Download ph104exp07_AC_RLC_Circuits_03

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PRINCETON UNIVERSITY
Physics Department
PHYSICS 104 LAB
Week #8
EXPERIMENT VII
AC CIRCUITS, RC “HIGH-PASS” FILTER,
AND RLC RESONANT CIRCUITS
Introduction. Most of electronics is based on the responses of a few circuit elements to time
varying voltages (AC). Resistors, capacitors, inductors, transistors, and diodes are by far the
most common circuit components; understand them, and you have the basis for understanding an
enormous variety of functions performed by electronic circuits. This week we concentrate on
circuits containing R, L, and C. In weeks #11-12 you will learn about voltage rectification by a
diode and amplification by a transistor circuit.
The lab allows you to breadboard several circuits, drive them with a sinusoidal voltage from a
signal generator, and study their behavior with an oscilloscope. What you learn is of general
interest, because any complicated waveform can be decomposed (by Fourier analysis) into a
superposition of sinusoids. Knowing the response of a circuit to sine waves allows you to find
the response to any waveform.
RC "High Pass" Filter: The function of this circuit is to block low frequency components of
the input signal from the output, but to “pass” high frequency signals. As you can see, the circuit
shown in the diagram below is a voltage divider, which differs from the one in Exp. III in that
one of the two elements—the capacitor—has a reactance whose value depends on frequency
1
Xc 
. This makes the division of the voltage between the two elements depend on
2 f C
frequency. In this circuit, the signal generator applies a voltage Vin=|Vin| ei2πft
(real part = |Vin|cos 2ft ) to the input of the circuit. The output, Vout  Vout e i ( 2 f t   ) is
measured across the resistor using an oscilloscope.
.01 F
From Sig. Gen. Vin
500 
To Scope
V out Using the
10x probe
Measure the ratio of the amplitude of the output voltage, to the amplitude of input voltage as you
change the input frequency. i.e. |Vout| / |Vin| as a function of f.
Hints: If you put the generator input on CH1 and trigger the scope from it, you can put the
output of the circuit on CH2 and compare the two signals directly. To avoid "loading"
your circuit with a cable to the scope, use the 10x probe supplied.
The circuit has a characteristic time, the time constant RC, which provides the characteristic
frequency:
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  RC
or
f char 
1
2 char

1
.
2RC
One way to start measurements is to read Vout over a broad range of frequencies, both above and
below the characteristic frequency, such as between 0.1fchar to 10fchar. Three or four
measurements on each side of fchar and one at fchar ought to be enough to tell you where the
interesting frequencies are in terms of the behavior of Vout . For this reason it is a good idea to
plot as you go.
Your plot could be of |Vout| / |Vin| as a function of f, but given the very broad range of f you
would be well advised to plot |Vout| / |Vin| as a function of log f or to use the three cycle semi-log
paper, with f along the log side. You might then want to take several more readings in the
vicinity of the interesting parts of the plot. You are not asked to make error calculations in this
part of the experiment.
There are fancier filter circuits that have a sharper turn on and better phase response as a function
of frequency, but this is the simplest high pass filter. How would you change this circuit to make
a simple "low pass" filter? Draw the proposed low-pass circuit in your lab notebook.
RLC Series Resonant Circuit: In the following circuit R, L, and C are in series, and the output
is measured across R. So, |Vout| / R is the magnitude of the current through each circuit element.
1 mH .01 F
From Signal
Generator.
Vin
500 
Vout
To Scope
using the
10X Probe
Calculate the resonant frequency ( fres = 1/2LC ). Set the output of the signal generator to
1Vpp and make a rough measurement of the resonant frequency fres by tuning the input frequency
through the peak, and compare the peak (resonant) frequency with your calculation. Do your
results agree within the uncertainties of the component values?
The frequency response of the circuit is important. Plot |Vout| / |Vin| as a function of f, going to a
frequency on either side of the resonant frequency at which the value |Vout| / |Vin| is down by a
factor of ten from that you measured at the resonant frequency (fres).
If you are interested, you can measure the resonance curve for R = 250  in addition to the curve
for R= 500 . Figure 31-19 in Tipler illustrates what you might expect to happen.
RLC parallel Resonant Circuit: In the following circuit, where the capacitor and inductor are
in parallel, and the combination is in series with a resistor, measure the voltage across the resistor
as a function of frequency, over the same range as you used with the series resonant RLC circuit
above, and make a plot of |Vout| / |Vin| as a function of frequency. Does the shape of the curve
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look the same as it did in the series circuit? You will use an LC parallel circuit again later in the
semester as part of a larger electronic circuit.
.01 F
From Signal
Generator.
500 
Vin
Vout
1 mH
To Scope
using the
10X Probe
As usual, you should spend some time writing your interpretation of the results in your notebook.
This is not just for your TA's edification. As you have probably noticed, thinking things through,
and stating them in your own words, is the route to understanding at a deeper level. Writing
makes you think.
Coaxial cables. As a sidebar, consider the cables you are using for this experiment. They are
the same ones used last week, in the scope lab. They are called coaxial cables, and they contain
two concentric conductors (hence the name). The center (or inner) conductor carries the signal
and the outer conductor is connected to ground. The concept of ground is very important in
dealing with voltages and currents that vary with time (AC). The drawing below shows a cross
section of a coaxial cable. [Note: To avoid radiating, coaxial cables are used to couple the
generator and the scope to the circuit. The outside conductors of the cables are connected to
ground at the generator and the scope, so one side of the circuit input and one side of the circuit
output are necessarily connected together.]
Outer insulation
Outer conductor
(Braided)
Inner insulation
(between Conductors)
Inner conductor
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OPTIONAL
In what we have done, we have left out an interesting part of the behavior of AC circuits, and that
is the phase difference between Vin and Vout across each of the components. If you have the time
go back and set up the series RLC circuit and measure the phase of the voltage across each
component compared to the phase of the input signal from the generator. The figure below is an
example of two waves (Vin and Vout) on the oscilloscope. In this example Vin leads Vout by 90o.
Vin
period : Vin 4 divisions
Vout 4 divisions
4 divisions = 360 o
1 division = 90 o
Vout
Vin leads Vout by 1 division (90o).
one period of
Vin
Phase difference
one period of Vout
OPTIONAL (Cont.) In the parallel RLC circuit you can also measure Vout as a function of
frequency across the LC combination. Even though this circuit is almost identical to the other
parallel RLC circuit you constructed earlier, there is one difference. The LC combination has
been moved so that one end of it is at ground. You will have to construct the circuit in this way
to be able to measure the output voltage across the LC combination. Measure the voltage across
the LC combination as a function of frequency, over a similar range as before, and make a plot of
|Vout| / |Vin| as a function of frequency. Does the shape of the curve look the same as it did when
you measured Vout across R in the parallel circuit? The following is a schematic of the circuit.
500

From Signal
Generator
Vin
.01 F
1 mH
Vout
To Scope
using the
10x Probe