Download Meters, Power Supplies and Generators

Meters, Power Supplies and Generators
1.
Meters
Generally analog meters respond to the average of the signal being measured. This is due to the
mechanical mass of the pointer and the RC response time of the electronics. Since the average
of most ac signals is zero, ac meters require more circuitry to measure values of time varying
voltages. Many meters can function as both current and voltage meters. Usually there are
separate inputs for the voltage and current functions. Trying to use the instrument as a
voltmeter, when the leads are connected to the current input will either destroy the meter or
blow a fuse.
Voltage Measurements
Voltage is analogous to pressure in a water pipe. And like pressure, it has to be measured
relative to a reference. A voltage is measured across a circuit component, to indicate the
voltage difference or voltage “drop”.
The dashed lines in figure 1 indicate that all parts are contained within one physical unit. In this
case, the resistance is a part of the meter and there is no way to separate it from the meter. An
ideal voltmeter has a resistance of 4S.
Figure 1. The Voltmeter
To measure voltage electronically, a voltmeter uses a known, stable, resistor. All voltage
meters draw current, because of that resistor. A typical digital volt meter (DVM) has a
resistance of 10 MS while some older analog meters may be as low as 3.2 kS.
Current Measurements
Current is the rate change of charge and is, therefore, a measure of the number of electrons per
second moving through a circuit. Since the current into and the current out of a lumped
component are equal, you cannot measure a current “drop” across a component. To measure
current you have to measure the actual charge flow through the wire.
This measurement is done by inserting relatively small resistor in series with the circuit and
measuring the voltage drop across the resistor. This is normally shown transformed into a
series resistor and an ideal (resistance of 0S) current meter. The series model is shown in
figure 2. In the typical digital multimeter (DMM), on a 2A range, the resistance is 100 mS.
Because a current meter has resistance, it will cause a voltage drop and may affect the operation
of the circuit. The actual amount of resistance depends upon the sensitivity of the meter. For
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example, the DMM on a 200 uA range has a resistance of 1 kS, while a nanoampere meter will
be more than 100 kS.
Figure 2. The Ammeter
Resistance Measurements
An ohmmeter applies Ohm’s Law to determine resistarnce. Ohm’s Law states the voltage =
resistance x current. By applying a known voltage (produced by an internal battery or
transformer) to a resistor and measuring the current flow, the resistance can be determined.
Power Measurements
A wattmeter measures the product of voltage and current to determine the power in watts.
Measurement Errors
This is a complex issue and we will only cover the basics. An error causes the measured value
to be different from the actual value. Human, or gross, errors are usually due to mistakes in
using or reading an instrument. Two examples are viewing an analog meter needle at an angle
rather than straight on (parallax error), and reading the wrong meter scale. Other errors may be
caused by the instruments themselves.
Plots of data (figure 3) typically include error
bars, which indicate the accuracy of the
measurement, the effect of the meter loading
upon the circuit, etc. Plots of theoretical
calculations can also include a tolerance to
account for the non-perfect circuit components
(ie ±1%, ±5%, etc), temperature variations, etc.
Figure 3. A Plot Illustrating Error Bars
Accuracy
The accuracy of a measurement is how close the value came to the actual value that exists, not
the theoretical one. Instrument accuracy is usually broken down into systematic errors and
random errors. The systematic errors are either instrument related (ie friction in a mechanical
meter pointer bearing) or environmental. The method by which the meter works (mechanical,
electrical, ..), and the “quality” of design and construction, greatly affect how large these errors
are. Quite often both of these are further broken down into static and dynamic errors. Dynamic
errors would be caused by the meter not being able to respond fast enough.
Precision
Precision pertains to the number of significant figures and the repeatability of a measurement.
High precision instruments provide more significant figures and have greater repeatability.
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Resolution
This is the smallest change in the quantity being measured that an instrument will indicate. For
a digital meter, this is simply one of the smallest digits. With an analog meter, this is usually ½
of the smallest divisions on the meter face.
Repeatability
The repeatability is a measure of the fluctuations which are due to noise and errors that are not
repeatable. When a measurement is repeated several times, and then statistically analysed, the
repeatability can be expressed as the standard deviation.
Uncertainty
This is the combined effect of accuracy, precision, repeatability, noise, and errors on the
measurement. It represents how uncertain the measurement is.
1.1 Calculating Meter Error
Analog Meters
The error for an analog meter is usually not explained in detail. However, most of the error is
due to the mechanical meter movement. This error is constant, across a given meter range,
regardless of the magnitude of the variable being measured. An analog meter stamped as being
accurate to 2%, is accurate to 2% of the full scale deflection (FSD).
For example, suppose a reading of 35.0 V (dc) was obtained on the 50 V range of a dc
voltmeter, that is accurate to 2%.
The error is: 2% * 50 VFSD = ±1 V
Therefore V = 35.0 ± 1 V (dc) or expressed as a percent V = 35.0 V (dc) ± 2.9%
Since the absolute error of ±1 V is constant for the range, the smaller the measured voltage is in
relation to full scale, the larger the percent error becomes. If this meter range was used to
measure a 9V battery the error would be ± 11%. For analog meters, it is more accurate to
measure values with the needle close to full scale.
Below is a table of the accuracy for various measurements made with the Simpson 260 meter.
Measurement
Accuracy:
± (% of full scale deflection)
DC voltage ranges
DC current (>50uA) ranges
AC voltage ranges
2%
2%
3%
Digital Multimeters
The DMM is the most common instrument you will encounter. The precision of a DMM is
usually expressed in digits. The most common model has 3 ½ digits. That means that you have
three “full” digits that are capable of indicating from 0 to 9 and one ½ digit. The ½ means that
a +1, blank ie. 0, or -1 can be displayed. There are also 4 ½ and 6 ½ digit meters as well as 3/4
digit meters. A 3/4 digit meter can display +2, +1, blank (0), -1 or -2 as the leading digit.
A DMM has two sources of systematic error. One part of the error is due to tolerances in
resistors. It is expressed as a percentage of the input and therefore varies with the magnitude of
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the voltage being measured. The second part of the error is due to the digital conversion
process. It is fixed for a given meter range and is expressed in the number of “digits” to which
the reading is accurate. Each “digit”, has the value of a single count of the right-most digit on
the display.
For example, consider a reading of 1.345V on a 2 V dc range. The meter displays a maximum
of 1.999 V on this range. The smallest change on the meter display is 0.001 V.
Then the errors are,
percent error: 0.1% * 1.345 V = 1.345 mV
digit error: + 1 digit = 1 * 0.001 V = 1 mV.
Therefore, V = 1.345 V ±2.345 mV or V = 1.345 V ±0.17%.
Now consider the same measurement on the 20 V range. The reading would have been 1.34 V
and,
percent error: 0.1% * 1.34 V = 1.34 mV
digit error: + 1 digit = 1 * 0.01 V = 10 mV.
Therefore, V = 1.34 V ±11.34 mV or V = 1.34 V ± 0.85%.
This shows that the most accurate measurements are made on the lowest meter range that will
accommodate the measured value.
If the meter were to read 16.32 V (rms) while measuring an 8 kHz triangle wave on a 20.00 V
RMS scale; how large is the error? The meter measures True RMS and we can trust a reading
done on a triangular wave. On the AC range the error is 0.5% + 2 digits. Then the errors are,
percent error: 0.5% * 16.32 V = 80.6 mV (rms)
digit error: + 2 digits = 2 * 10 mV = 20 mV (rms)
Therefore V = 16.32 VRMS ± 101 mVRMS or V = 16.32 VRMS ± 0.62%.
Below is a table of the accuracy for various measurements made with the Fluke 8010A model.
Measurement
Accuracy:
± (% of reading + # least significant
digits)
DC
DC current (up to 2A)
AC, 45 Hz to 10 kHz
AC current (up to 2A range, 45 Hz to 2 kHz)
Resistance (up to 200 kS range)
Resistance (2000 kS and 20 MS ranges)
0.1 + 1
0.3 + 1
0.5 + 2
1.0 + 2
0.2 + 1
0.5 + 1
1.2 Meter Loading
Every meter affects the circuit it is connected to by drawing current (voltage meter) or having a
voltage drop (current meter). In later years you will learn more about other ways in which a
meter affects a circuit (capacitance, inductance, adding noise, ...).
Analog Meters
You can calculate the resistance between the terminals of a voltmeter, and determine if it will
affect your circuit significantly. An analog voltmeter’s resistance is usually specified as a
sensitivity in ohms/volt. The resistance for a particular voltage range is determined by
multiplying the sensitivity by the full scale voltage on that range. Some meters may give the
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total resistance while others give the current required for full scale deflection. As long as the
meter draws much less current than the component across which it is connected, you can say
that its effect will be small. A better technique is to calculate the error introduced, by the
current that flows through the meter, and see if it is less than the accuracy to which you want to
make a measurement.
Ammeters are more complex. The standard current shunt (precision resistor in the meter) has a
50 mV drop at the maximum current rating. Since this voltage is usually small, an ammeter
should not affect the circuit too much. However, an ammeter does affect a circuit by adding
inductance. This will be explored more later. Remember that every time you change the range,
the shunt resistance changes. Since the shunt resistance, in a normal meter, can vary from
milliohms to kilo-ohms, using the wrong current range can easily affect your circuit. In
comparison, a voltmeter’s resistance will typically only vary from 100 kS to 10 MS.
Digital Meters
For all ac and dc voltage ranges, the DMM has a fixed input resistance which is typically
10MS,. On the current range, the meter will usually have a 200 mV drop at the maximum
current, but the resistance is different for each range.
Digital meters are usually more accurate, since they remove parallax and other mechanical
errors. However, if you do not know how to select the range properly, it is very easy to obtain
errors as large as any analog meter. This happens quite often on the current ranges.
1.3 Meter Waveform Shape and Frequency Dependence
The more common meters measure the rectified average voltage, while better ones measure the
root mean square (RMS). Unless you know what the shape of the waveform is, and understand
how the meter measures a voltage, the number that you read will be useless. Each of the
different methods gives the same voltage for a sinewave in a certain frequency range. However,
they will all be different if given another waveshape.
Ac meters are calibrated at one sinusoidal frequency to read the RMS voltage or current.
However, most measure the rectified average of the ac component of a signal. The rectifier
circuit acts like an absolute mathematical function. The ac component is what you have left
when you remove the average or dc voltage from a signal. In real life, when you set a meter to
read an ac signal you not only remove the dc signal but you also remove some of the low
frequencies of a waveform (ie. the meter acts like a high pass filter).
Meter bandwidth is the frequency range over which measurements are accurate. It more
generally refers to the frequency range over which a circuit or instrument functions properly.
For example, a Fluke 8010A digital meter should not be used below 45 Hz or above 50 kHz.
The error goes from 0.5% to 1.0% error when the frequency is over 10 kHz, and 5.0% when the
frequency is between 20 kHz and 50 kHz. Oscilloscopes and all other instruments also suffer
from similar effects.
Before you can use a meter, you must consider the Crest Factor of the waveform being
measured. It is the ratio of the peak voltage to the RMS voltage. Mechanical meters are slow
to respond because the needle, as a physical system with mass, takes time to accelerate.
Electronic meters also have similar problems and this is responsible for the use of the Crest
Factor. Some examples are given in the following table.
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Waveform
Crest Factor
Square wave
Sine wave
Triangular wave
White noise
1.0
1.414
1.732
3.0 to 4.0
The Fluke 8010A meters only measure the correct rms value if the Crest Factor is under 3.0.
So if, for a sinewave, you measure the rms voltage and measure the peak voltage on an
oscilloscope (that can handle the waveform without introducing more errors), you can see if the
meter is reading the rms value properly. The Crest Factor is more difficult to calculate for
rectangular waveforms. A good instrumentation book or instrument manual will explain this.
An rms reading meter measures the root of the mean of the square of the signal (proportional to
the power) or:
The purpose of an rms equivalent value of a waveform, is to simplify power calculations by
providing an equivalent dc voltage, that would develop the same average power in a resistive
load. If a voltage waveform is not described, but you know that it is equivalent to 10 V (rms),
then you will have 100W of average power dissipated in a 1S load (ie.PAVERAGE = VRMS *VRMS
/R) . If you did not know the rms voltage, the only way to calculate the power would be to do
an integration, from an approximation of the waveshape as seen on an oscilloscope. This only
works for resistive loads because rms value is a magnitude and does not consider phase
information. A meter that reads an average rectified value for a waveform of period T, indicates
a value
Therefore meter scales are calibrated to read 1.11 * Vaverage, and since 1.11 * 0.637 = 0.707, the
reading is the rms value for a sinewave and a sinewave only.
Notes:
1)
As 0.637 VPK is the average value of fullwave rectified sinusoids only, a rectifying
averaging meter is only accurate for sinusoidal waveforms. The multiplier 1.11, known
as the form factor, is specific to a pure sinusoidal waveform. Averaging ac meters are
therefore, only accurate for sinusoidal waveforms.
2)
The above discussion assumes that the meter uses a fullwave rectifier. A second type,
called a half-wave rectifier, exists and would read a different voltage because it only
responds to the positive parts of a waveform. Because of this, a half-wave rectifier can
give very strange measurements if the waveform is not symmetrical about 0V.
Here is a table of how some meters would respond to common signals of 1 V (peak) or 2 V
(peak-to-peak). The dc average value will usually be 0V for a sinewave since sinewave
generators usually have no dc voltage while square or triangular wave usually start from 0V and
go to some positive or negative voltage (single ended signal generator).
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2.
Waveform
1 VPK
DC average
voltage
AC rectified average
voltage * 1.11 (A)
RMS
volts
(B)
% difference
(A), (B)
Square
Sine
Triangular
±1 or 0
0
±0.5 or 0
1.11
0.707
0.555
1.00
0.707
0.577
+11.0%
+0%
-3.8%
DC Power Supplies
A dc power supply may have a fixed voltage output (usually accurate to ± 5%) or may be
adjustable. Adjustable supplies have a control which allows one to change the dc voltage.
Both types have two output leads where one is indicated as being positive (with respect to the
other lead).
The Goldstar GP-105 power supply also has an adjustable current limit. This feature, shuts off
the output voltage (and produces a beeping alarm until the power supply is turned off) when
the current goes beyond a certain limit. To resume operation, the external circuit should be
checked and/or the power supply’s current limit needs to be raised (turning dial clockwise)
before turning the power supply on again. Because of this, the power supply will act like a
voltage source until the current limit is exceeded. The current limit control should be set before
you perform the lab experiment. The best way to prevent circuit parts from exploding due to
overheating is to limit the current to 100 mA. Most components will not explode, or be
destroyed, with 100 mA the way that they would with 1.5A. Press the “current limit” button so
that the present current limit is displayed on the power supply’s meter. Adjust the current
limiting knob to the maximum current you require.
Power Supply Connections
Most power supplies are “floating”. This means that neither the positive, nor negative outputs
are connected to ground or any common point. This means that you can connect the power
supply in any way, even several hundred volts above ground. A non-floating power supply has
one lead grounded or connected to a common point. This means that there is only one lead
which can be connected anywhere in a circuit since the common or grounded one cannot be
moved. These power supplies may be referred to as single ended. The word single means that
you can only have a positive or negative voltage from the supply. If the supply is double ended,
you can obtain either a positive or negative voltage from it.
A Goldstar GP-105 variable DC power supply is shown in figure 4 and its front panel controls
are described below.
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Õ.
POWER: Push on.
LED power on indicator.
Panel METER ZERO ADJUST.
METER SELECTION SWITCH
V for voltage.
A for current.
CURRENT LIMIT switch: when
pushed in the panel meter indicates
the output current-limiting value
set.
PANEL METER. Use as an
indicator. No precision given for
this meter.
VOLTAGE CONTROL: Adjust
“VOLTAGE” of the output at the +
and - terminals.
CURRENT CONTROL: Adjust
“CURRENT” control to desired
maximum output current allowable.
OUTPUT TERMINALS: Connect
the load across the “+” and “-”
terminals.
The “ ” symbol designates the
common terminal which is
connected to earth via the
power cord.
NOTE:
Figure 4. Power Supply Front Panel
The “+” or the “-” can be connected to the common.
Hence you can have a positive common (or ground) or
you can have a negative common (or ground).
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3.
Signal Generators
A signal generator provides a time-varying signal to test circuits. This can be anything from a
simple sine, square or triangular wave up to a TV station signal with different types of noise
added. This symbol and basic circuit model for a single-ended (notice the grounded output)
generator are shown in figure 5.
Figure 5. Signal Generator
ROUT is the “output” resistance and may sometimes be called RINT or “internal” resistance. Every
electronic circuit has a certain amount of resistance. Signal generators are usually 600S, 75S,
50S or some other value due to varying industry standards. You have to keep the output
resistance in mind. Whenever you draw current from a signal generator, the voltage at the
output terminals will change due to the voltage drop across the internal resistance.
Signal generators, like dc power supplies, can have different properties. They may have one of
the outputs connected to ground or have a circuit common point. This is a single-ended
generator as opposed to a floating one, where neither of the outputs is connected to a common
or ground. The generator may be unipolar, where the voltage is always of one polarity, or it
may be bipolar, where the voltage is both positive and negative at different times.
Generally, sinewave generators are bipolar and squarewave generators are unipolar. Unipolar
generators are further broken down into positive and negative. A positive, unipolar,
squarewave generator produces squarewaves that start at 0V, go up to some positive peak, and
then return to 0V in each cycle.
Signal generators have imperfections. The waveforms are not pure. There can be noise or
distortion in the output. Noise is a random signal and distortion is a change in or distortion of a
'pure' signal. An ideal sinewave generator should produce v(t) = sin(t), while a distorted signal
could be v(t) = sin(t) + 0.1 * sin(3t).
The frequency or amplitude of a generator output voltage will not be stable. The user is
expected to keep this in mind. Each generator has an amplitude and frequency control. The
controls generally work in ranges so you will usually see a range control that limits the
minimum and maximum frequency or voltage and a fine control to adjust within the range.
With time, and as the instrument heats up, the frequency and amplitude of the signal generated
will change.
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Function Generators
A function generator is a signal generator that is capable of producing more than one waveform
shape. The B&K Precision model 3010 function generator is shown in figure 6.
Figure 6. B & K Precision Function Generator
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Power Switch
Frequency Range Selection Buttons
Waveform Function Selection Buttons
Amplitude Dial
DC Offset Dial
Frequency Dial marked from 0.1 to 10
(multiplies by range)
Ô. TTL Level Output Connector
Õ. Common Connector
Ö. Function Generator Output Connector
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