output voltage. Also measure
the average input current from each source by taking
advantage
of
the
series
resistors.
19.8.4 Study questions
1. How do you expect waveforms for an R-L load to
change with frequency?
2. An alternate method for control of Vout(wanted) is to add a
third switch across the output combination. This allows
zero as a possible output value. The duty ratios can then
be adjusted so that Vout changes. Assuming that the dc
component remains at zero, find Vout(wanted) as a function
of D for this control scheme.
3. What is the effect of a resonant load, such as that in
Part I?
4. What is the efficiency of the converter
circuits tested above?
19.9 Experiment -- PWM Inverters
19.9.1 Introduction
This experiment introduces pulse-width
modulation circuits. The intent is to gain
familiarity with the waveforms and
concepts of pulse-width modulation as it
applies to power electronics. The PWM
inverter will be examined in the context of
an ac motor drive. Basic ac drive concepts
will be one feature of this experiment. The
typical PWM waveform shown in Figure
19.50 has a switching frequency of 960
Hz.
Control of output voltage in dc-ac
converters is critically important in a wide
range of applications. Backup ac power supplies require
control of voltage so that Vout can be varied independent
of the input source. Ac motor drives require control of
both Vout and fout to achieve good performance. There are
two methods in common use for controlling the output
voltage (and power) of an inverter. The first is to adjust
the relative timing of switching functions in a bridge. The
49
Elektrik Devreleri
load voltage depends on the relative phases. This "phase
displacement control" is often used in very high power
situations, such as locomotive controls, where the
switches are slow SCRs.
The second method, pulse-width modulation (PWM)
divorces the switching function frequency from the
intended properties of Vout. This method can provide the
desired results if the switches can be operated much
faster than fout. To understand PWM, consider a very fast
square wave. The duty ratio can be varied slowly between
0 and 100%, in a manner similar to pulse width control in
dc-dc converters. In a buck converter, for example, this
would have the effect of slowly changing Vout(ave). This
slow change can be sinusoidal perhaps, which gives a
slow sinusoidal change in the average value of Vout. Here
"slow" simply means much more slowly than the
switching function. Vout can easily change at the rate of 60
Hz if, for example, a switching frequency of 10000 Hz is
used.
identical to a two-quadrant buck converter. The pulse
width is intentionally varied, rather than held nearly
constant as in the dc-dc case.
Convenient speed control for ac motors has been a
desired goal almost since such machines were invented.
The ac induction motor, for example, is mechanically
simple and rugged, requires no electrical connections
between stationary and rotating parts, and is inexpensive.
Unfortunately, the induction motor lacks the easy control
of a dc motor. Ac motor speed control in general requires
adjustment of the motor input frequency. The speed
depends on frequency in a direct manner, and the ability
to vary f solves much of the problem. Unfortunately, it is
not entirely trivial to vary the frequency applied to a motor.
Ac motors are basically inductive, and have a frequencydependent impedance. As the frequency is lowered, input
current and internal magnetic flux rise. To counteract
these effects, the voltage must change along with
frequency. If the voltage is altered in the correct manner
as a function of frequency, an ac motor
can be made to look almost like a dc
motor in terms of speed and torque
control.
Until PWM converters were feasible, the
process of altering fout and Vout together
was exceedingly difficult. Ac motor
controllers were almost unknown twenty
years ago, and those which did exist were
expensive,
complicated,
and
used
additional motors for energy conversion.
Today, ac motor drives are beginning to
displace dc motors in some applications.
These drive units are nearly always based
on
PWM.
19.9.2 Basic Theory
The half-bridge inverter in Figure 19.51 has output Vout =
(2q1 - 1)Vin. If the duty ratio is varied with time as
some modulating function M(t), Vout becomes
Remember that D must be between 0 and 1. With
½[k·cos(outt)+1] for M(t), Vout is
In practice, implementing this slow variation of pulse
width is exactly the same as designing a dc-dc converter.
The only issue is to place Vout in two quadrants. And, in
fact, the full-bridge inverter operating under PWM is
50
Pratik devreler / N. Abut
Part 1: Voltage-sourced PWM inverter, R-L load
1. Set up two FET control boxes in a
master-slave configuration, to form a
half-bridge inverter. Be sure to include
the capacitors and resistors shown with
the power supply input.
Notice that this is not in the form of a Fourier series -time appears in several places, as does sin[ncos(outt)].
This can be decomposed into a Fourier series by using
properties of Bessel functions. The necessary relations
appear among the trigonometric identities in the
Appendix. The Fourier components appear at
frequencies of nswitch ± mout. The components drop in
amplitude quickly for increasing m, but slowly for
increasing n. It is easy to use a series R-L load as a lowpass filter (just as in the dc-dc buck converter) in order to
separate fout from the unwanted components. This
function can be performed by a deliberate R-L load, or by
a motor winding or transformer. The experiment
procedure below illustrates both PWM and the filtering
process.
2. Set the power supply current limit, if there is one, for
about 1.5 A, and the voltage to zero. Set the master duty
ratio to about 50 % and the slave to 100 %.
3. Set up the waveform generator at your bench to
produce a sinusoidal voltage, with frequency of about 50
Hz, such that the lowest voltage is 1 V and the highest is
3 V (sine wave with 2 Vp-p and 2 V dc offset). Connect this
voltage to the duty ratio input on the master converter
unit.
4. Connect oscilloscope leads across the load resistor
and across the converter output (refer Figure 19.52).
Turn on the FET boxes and the input power supply. Set
fswitch as low as possible.
5. Monitor the average value of Vout, and observe the
power supply currents. Adjust the function generator to
get near zero average output.
6. Sketch the Vout waveform. Can you see the modulating
process? Record the RMS voltage current, and power
into the load resistor. Measure average dc voltage across
the 1 series input resistors.
7. Increase fswitch to about 50 kHz.
8. Decrease the amplitude of the function generator
modulating waveform by about 50%. Sketch the
Vload waveform. Record meter data as in step 6.
19.9.3 Procedure
51
Elektrik Devreleri
4. Change the sine wave frequency and amplitude to
observe an ac motor control function.
Part 2 -- Induction motor drive
1. Turn off the power supply. Replace the R-L
load with a series combination of 5 and a
transformer winding of 12.6 V rating.
2. Place a 1000 load across the transformer secondary
terminals. Turn on the power supply, and measure the
RMS and average voltage across this resistor, and
observe and sketch the waveform. Be aware of the
relatively high voltage level.
3. With the supply off, wire a single-phase motor into the
circuit, as shown in Figure 19.53. Apply power. Sketch
the converter output voltage and resistor voltage
waveforms (refer to the Figure).
52
19.9.4 Study questions
1. For this type of converter, how do you expect
waveforms for an R-L load to change with switching
frequency? With modulating frequency?
2. Why is PWM advantageous in ac motor control?
Pratik devreler / N. Abut
3. Draw the full-bridge inverter for PWM. What
relationships would you expect among the various
switching functions?
the current becomes zero. This provides several
characteristics:
4. Compute and tabulate the converter's efficiency from
your part 1 data.
5. Compare PWM with the simpler inverter scheme of the
previous
experiment.
Simple ac regulators can be realized with TRIACs, since
they will perform phase control or integral cycle control on
a resistive load without trouble.
19.10 Ac-Ac Conversion
The TRIAC is difficult to use when dc currents or voltages
are involved, since conditions needed for turn-off may not
appear.
19.10.1 Introduction
Direct frequency conversion, as introduced in Chapter 7,
is one framework in which to study the ac-ac converter. In
this experiment, we will examine converters of this type.
The bilateral switch is beginning to gain in importance,
and one device set which performs this function will be
examined. Many applications which require ac output,
especially motor drives and related transportation areas,
would appear to benefit if power could be converted
directly from the ac mains. Today, a few workers in power
electronics would dispute this, and claim that conversion
via a dc link is superior to direct ac-ac conversion. In
principle, however, the reduction in switching network
complexity, along with the possibility of extending ac-ac
conversion into such areas as power amplifiers, makes a
direct ac-ac converter a kind of "ultimate dream." A
generic ac-ac unit would serve for any possible
conversion function, including rectification and inversion.
In the long run, a power bilateral switch will open up a
wide range of new processes and applications for power
conversion, just as the SCR did during the 1960s.
A TRIAC of given size does not use semiconductor
material very effectively, and has much lower ratings than
two SCRs which are half as big.
TRIACs are common in consumer products which benefit
from simple ac regulators. Some such devices are used
in certain ac motor control applications, particularly those
which resemble phase controlled ac regulators. TRIACs
have limitations on levels of externally applied dv/dt and
di/dt. The devices are also relatively slow to turn off.
These limitations confine them mainly to power mains
frequencies.
The TRIAC is a very limited bilateral switch. An
alternative is to combine multiple switches of other types
to form a true bilateral device. For example, two switches
of type
can be placed in inverse series to form an
equivalent
. The gates of the two sub-units are
operated from the same switching function. Possible
implementations appear in Figure 19.54. It is actually
relatively convenient to implement the FET version shown
in the Figure, since the gate drive can be used without
19.10.2 Realizing the bilateral switch
Any converter can be built from a bilateral
switch. While this makes it a powerful tool, its
properties are not always advantageous. For
example, it is easier to build a reliable dc-dc
buck converter with a transistor and a diode
than with bilateral switches. There is no
alternative for ac-ac conversion, and in fact a
bilateral switch brings advantages to certain
other converter types.
The TRIAC approximates full bilateral capabilities. This
device, in effect, is a set of inverse-parallel SCRs, built
together, and sharing a single gate. The TRIAC is
controlled just like an SCR -- once on, it remains on until
change in most cases. The BJT version is more
problematic, since applied base current must support
both devices without any balance troubles.
53
Elektrik Devreleri
Set up a two-phase to one-phase ac-ac converter based
on dual FET bilateral switches, as shown in Figure 19.55.
19.10.3 Basic Theory
Once a bilateral switch is available, it is
relatively simple to operate an ac-ac converter.
The requirement is that switching functions
contain a Fourier component at a frequency
fswitch = fin ± fout. The most straightforward way to
accomplish this is to set fswitch to either the sum
or difference of input and intended output
frequencies. Thus conversion of 60 Hz to 400
Hz would result if a switching frequency of
either 340 Hz or 460 Hz were applied, for
example.
Apply a switching function at some frequency, and
observe results at the output terminals. Record your
observations.
Very often, the input frequency is known and fixed, and
variation of the output frequency is important to an
application. This is true of ac motor drives, for example. It
is sometimes useful to consider the switching frequency
as fin plus some modulating function. For example, if the
switching function phase is made to be a function of time,
M(t), a switching function will take the form
This is "phase modulation," since phase is a function of
time. Phase modulation reduces trivially to the form
fswitch = fin ± fout if M(t) is set to ±outt. This form of switching
function is easy to implement, and is referred to as "linear
phase modulation" since M(t) is a linear function of time.
The choice M(t) = +outt is given the special name
"Universal Frequency Converter" (UFC) since it works for
any choice of fin or fout. The choice M(t) = -outt gives rise to
a "Slow-Switching Frequency Converter" (SSFC), and
has the constraint that fin fout. Both of these types are
statements of the simplest choices of switching
frequencies. Other choices of M(t) can be made. These
are nonlinear phase modulation methods, with almost
unlimited possibilities. Many nonlinear phase modulation
techniques allow control of power flow even with passive
loads.
It should be pointed out that phase modulation is not the
only way to perform ac-ac conversion. Pulse-width
modulation can also be used, since PWM allows the
creation of nearly any Fourier component, given a fast
switching frequency. PWM methods are being discussed
for use in ac output converters which allow ac or dc
input.
19.10.4 Procedure
54
Pay special attention to the waveforms which appear
when the switching frequency is exactly equal to the input
frequency. This case is particularly easy to simulate and
study.
19.10.5 Study Questions
1. Draw some expected waveforms for two-phase to onephase ac-ac conversion. Do the experimental results go
along with these?
2. What would have been the effect of a resonant load?
3. How would PWM provide advantages in this ac-ac
converter?
Pratik devreler / N. Abut
19.11
Frequency
Components
Characteristics
of
Passive
can be modelled with a parallel-plate geometry, shown in
19.11.1 Introduction
The next two experiments will study the behavior
of real passive components. In the first
experiment, basic operation of realistic capacitors,
inductors, and resistors will be examined. The capacitors,
inductors, and resistors used in circuit analysis have ideal
properties: ic = Cdvc/dt, vL = LdiL/dt, and vR = RiR.
However, real devices are not ideal. In the context of
power electronics, these effects are often important.
Wires have resistance and inductance, coils of wire have
capacitance between the turns, and so on. In order to use
passive components in power electronic circuits, it is
important to understand what the effects are, how they
are characterized and measured, and the implications for
design.
Figure 19.56. The capacitance value depends on the
plate spacing d, the plate area A, and the dielectric
constant of the insulator, , according to the relation C =
A/d. A large value of capacitance requires large plates,
small spacings, and high dielectric constants.
19.11.2 Basic theory, capacitors
When two conductors of any shape are placed in
an electric field, a charge develops on each one.
In a system which consists only of perfect
conductors and perfect insulators, the charge Q
depends on voltage in a linear fashion, so that Q =
CV. If capacitance is constant (e.g. the conductors
are stationary), this leads to the simple relationship
i = Cdv/dt. A real capacitor must provide
conductors to hold the charge, wires to allow
application of voltage, insulation which physically
supports and separates the conductors, and a protective
package
to
prevent
damage. This
naturally
complicates
the
real
behavior.
There are two common classes of commercial
capacitors. The first consists of two flat metal conductors,
separated by a dielectric layer. The second type, known
as the "electrolytic capacitor," consists of an oxidized
metal conductor and a nonmetallic conductor. Both types
The nonideal effects are relatively clear: the wires and
plates introduce series inductance and resistance, and an
imperfect dielectric could allow some current flow
between the plates. A candidate circuit model emerges,
given in Figure 19.57.
This circuit model can be simplified if the capacitor is
operated at some specific frequency. Then the parallel
portion can be transformed into a series equivalent. This
gives the standard model shown in Figure 19.58. Many
manufacturers use this standard model as a basis for
describing their capacitors. The equivalent series
resistance (ESR, another name for the Rs of the circuit)
is often given at some frequency, such as 120 Hz.
The equivalent series inductance (ESL) is often given
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Elektrik Devreleri
in the form of a "self-resonant frequency," fr. The
properties of the standard circuit include:
leakage current levels are much higher, which means
Voltage drop across the ESR, which reduces
the stored charge relative to expected values.
The resonant effect of the series R-L-C circuit
means that a plot of impedance vs. frequency will fall at
first (capacitive impedance), reach a minimum, and then
rise
(inductive
impedance).
ESR is smaller and df is higher; and the effective plate
surface area is very high, which allows high values of
capacitance per unit volume.
Above fr, the device is an inductor!
Any current flow produces loss in the ESR. The higher
the frequency of the applied voltage, the higher the
current and losses.
The circuit does not model real behavior well at very low
frequencies. For instance, the original circuit of Figure
19.57 shows that some leakage current will flow when a
dc voltage is applied. Real capacitors show this effect,
but the standard model does not include it.
The ESR mainly represents the dielectric properties.
Dielectrics do not usually act in accordance with Ohm's
Law. Because of this, the ESR is generally a kind of
nonlinear resistance; for example, it varies with
frequency. One traditional way to characterize such
materials is with the "loss tangent." The loss tangent, also
called tan or "dissipation factor" (df), is defined as the
ratio of resistance to reactance for a series R-X circuit.
For the standard model of the capacitor, tan = RC. The
loss tangent has a characteristic value for a given
capacitor dielectric material, regardless of the plate
geometry. Many dielectric materials are characterized by
a loss tangent which is roughly constant over a wide
frequency range. For these reasons, loss tangent or df is
often given in capacitor specification sheets. The ESL is
related to packaging and lead structure, since wire
inductance is the most important factor.
In electrolytic capacitors, the insulating layer is formed
through an electrochemical reaction between the two
conductors. If voltage of the wrong polarity is applied, the
reaction reverses, and the insulating layer is destroyed.
The device becomes a resistor, and usually overheats
and fails quickly. When the correct polarity is applied, the
electrolytic capacitor shows the same general properties
as the simple dielectric version, with two changes: the
56
19.11.3 Basic theory, inductors
Inductors are formed simply by wrapping a coil around a
magnetic material. Current in the coil creates magnetic
flux in the material. If the material is linear, the flux is
proportional to current, so that = Li. The constant of
proportionality in this case defines inductance. By
Faraday's Law, if this flux varies with time, it gives rise to
a voltage vL = Ldi/dt. Magnetic materials in general
are not linear; these effects will be studied in more detail
in the next later experiment.
Even without considering the effects of nonlinearities,
some aspects of real inductors should be clear. The wire
coil has resistance. Incoming and outgoing wires act a bit
like parallel plates. A simple circuit model might be that in
Figure 19.59.
The symbol ESR is often used for the effective resistance
in inductors. As in the capacitive case, the loss tangent is
defined as the ratio of resistance to reactance. It is hard
to build inductors which handle high energy levels and still
have very low loss tangents.
Inductor types are defined mainly by the magnetic
material. This can be a linear material, such as air, or any
magnetic material. Good linearity is a desirable feature,
so most practical inductors have an air gap. In this
experiment, two inductors will be tested for their ESR
values
and
resonant
frequencies.
Pratik devreler / N. Abut
costly than the simple types.
In this experiment, we will briefly examine the
characteristics of standard wirewound resistors. This will
serve as an introduction to the overall problems with real
resistors.
19.11.6 Procedure
19.11.4 Basic theory, resistors
Resistors are generally taken for granted in electrical
networks. However, they are subject to nonlinear effects
like other components. Consider that Ohm's Law is really
an approximation, based on a highly simplified model of
electron behavior in metals. Nonmetals do not usually
follow this behavior. The general tendency is that the
higher the resistivity of a material, the less linear its V vs.
I behavior is likely to be. The parts must have
connections, which implies a series inductance. A basic
model is shown Figure 19.60.
Even in materials which follow Ohm's Law, other effects
are important. All materials, including metals, vary in
resistivity as a function of temperature. For most metals,
the variation is approximately linear. In power
electronics, heat loss and temperature effects
are almost always significant. Since resistance
values change with heating, it can be hard to
predict the actual value of a given resistor.
Part 1: Reference measurements
1. Your instructor will assign a set of capacitors,
inductors, and resistors to each team. If a bridge or
similar instrument is available, gather data at a specific
frequency for Cs, Cp, Rs, Rp, Ls, Lp, and D = df for each of
your assigned parts. Special emphasis should be placed
on the values relevant to the various models.
Part 2: Frequency sweeps
1. Insert one capacitor in the circuit in Figure 19.61. If the
capacitor is electrolytic, be sure to observe the polarity
marks, and add a dc offset to Vin so that Vc > 0 always. If
it is not electrolytic, use an offset of zero. If the capacitor
is less than 0.5 µF, substitute a 1 k resistor for Rs.
There are several major types of resistors:
Composition and metal
oxide resistors
are
formed as a block (or cylinder) of nonmetal. The
material resistivity and stability are important
considerations. Carbon composition resistors were once
the most common. Most materials of this type are
relatively
sensitive
to
temperature
shifts.
Film resistors are usually formed by depositing a metal or
carbon film on a ceramic substrate. In industry, they are
often preferred over composition types. Precision
resistors are usually formed with metal films.
Wirewound resistors are common at high power levels. A
coil of wire, usually nichrome, is wrapped around a
ceramic rod or tube in the simplest arrangement. While
this is a convenient way to spread out heat, it adds a
significant inductance. Special versions which are double
wound to avoid excess inductance can be obtained.
These "non-inductive" versions are substantially more
2. Set Vin at 1000 Hz, and observe Vin and Vc on your
oscilloscope. Measure the peak-to peak amplitudes and
the phase shift between them in degrees. (Hint: Phase
measurements can be made more easily by adjusting the
57
Elektrik Devreleri
oscilloscope to measure time differences.) Use
the highest available Vin value.
3. Look for the resonant frequency of the part
by adjusting fs until the phase shift is close to
zero. The amplitude will be close to minimum
for a capacitor. Record amplitudes of Vin and
Vc at this frequency.
4. Choose at least three frequencies below
resonance and three above it; also make a
measurement at 1 kHz. The frequencies you
choose should cover roughly a factor of 100 in
frequency. Record amplitudes of Vin and Vc, and
the phase shift between them, at each of these
frequencies.
5. Repeat parts 1-4 for your other assigned
capacitors and inductors. In some cases, you may want
to change the resistor value to allow better
measurements of Vc. If you do this, be sure to use R 50 ,
and be sure to record the R value actually used for each
part measured. A value R = 1000 is suggested for
inductors.
frequency sweep data. Compare the 1000 Hz results to
the RLC meter data.
6. Discuss how your data conform to the proposed simple
models.
Part 3: Power resistor tests (these can be performed
during frequency sweeps)
1. Connect a wirewound resistor to a variable dc supply.
2. Adjust the voltage and current to draw about 10% of
the rated power, or 1 W, whichever is less. Record the
voltage and current, then let the part warm up for at least
5 minutes. Record the voltage and current again.
3. Adjust the voltage and current to draw about 50% of
rated power, or 10 W, whichever is less. Wait at least five
minutes, then record the voltage and current.
4. Repeat step 3 for 100% of rated power.
19.11.7 Study questions
19.12 Magnetics
1. Use data for Vin, Vc, and phase to compute the
impedance for each tested capacitor and inductor.
19.12.1 Introduction
2. Plot impedance magnitude and phase vs. frequency for
each capacitor and inductor.
3. Plot resistance vs. power for the wirewound resistor.
4. Calculate ESL for each capacitor based on the
resonant frequency you measured.
5. Calculate ESR at 1000 Hz and at a frequency near
resonance for each capacitor and inductor from your
58
This experiment provides an overview of many concepts
of magnetic component design. It concentrates on
inductor and transformer design for high-speed
converters, and on magnetic properties of materials. In
power electronics, both the energy storage capabilities of
inductors and the potential-shifting properties of
transformers are important in converter designs. But the
requirements are much different from those in other
electrical engineering areas. High power levels are often
Pratik devreler / N. Abut
an issue at relatively high frequencies. Losses must be as
low as possible.
Modern switching converters and their applications take
full advantage of the latest magnetic materials. Highperformance motors use advanced permanent magnet
materials, as well as PWM inverters. The magnetic
amplifier and saturable reactor -- power amplifier
technologies of the 1940s -- are making a strong
comeback in power electronics because of new
materials. Material properties are inextricably linked to
magnetic components, even more than for capacitors.
Two important reasons for this involve the behavior of
"magnetic conductors." Highly permeable materials with
the ability to direct magnetic flux are only a few orders of
magnitude better than air or vacuum. They have limited
capacity for carrying magnetic flux. A second difficulty is
that the most permeable materials are metals -- they
carry magnetic flux, but also carry electric flux, so that a
time-changing magnetic flux will create current flow and
losses in the materials.
19.12.2 Basic theory
The important concepts of magnetic circuits, magnetic
domains, the hysteresis loop, and saturation lead to
design considerations for devices. In the laboratory, we
will examine candidate designs for inductors and
transformers. Any real magnetic material exhibits a
maximum value of B, called the saturation flux density
Bsat, beyond which it displays permeability close to that of
vacuum. Since the flux in a material is found as Ni/,
where is reluctance, the current ultimately determines
whether the saturation flux density has been reached.
Alternatively, the flux is given by /N, or v dt/N. The integral
of voltage ("voltseconds") determines the flux, within
some integration constant.
In a transformer, saturation must be avoided so that
leakage flux stays low. For ac applications, this means
that only the voltsecond integral is relevant. If a dc current
is imposed on a transformer, an additional flux
contribution will appear. In most power-frequency
transformers, the number of turns is high, and dc current
must be avoided. In an inductor, dc current is almost
always needed, so that a net energy can be stored.
Inductors must be designed to tolerate high levels of dc
current, while providing consistent, linear, inductance.
These two requirements are in conflict with the need for
inductors of substantial value.
Another important issue in modern magnetics design is
the current capacity of the wire used to wind the magnetic
device. For instance, a design might call for a great many
turns and a small core. While this is possible when small
wire is used, the wire might melt if the intended currents
are applied. It is not uncommon to require hundreds or
even thousands of windings in power frequency devices,
and the temptation to use ever-smaller wire is great. To
realize a design, it is helpful to realize that only a fraction
of any core opening can actually be filled with wire (some
must be allowed for insulation and for air spaces around
loose windings). It is also helpful to have some guidance
about current capabilities of copper. While no absolute
rules can exist, it is often safe to impose currents of up to
500 A/cm² on a copper wire. This number gives some
rough assistance in picking the wire sizes needed.
A transformer design procedure might be as follows:
Identify the frequency, voltage, current, and power
requirements.
Choose a wire size adequate for the current.
Find the voltsecond level needed to meet ratings.
Identify a magnetic core with low losses over the intended
frequency range, and proper , A, and winding opening
size to support the necessary flux.
Compute winding and core losses to see if they are at
acceptable levels.
Build and test the device.
An inductor design would seek to:
Identify the frequency,
requirements.
voltage,
and
dc
current
Identify the energy storage or L requirement.
Choose a wire size as needed.
Find the voltsecond level needed.
Compute a gap length, if necessary to meet energy and
idc requirements.
Build and test the device.
19.12.3 Procedure
Part 1: Core hysteresis loops
1. You will be assigned several test cores of various
types. Use a ruler to obtain geometric data for each one,
or use manufacturer's data.
2. Wrap approximately 25 turns of wire around each
toroid test core, and 40 turns around each pot core.
3. Measure the inductance of each device with the bridge
or equivalent instrument, if available.
59
Elektrik Devreleri
4. Place each core, in turn, in the circuit shown in the
figure 19.64, with proper choices of R and C. Be sure to
include the 50 resistor Rs.
5. Use the oscilloscope in the X-Y mode to observe the
hysteresis loop at some frequency. Sketch the loop in
your notebook. Measure the slope of either side of the
loop near the origin (B=0 and H=0). Don't forget to make
note of the slope units.
19.12.4 Study questions
6. Decrease the applied frequency until a saturation effect
is obvious. Again, sketch the waveforms. Measure the
slope of the loop as far into saturation as possible. Also
record the vc value at saturation.
2. Calculate Bsat from your hysteresis curves. What
voltsecond rating do you expect for your 25 turn
inductors? How do the converter and transformer results
compare to your expectations?
7. Apply a small dc offset from the input supply, and
observe the change in the loop. Record your
observations. Keep in mind that vc measures the integral
of
voltage,
and
not
directly.
3. How would a dc current load affect the output of a
transformer?
1. Calculate the permeability of each core at 1000 Hz. Do
your numbers agree with bridge or equivalent
measurements?
4. How many turns would be required to create a 10 mH
inductor with each of your cores? What would the dc
current rating be, based on saturation limits?
Part II -- Transformer design and testing
1. Create a transformer by adding a second 25
turn winding on one of your test cores specified
by your instructor.
2. Observe transformer performance by using
the circuit in Figure 19.63, with Rload = 1 k. Vary
the source voltage frequency and amplitude so
that saturation effects can be noted. You should
sketch waveforms which demonstrate both
saturated action and correct transformer action.
4. Use a 1N4004 diode in series with 50 as a
load,
and
repeat
your
observations.
19.13 Converter Design Project
19.13.1 Introduction
The intent of the last experiment (normally conducted
over a period of about a month) is to provide overall
experience with a converter design problem. Each group
60
Pratik devreler / N. Abut
will design, build, and test a different dc-dc converter. The
initial effort tests a basic design with lab boxes,
and considers effects of capacitor ESR and
switch forward voltage drop.
Vout = q1Vin - q2Vforward(diode), Vout(ave) = D1Vin - D2Vfor
The first consideration is to create a paper
design as the basis for starting the project:
Begin with one of the specification sets listed at
the end of this Section. For a dc-dc converter,
start with a switching frequency of 100 kHz.
Draw a converter circuit capable of performing the
intended function.
If Vfor is assumed to be roughly 1 V, the average value of
Vout can be found as
Given your specifications, find the switching frequency for
which L > Lcrit.
Vout(ave) = D1Vin + D1 - 1
Compute the range of load resistances which correspond
to the stated output power levels.
Find the value of capacitor necessary to meet the
intended ripple requirements.
In the final experiment, our previous work will culminate in
the design of an actual converter. The first activity will test
the basic design values, with the objective of developing
a tentative circuit. Effects of capacitor ESR and switch
voltage drops will be examined. The second activity will
concern implementation of the actual switches, along with
their switching functions. The last effort will examine
power loss and heat transfer considerations, and will
include
tests
of
the
finished
converter.
The input current is still Iin = q1Iout, so Pin(ave) = D1VinIout.
But now,
Pout(ave) = D1VinIout - D2VforIout,
which gives an efficiency of
19.13.2 Refining the models
= 1 - (D2Vfor)/(D1Vin).
Voltage drops can be integrated into converter design in a
straightforward manner. Consider the circuit shown in
Figure 19.64, in which an ideal diode and a voltage
source have been used to model a real diode. The output
voltage Vout can be written in terms of switching functions
as:
This is certainly less than 100 %, and represents the loss
in the real diode while it is on. A series resistor could also
have been included as part of the diode or transistor
models.
61
Elektrik Devreleri
1. Obtain an inductor, or design a pot-core inductor to
meet your requirements. Use this
inductor, along with an FET control box,
to build a converter as designed in your
preparation. Be sure to place a
capacitor across Vin, so that it will
appear as a voltage source.
2. Observe Vout under a range of
conditions. Be sure to test for a variety
of values within your required converter
operating range. Sketch Vout under what
you find to be roughly worst-case
Vout ripple. Be sure to record duty ratio
data, along with sufficient data to
calculate efficiency.
3. Observe voltage drops across the FET and the diode
under your range of operating conditions. The intent is to
gather data to support circuit models of your actual diode
and FET.
4. If the converter you have built does not meet the
specifications for output ripple, try other capacitors in an
effort to solve the problem. Experience with your
converter circuit is probably more important than meeting
all specifications in detail.
Capacitor ESR means that capacitors do not really show
any ideal voltage characteristics. For example, an
electrolytic capacitor with tan = 0.10 and C = 200 µF
would have ESR of 4 m at 20 kHz. Consider the effect in
the boost converter shown in Figure 19.65. When switch
#1 is on, the output current charges the capacitor, but
there is a voltage drop across the ESR which appears at
the output. As switch #1 turns off, the internal capacitor
voltage Vc stays quite constant, but the capacitor current
changes abruptly, which in turn reverses the voltage drop
across the ESR, and causes an abrupt shift in Vout. The
output voltage for this converter can be calculated without
too much trouble, if the capacitor voltage is assumed to
change in a linear manner. The Vout waveform is shown in
Figure 19.66.
As indicated in Figure 19.66, the ESR voltage drop can
be a significant fraction of the output voltage ripple. If a
maximum output ripple is specified, the value of ESR at
the switching frequency will have to be taken into account
when designing the converter. For example, the above
converter displays output ripple of about 240 mV,
although a ripple of less than 160 mV would have been
expected if the capacitor were a perfect 200 µF device.
5. In the next part of the design project, you will select
actual FET and diode parts, in place of the FET box. Be
sure you have collected all data needed for models of
your devices and for the capacitors. Also, observe
inductor current to confirm the critical inductance value.
19.13.4 Study questions -- part I
1. Model the on condition of the FET as a 0.3 resistor,
and the on condition of the diode as a 1 V drop. What
value of Vout vs. duty ratio would be expected for your
converter? Does this agree with measured data?
2. Will you need an FET with lower resistance to meet the
requirements?
3. Compute the ESR of your capacitors from the
waveform data.
4. Find the peak currents and voltages in your inductor
and capacitor.
5. Two common problems in dc-dc converters are: (a) the
user accidently connects the input voltage in the reverse
direction, and (b) a short circuit is accidently connected at
the output. Would the converter you are designing be
able to handle these faults? If not, how might it be
altered?
19.3.3 Procedure, part I
19.13.5 Gate drive implementation
62
Pratik devreler / N. Abut
At this point, it is logical to fully implement the converter
design with discrete components in place of the
laboratory boxes. An ideal switch requires a third gate
terminal which controls its state. In the ideal case, a
switching function is applied directly to this gate (without
regard for electrical ground or isolation). The switch is
instantaneously on whenever the gate is high, and
instantaneously off whenever the gate is low. While the
concept of a gate terminal carries over to real switches,
there is a host of new considerations introduced by a real
gate.
The potential at the gate normally has restrictions relative
to the potentials on the switch terminals. Operation of a
real gate requires energy (and hence power and time);
these must be supplied from some drive circuit. As you
might guess, there is a time difference between the
application of a gate signal and the actual switching
action. In addition to gate characteristics, semiconductor
switches have internal properties, such as resistance and
capacitance, which limit time rates of change of voltage
or current even with a perfect delay-free gate signal.
designed to charge this capacitance sufficiently. The
channel will invert when the gate voltage exceeds a
threshold level, Vth. In fact, the gate voltage must be
maintained at a level considerably greater than Vth, so
that enough charge will be present in the channel for low
effective channel resistance. The gate drive must
therefore apply an "overdrive" gate voltage, for switching.
To turn the FET off, the gate region must be discharged,
and the gate voltage must be maintained below Vth. Real
devices have wide error tolerances on Vth. For example,
the MTM15N35 FET can have any Vth between 1.5 and
4.5, depending on the device and the operating
temperature.
Some gate drive design considerations are apparent:
For turn-on, the drive must rapidly charge the gate to a
voltage much higher than Vgs, while not exceeding the
dielectric breakdown limit of the gate insulator. Typical
gate-source capacitance values range from several
hundred to several thousand picofarads.
A gate drive typically tries to minimize commutation time
while not adding significantly to power requirements. Gate
drives are low-power electronic circuits, and are designed
much differently from the converters in which they
operate. They are still switching circuits, however, so
many concepts of switch networks still apply.
For turn-off, the drive must rapidly discharge the gate to a
voltage lower than Vth, again without exceeding dielectric
limits.
19.13.6 Basic theory -- gate and base drives
Vth between 2.0 and 4.0 V.
The major classes of gated power semiconductors -thyristors, BJTs, and FETs -- have distinct gate drive
requirements. For example, a BJT can be modelled as a
current-controlled current source, and requires current
into the base when it is to be on. This current is supplied
at low voltage (so that power is low), but can be as high
as a tenth or more of the switch on-state current. In the
case of the FET, the steady-state gate current is
essentially zero, and the gate voltage determines switch
operation. The SCR, as a typical thyristor requires only a
pulse at the gate in order to turn on. Gate turn-off
thyristors (GTOs) also require only pulses, although a
substantial negative gate current must be applied to turn
the devices off.
Limits on gate-source voltage (gate dielectric breakdown
limit):
The basic requirements are simple enough, but details
add great complexity. Let us first examine the FET, which
has relatively simple gate characteristics. To turn the FET
on, the gate region must be charged. The region
represents a capacitance, and the gate drive must be
Several device specifications are important in the FET
gate drive design. Referring to the IRF521, a typical
power FET, notice the following relevant information:
-20 V < Vgs < +20 V.
Maximum gate current level: 1.5 A (absolute value).
Gate-source input capacitance: 600 pF.
With these data, it is possible to design many different
gate drive circuits. Consider the performance of a simple
gate drive, consisting of a nearly ideal switch operated
from a voltage source of 50 output impedance. At turnon, the gate capacitance is uncharged, and the maximum
gate current is simply Vin/Rs, or 0.24 A in this example.
The RC time constant is 30 ns so this gate drive will
charge the gate to more than 10 V in about 60 ns. The
actual device turn-on time of 110 ns is reasonably
consistent with this number. Slightly faster turn-on could
be achieved by using a smaller Rs. A value as low as 8
can be used without excessive gate current.
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Elektrik Devreleri
The gate drive can be designed so that
current is drawn only in a brief pulse. In
principle, most of the ½CV² energy in
the gate can be recovered, so that power requirements
are very low.
A typical high-performance gate drive circuit appears in
Figure 19.68.
At turn-off, the gate must discharge through the second
resistor. This resistor has the undesirable effect of
drawing power whenever the FET is on, so is kept
relatively high. It also acts as a voltage divider for Vgs. For
the circuit of Figure 19.67, turn-off is quite slow.
More specific requirements on the gate drive are
becoming apparent:
The main drawback of FET gate drives is the need to
apply a substantial voltage between the gate and source
as long as the device is to be on. In many converters, this
is not a trivial manner. The familiar buck dc-dc converter
is shown in Figure 19.69. For the unit of Figure 19.69 to
work, a voltage equal to Vin + 10 V must be applied to the
FET gate whenever switch #1 is to be on. This second
voltage source, higher than the available source, can be a
major stumbling block in building a converter. If the
switch is relocated as in Figure 19.69b, the problem of
higher voltage level is alleviated, but the output is no
longer referred to ground potential. The voltage
The gate drive must provide a voltage between
the gate and source of about 10 to 18 V, with
low source impedance, for fast turn-on.
The gate drive should provide a low impedance
discharge path during turn-off. This path can
apply zero volts across the gate and source, or
could use Vgs < 0 if a negative voltage source is
available.
requirements of FETs sometimes make
them difficult to use in many situations.
Bipolar transistors need only a fraction
of a volt on the gate (base) terminal. The base behavior is
far more complicated than the FET's gate behavior. A
BJT base drive must supply enough current to guarantee
that the transistor will be fully on. This means that Ib must
be chosen to be larger than the expected collector current
Ic/. In power transistors, can be quite low -- values of 5 or
64
Pratik devreler / N. Abut
less are not unusual for devices rated over ten amps.
Furthermore, in order to operate the device at the highest
possible speed, an overdrive current pulse should be
applied at turn-on. This pulse is usually chosen to be
nearly equal to Ic. Such high currents are difficult to
achieve, since they call for impedance levels well under 1
.
The 2N3055 can serve as a guide for base drive design.
This device allows a base current as high as 7 A. The
voltage at the base terminal will not exceed roughly 1.5 V.
The gain value can be as low as 5, so that base current
of about 3 A might be needed if Ic approaches the
maximum value of 15 A. A candidate base drive circuit is
shown in Figure 19.70. The major difference between this
and the FET drive is that it involves much lower
impedances. Many base drive circuits include
transformers to obtain high currents and low impedances.
Most SCR applications are tied to an ac power line
frequency, so that turn-on speed is often not a major
consideration. With this in mind, it is relatively easy to
build an SCR gate drive, provided certain details are
considered. A controlled rectifier circuit is shown in Figure
19.71. The load inductance normally makes the operation
consistent with periodic steady state. However, take the
case of circuit start-up. Inductor current
is initially zero, and three-phase
voltages are applied to the SCRs.
While a gate signal is applied to SCR A,
the inductor current changes as vL/L. A
large inductor will mean a slow change,
and a long time may pass before the
SCR anode current exceeds the
"holding" value. To alleviate this, a
small resistor can be added as a ballast
load, to ensure SCR turn-on latching.
Otherwise, the circuit might not operate.
19.13.7 Basic theory -- snubbers
Thyristors, as latching devices, are much different from
transistors. A signal must be applied to the gate only until
sufficient anode current flows. Then the gate signal can
be removed. For example, the 2N6508 requires a gate
signal of 75 mA or more at a voltage of up to 1.5 V. The
gate signal will not be needed once the anode current
reaches a "holding current" of 40 mA. This can occur as
little as 2 µs after the start of the gate pulse. A pulse
transformer can serve as a suitable driver for such
requirements. This has the important advantage of
isolation of the gate.
For some converter designs, very high momentary
voltages appear across the FET during the Part I
procedures, especially if the layout is loose. Power FETs
can easily be destroyed when a Vds value beyond their
limit appears. High momentary voltages can occur even
in relatively low voltage converters. Each circuit
connection, wire, or component, has inductance, and thus
behaves as a current source over short time intervals.
When one attempts to reduce any current by switching
action, a negative voltage vL = L(di/dt) will be produced.
The faster the switch, or the larger the inductor, the more
extreme this negative voltage. In an FET switching 10 A
in 100 ns, even with a circuit inductance as low as 1.0
µH, a voltage of 100 V will be generated, independent of
the converter voltage levels. This voltage will appear
across the switch as it turns off, causing commutation
loss and possibly approaching the switch voltage limits.
This effect is detrimental, since it leads to extra losses
and even switch failure. It is necessary
to minimize the circuit inductance, and
to keep di/dt sufficiently small. Leads
should be short and of proper size.
Loops or other features which enhance
magnetic field coupling must be
65
Elektrik Devreleri
avoided. It is desirable to act upon the switching trajectory
itself. After all, the problem here is a switching trajectory
which reaches voltages much higher than any circuit
voltage when current is still high.
capacitor charges up to Voff. But at transistor turn-on, the
snubber circuit diode prevents current flow from the
snubber capacitor. The second resistor, R2, discharges C
during the transistor's on-time so that the snubber will
again be ready for turn-off.
This simple snubber is very popular,
and has been used successfully in a
wide range of circuits. This snubber is
known as a lossy snubber, since
energy is dissipated in its resistance
components. The intent is to decrease
the total switching losses by adding a
lossy snubber. Lossless snubbers,
which use only switches and energy
storage elements, are feasible, and have been discussed
in
the
literature.
19.13.8 Procedure -- part II
1. We will study an FET gate drive in the context of your
converter. Obtain an FET and diode with ratings
appropriate
to
your
converter.
Measure
the
characteristics of these devices on the curve tracer.
Circuits which act directly on the switching trajectory are
called snubbers. The function of a snubber is to shape
the switching trajectory and hence protect the switching
device. For this reason, most snubbers are wired directly
to a switch, and would be considered an actual part of the
switch itself for purposes of converter design. For
example, a capacitor can be placed across the
semiconductor, so that some of the energy needed by the
load during commutation is provided by the capacitor. A
resistor might be used to discharge the capacitor one the
switch has reached the new operating state.
A simple RC snubber causes the switch voltage to
change relatively slowly (beginning at about zero) during
turn-off. Unfortunately, the opposite occurs during turnon. In this case, the transistor voltage changes slowly,
beginning at Vin, during switching. The switching power
loss will actually increase. It is apparent that a turn-off
snubber and a turn-on snubber have different
requirements. To avoid this difficulty, it is necessary to
add circuitry so that the simple RC snubber discussed
above will operate only during transistor turn-off. A switch
is needed! This switch needs to carry current only during
commutation, so that its ratings can be based on
momentary performance, rather than on continuous
capabilities. A possible snubber circuit is shown in Figure
19.72. During turn-off, it causes voltage to change
relatively slowly. While the transistor is off, the snubber
66
2. Assemble the drive circuit shown in Figure 19.73. The
SG3526 integrated circuit is a controllable pulse
generator for use in dc-dc converters. Notice that the
circuit includes a snubber.
3. Insert the FET and diode into your converter circuit.
Pay attention to grounds and to isolation requirements for
voltage sources.
4. Observe the FET voltage and current, and the gate
voltage. Choose a reasonable value of frequency and
duty ratio, based on your converter requirements. Sketch
the waveforms. What are the turn-on and turn-off times of
your switches?
5. Vary the duty ratio and frequency. Again observe the
FET signals. Take data necessary to find effects of D and
f on rise and fall times. Be sure to observe the effect of
very high switching frequency.
6. Use the X-Y mode of your oscilloscope to observe and
sketch the switching trajectories. Think about how the
snubber affects them.
7. Check your converter to see if it meets the
specifications. Try making adjustments where necessary.
What are the input voltage and power limitations of your
converter?
Pratik devreler / N. Abut
intent. At least some of these difficulties can be mitigated
through the use of feedback control concepts. The basic
idea, as taught in a first Control Systems course, is to
subtract some fraction of the circuit output from an
intended "reference" value, and use the result as a new
input signal. When this is done, the output can be made
almost arbitrarily close to the desired value even in the
presence of load changes, supply changes, residual
drops across switches, and other disturbances.
19.13.11 Basic theory -- converter control
Of the many ways to implement feedback control in a dcdc converter, perhaps the simplest is called output
voltage control. Here, the output voltage is sensed and
subtracted from a given reference value. The result is
amplified, and applied to the duty ratio input of a PWM
circuit. A block diagram is shown in Figure 19.74. In a
buck converter which uses this circuit, the input-output
relationship
can
be
written:
Vout = k(Vref - Vout)Vin.
19.13.9 Study questions -- part II
Simplifying this,
1. Compute (approximately) the power used in your gate
drive circuit. How is converter efficiency affected?
Vout(1 + kVin) = kVrefVin.
2. Include the curves gathered in the lab on the curve
tracer for your devices. What is Vth for your FET? What
voltage
drops
and
resistances
model
your
semiconductors?
If k is large so that kVin >> 1, then both sides can be
divided by kVin to give
3. Calculate a value of gate capacitance from your
measured fall time. Is the value consistent with
the data sheets?
Vout = Vref.
4. Use the data to predict the performance of
your converter. Can the specifications be met
with
these
parts?
19.13.10 Thermal performance and feedback
control -- introduction
Now that the converter has been constructed (and
presumably operated with some success), key
operational issues such as feedback control need to be
considered. The designer of a converter has relatively
little control over how the unit is used. The most obvious
unknowns are the input power source and the output
load, but additional conditions such as ambient
temperature, residual voltages, time-rate-of-change of the
load, response to a short-circuit or to an open-circuit
applied at the load terminals, device protection, reliability,
cost, and electromagnetic performance often depend on
customer requirements rather than on the designer's
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Elektrik Devreleri
It is easy to show that this result applies even when
residual switch voltages are included: a large gain will
produce output equal to the reference value, in spite of
changes in supply, load, or other uncontrolled
parameters, as long as the converter duty ratio is within
the allowed limits.
While this style of proportional gain feedback is
simple and appealing, it has two important
drawbacks. The first is that the output is not
exactly equal to the input, even in steady state,
because k cannot be infinite. This should be
clear when you consider that the converter duty
ratio D is given by D = k(Vref - Vout). Since we
expect D to have some value greater than zero,
the value Vref - Vout must also be greater than
zero. A second drawback is that if k is too large,
then any slight disturbance will drive D to the
limits 0 or 1, and the converter output will jump
around almost at random. One alternative is to
add an integrating element D = k(Vref - Vout) +
1 V) between the base and the emitter. If the base is set
to 6 V, for example, we might expect about 5 V at the
emitter. Consider the effect of an external load change
which attempts to decrease Ve. Then more current will
flow into the base, and Ic will increase since it is given by
Ib. The emitter current will rise, which would be expected
to result in an increase in Ve. Similarly, an attempt to
increase Ve will produce lower emitter current.
kivref - vout to the control. This eliminates steady-state
error without requiring extreme gain.
This simple circuit will work as long as the output pass
transistor is in its active state. The transistor must not act
as a switch. This, in turn, requires that there be sufficient
voltage at the collector so that saturation is always
avoided, and that there be sufficient base current to avoid
cutoff. One way to assure both of these is to keep Vc >
Vout + 2 V, and to use a high-gain transistor with a high
bias current through the zener diode. For a pass
transistor with = 25, and Iout < 2 A, the required bias
current is 80 mA. The zener diode thus requires power of
0.08 × 6, or about ½ W. A final circuit, designed for Vout +
2 < Vc < Vout + 5, is given in Figure 19.76. With a 10 W
load, this regulator is about 68 % efficient with 7 V input
and 43 % efficient with 10 V input. Even though the
efficiency is not good, the output quality is very high.
Converter control can also be implemented with series
regulators for output filtering. Consider the regulator
circuit below. The zener diode has been used to provide a
reference signal for the series regulator. The output
transistor exhibits a small voltage drop (typically less than
68
19.13.12 Basic theory -- thermal effects
Power lost in a semiconductor (or anything else) is
converted to heat. Naturally, this will cause a temperature
rise in the semiconductor. Semiconductor devices have a
Pratik devreler / N. Abut
maximum temperature at which they can function -typically between 100C and 200C. We must ensure that
the semiconductor temperature will remain below its limit
under operating conditions. To do this, it is important to
understand some basic concepts of heat flow.
Temperature can be defined as a potential associated
with heat flow, just as voltage can be defined as a
potential associated with current flow. In solid
substances, the flow of heat follows Fourier's Law of Heat
Conduction, which states that the heat flux per unit
area q (the units are W/m²) is proportional to the
temperature gradient in the material. The constant of
proportionality is defined as thermal conductivity, and is
given the symbol k, so that
Fourier's Law represents the effect of heat conduction
(heat flow between solid objects in physical contact).
When fluids are involved, the heat flow is referred to as
"convection," in which motion of the fluid carries away
much of the heat. Again, the heat flux depends on a
temperature
difference,
and
a heat
transfer
coefficient, h can be defined so that
oxidized aluminum 0.10
flat black paint 0.90
A flat black heat sink with temperature of 50C and e = 0.9
will transfer 0.04 W/m² to surroundings at 20C. In many
situations, radiation heat transfer can be neglected.
In the case of both conduction and convection, heat flux
depends linearly on a temperature difference. The
thermal conductivity can be used to define a "thermal
resistance," analogous to electrical resistance. The total
heat flow in watts can be multiplied by the thermal
resistance to give the temperature difference, so that the
temperature of a semiconductor T j is equal to Ploss(ja) +
Ta, where ja is the thermal resistance in K/W between the
semiconductor and the surrounding ambient, and T a is
the ambient temperature. (Please realize that only
temperature difference is involved, so that units of K
become equivalent to units of C. Most manufacturers give
in C/W.)
19.13.13 Procedure -- part III
The heat transfer coefficient is much more complicated
than thermal conductivity, since it includes flow rates,
directions, the surface area of the heat generator, and a
variety of other parameters.
Converter checkout (open loop):
The third type of heat transfer, radiation, is more
complicated still. In this case, heat flux is proportional to
the fourth power of the temperature difference. The result
is
2. Check the operation of your converter over its full
range. Make note of any combinations of Vin and Pout for
which you could not meet the specifications, and
determine the issues associated with the limitations.
where is the Stefan-Boltzman constant, = 5.670108 W/(m 2K4), and e is the "emissivity" of the object, e =
qactual/qideal. Typical values of e are:
3. Measure and record the temperatures of the switching
devices under conditions of maximum load and minimum
Vin. Let the circuit stabilize for about ten minutes, but shut
it down if your measured values go beyond 120C. If the
temperature reaches steady state, record it and record
electrical information to allow you to calculate power loss
in the FET and the diode.
Material emissivity
1. Operate your converter over its specification range.
Measure its efficiency under several operating conditions.
3. Take temperature measurements at two other
combinations of Pout and Vin.
polished metal 0.05
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Elektrik Devreleri
CONVERTER SPECIFICATION SETS
The basic specification sets here cover a wide range of
dc-dc converter designs and applications.
A.
Input Voltage Range: 5 V to 9 V
Output Voltage: 12 V ± 1 %
Output Load Range: 5 W to 20 W
Feedback control checkout:
4. During the temperature stabilization time, build the
circuit of Figure 19.77 for use in a feedback loop. Notice
that the circuit output is 10(Vref - Vout).
5. Insert the feedback control unit into the converter, as
follows:
a) The circuit output attaches to the "sense" input of the
SG3526.
b) The "voltage" input attaches to the converter output.
c) The ground node attaches to the converter output
ground.
d) For a buck converter, connect the "current" input to
ground.
e) For a buck-boost converter, place a 0.1 resistor in
series with the inductor, on the ground side. The voltage
on this resistor goes to the "current" input.
f) For a boost converter, place a 0.1 resistor in series with
the converter input source, on the ground side. Connect
the voltage on this resistor to the "current" input.
6. Set up the converter with minimum load. Turn it on,
and determine whether the control circuit is functioning.
7. Vary Vin, and observe the control action on Vout. What
is
the
circuit
line
regulation?
B.
Input Voltage Range: 10 V to 25 V
Output Voltage: -12 V ± 2 %
Output Load Range: 5 W to 20 W
C.
Input Voltage Range: -4.5 V to -16 V
Output Voltage: 5 V ± 1 %
Output Load Range: 10 W to 25 W
D.
Input Voltage Range: 10 V to 35 V
Output Voltage: +5 to +12 (adjustable) V ± 50 mV
Output Load Range: 0 W to 20 W
E.
Input Voltage Range: 12 V to 40 V
Output Voltage: either +80 or -80 V ± 3 %
Output Load Range: 10 W to 20 W
F.
Input Voltage Range: 10 V to 15 V
19.13.14 Study questions -- part III
Output Voltage: -16 V ± 2 %
1. Estimate the thermal resistances jc and ja from your
temperature data and from measurements of power loss
in your switches.
Output Load Range: 2 W to 20 W
2. Discuss your converter design project results in
some depth.
Input Voltage Range: 7.0 V to 14 V
G.
Output Voltage: 5 V ± 1 %
70
Pratik devreler / N. Abut
Output Load Range: 0 W to 50 W
Output Load Range: 50 W to 100 W
(battery powered)
O.
H.
Input Voltage Range: 25 VRMS, 50-60 Hz
Input Voltage Range: 14 V to 25 V
Output Voltage: 13 V adjustable ± 1 V, with current
limited to 5 A
Output Voltage: 12 V ± 1 %
Output Load Range: 0 W to 70 W
Output Load Range: 0 W to 20 W
P.
I.
Input Voltage Range: 25 V to 50 V RMS, 60 Hz
Input Voltage Range: 9 V to 15 V
Output Voltage: 12 V ± 1 %
Output Voltage: 24 V ± 3 %
Output Load Range: 50 W to 100 W
Output Load Range: 12 W to 35 W
Q.
J.
Input Voltage Range: 22 V to 26 V
Input Voltage Range: 3 V to 8 V
Output Voltage: 122 cos(120t) V ± 0.2 V
Output Voltage: 5 V ± 1 %
Output Load: 50 W
Output Load Range: 0 W to 25 W
R.
(battery powered)
Input Voltage Range: 5 V to 12 V
K.
Output Voltage: 1 to 2 V ± 0.02 V (mean is adjustable)
Input Voltage Range: 8 V to 15 V
Output Load: 20 to 40 A
Output Voltage: 6 V ± ½ %
Output Load Range: 0 W to 20 W
Summary Specification Sheets for Parts
L.
Input Voltage Range: 10 V to 25 V
IRF 520 and IRF 521 (MOSFET):
Output Voltage: -12 V ± 1 %
Rating Symbol Maximum limit
Output Load Range: 0 W to 35 W
Drain-source voltage VDSS 100 V (520), 60 V (521)
M.
Gate-source voltage VGS ±20 V
Input Voltage Range: 25 V to 40 V
Drain current ID 8 A continuous, 32 A peak
Output Voltage: 12 V ± 1 %
Junction temperature TJ 150C
Output Load Range: 50 W to 100 W
N.
Input Voltage Range: 12 V to 18 V
Output Voltage: 24 V ± 1 %
Characteristic Symbol Typical value
Thermal resistance, junction-case JC 3.12 K/W
junction-ambient JA 62.5 K/W (no sink)
Residual current, VGS=0, VDS=max IDSS 0.2 mA
71
Elektrik Devreleri
Gate threshold voltage VGS(th) 2 to 4 V
Collector current IC 15 A continuous
On-state resistance, VGS=10 RDS(on) 0.3
Base current IB 7 A
Input capacitance Ciss 600 pF
Junction temperature TJ 200C
Turn-on delay time td(on) 40 ns
Characteristic Symbol Typical value
Rise time tr 70 ns
Thermal resistance, junction-case JC 1.52 K/W
Turn-off delay time td(off) 100 ns
Residual current, IB=0, VCE=30 ICE0 0.7 mA
Fall time tf 70 ns
Dc current gain hFE 40 (IC=4 A), 5 (IC=10 A)
IRF 351 and MTH15N35 (MOSFET):
Collector-emitter saturation voltage VCE(sat) 1.1V (IC=4A),
3V (IC=10A)
Rating Symbol Maximum limit
Turn-on delay time td(on) 0.1 µs
Drain-source voltage VDSS 350 V
Rise time tr 2 µs
Gate-source voltage VGS ±20 V
Storage time ts 2 µs
Drain current ID 15 A continuous, 60 A peak
Fall time tf 2 µs
Junction temperature TJ 150C
Characteristic Symbol Typical value
2N6508 (SCR):
Thermal resistance, junction-case JC 0.83 K/W
junction-ambient JA 30 K/W (no sink)
Residual current, VGS=0, VDS=max IDSS 0.25 mA
Gate threshold voltage VGS(th) 2 to 4.5 V
On-state resistance, VGS=10 RDS(on) 0.3
Input capacitance Ciss 3000 pF
Turn-on delay time td(on) 35 ns (351), 60 ns (15N35)
Rating Symbol Maximum limit
Blocking voltage (forward or backward) VAK(off) 600 V
Peak gate current IGM 2 A
Forward current IT 25 A RMS, 16 A ave,
300 A ½ cycle surge
Junction temperature TJ 125C
Rise time tr 65 ns (351), 180 ns (15N35)
Characteristic Symbol Typical value
Turn-off delay time td(off) 150 ns (351), 450 ns(15N35)
Thermal resistance, junction-case JC 1.5 K/W
Fall time tf 75 ns (351), 180 ns (15N35)
Residual current, IG=0, VAK=max IT(off) 2 mA
2N3055A (BJT):
Gate trigger current IGT 25 mA (75 mA worst case)
Gate trigger voltage VGT 1 V
Rating Symbol Maximum limit
Holding current IH 35 mA
Collector-emitter voltage VCE0 60 V
On-state residual voltage VAK(on) 1V (IT=3A), 1.8V (IT=50A)
Base-emitter voltage VBE -7 V
Turn-on time tgt 1.5 µs
72
Pratik devreler / N. Abut
Turn-off time tq 35 µs
SG3526 Operation
Critical rate of rise of off-state voltage dv/dtC 50 V/µs
The SG3526 contains several modules:
MUR3040PT (ultra-fast power rectifier):
A +5V series regulator for logic power and to provide a
reference signal. the regulator works over an input range
of +8V to +35V.
Rating Symbol Maximum limit
An undervoltage lockout circuit to shut the IC down and
reset it if the +5V level falls too much.
Peak reverse voltage VR 400 V
Forward current, per leg IF(ave) 15 A, 150 A ½ cycle surge
An oscillator to provide a triangle waveform and a clock
pulse train over the range 1 Hz to 400 kHz. The period is
approximately ½(RC), where R and C are the timing
components connected at pins 9 and 10, respectively.
Junction temperature TJ 175C
Characteristic Symbol Typical value
Thermal resistance, junction-case JC 1.5 K/W
junction-ambient JA 40 K/W
Reverse current, VR=max IR 500 µA
Forward voltage, IF = 15 A VF 1.2 V
Reverse recovery time trr 60 ns (max)
SG3526 (PWM control integrated circuit):
Rating Symbol Maximum limit
Supply voltage VS 40 V (max), 7 V (min)
Logic input voltage (pins 5, 8, 12) Vin -0.3 to +5.5 V
Analog input voltage (pins 1, 2, 6, 7) Vin -0.3 V to VS
Junction temperature TJ 150C
Characteristic Symbol Typical value
Thermal resistance, junction-ambient JA 66 K/W
An amplifier (a bit like an op-amp) with gain-bandwidth
product of 1 MHz. This amplifier is actually a
transconductance device, and compensating capacitance
of 100 pF or so must connected from pin 3 to ground to
make it work properly.
A comparator for pulse-width modulation. The oscillator
triangle is compared to the amplifier output to generate
the main PWM square wave.
Dual totem-pole outputs. These outputs can drive up to
200 mA loads at up to 35 V. They are designed primarily
for MOSFET gate drives.
Pulse-steering logic. To allow tightly balanced operation
of two converter switches, this logic directs PWM output
pulses to alternate gate drives. For example, one pulse
goes to the top gate drive, the second to the bottom gate
drive, and so on. While this balances the two outputs, it
also limits the output duty ratio to just under 50%. The
outputs can be or-ed to give 0-100% duty.
Double-pulse lockout logic. If the amplifier output crosses
the triangle wave more than once per clock period,
multiple PWM pulses are produced. The double-pulse
logic ensures that only the first pulse is accepted. No
others will have any effect until the logic resets with the
next clock pulse.
Current comparator. This separate op-amp allows an
external current shunt to be used for protection. If more
than about 100 mV is imposed between pins 6 and 7, the
circuit will shut down until the current falls again.
Frequency range f 1 Hz to 500 kHz
Some other features:
Reverse current, VR=max IR 500 µA
Forward voltage, IF = 15 A VF 1.2 V
Each pin actually serves as both input and output.
Reverse recovery time trr 60 ns (max)
73
Elektrik Devreleri
The clock can be synchronized externally by imposing a
150 ns square wave at pin 12. This simply overrides the
internal clock.
A resistor at pin 11 (normally 0 ) can adjust the output
dead time, i.e. the time between turn-off of the top output
and turn-on of the bottom output. RD = 0 gives about 1.5
µs of dead time, while 10 gives about 5.5 µs when the
oscillator is at 40 kHz.
To drive a single MOSFET over the full 0-100% duty
range, it is necessary to use both IC outputs in an OR
configuration.
1.
J.A.Sabate et al. Design considerations for high- voltage
high-power
full-bridge
zero-voltage
switched
PWM
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2.
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3.
R.W.De Doncker et al. The auxiliary resonant commutated
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4.
R.Redl, N.O.Sokal, and L.Balogh. A novel soft-switching fullbridge dc-dc converter; analysis, design considerations and
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Hamada. Soft-switching PWM converter using saturable
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6.
Harada, Kojima, Ishihara, and Todaka. New control scheme
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Michihira, Yonemori, and Nakaoka. Resonant-pole type ZVSPWM dc-dc converter using
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10. P.M.Espelage and B.K.bose, "High-frequency link power
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11. L.Gyugyi, et al, "The high-frequency base converter" ,IEEE
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12. M.Kayama, et al."High-frequency DC/AC converter with
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13. Jump
up^ http://www.solarelectric.com/lib/wind-sun/PumpInverter.pdfHow to Choose an Inverter for an
Independent Energy System
14. Jump
up
to:a b http://www.wpi.edu/Pubs/Eproject/Available/E-project-042507092653/unrestricted/MQP_D_1_2.pdf
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power
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Oxford:
Newnes.
p. 97. ISBN 0080473911.
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Survey of Topologies, Controls, and Applications”. IEEE
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738.doi:10.1109/TIE.2002.801052.
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18. Owen, Edward L. (January–February 1996). “Origins of the
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