Physics 104 Lab Handout #7



PRINCETON UNIVERSITY PHYSICS 104 LAB

Physics Department 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 [pic]. This makes the division of the voltage between the two elements depend on 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, [pic] is

measured across the resistor using an oscilloscope.

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:

[pic] or [pic].

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.

Calculate the resonant frequency ( fres = 1/2LC ). 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 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.

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.]

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.

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.

-----------------------

Outer insulation Outer conductor Inner insulation Inner conductor

(Braided) (between Conductors)

500 (

.01 mðF

Vin

V out

From Sig. Gen.

To Scope

Using the

10x probe

1 mH

500 (

Vin

.01 mμF

Vin

V out

From Sig. Gen.

To Scope

Using the

10x probe

1 mH

500 (

Vin

.01 μF

Vout

From Signal

Generator.

To Scope

using the

10X Probe

From Signal

Generator.

To Scope

using the

10X Probe

Vout

500 (

1 mH

Vin

.01 μF

Vin

Vout

one period of Vout

one period of Vin

period : Vin 4 divisions

Vout 4 divisions

4 divisions = 360 o

1 division = 90 o

Vin leads Vout by 1 division (90o).

Phase difference

From Signal

Generator

To Scope using the

10x Probe

Vout

500 (

1 mH

Vin

.01 μF

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