PH337 Electronics
Experiment #2

OSCILLOSCOPE LAB

OBJECTIVES

  1. Learn how to use an oscilloscope--the proper use and treatment of a lab rat's best friend.
  2. Measure the "gain" of a low-pass RC filter
    1. study amplitude characteristics
    2. study phase behavior

DISCUSSION

In general the gain of any circuit is defined to be the ratio of the "output/input". We will show, for a particular RC circuit known as a low-pass filter, that the magnitude of the output divided by the input is:

|V1|/|V2| = [1 + (wRC)^2]^-1/2
Note the following about the voltage gain as a function of frequency: This last frequency, w_B = 1/RC, is given the name, "the break frequency" of the filter circuit. It is an interesting point on the voltage gain vs. frequency curve because the "power" available to the impedance is reduced by 1/2.
(Aside comment) Because of the range of the changes in electronic circuits, log scales and units are often used; specifically, "decibels" defined as:
power gain_dB = 10 log_10 [P2 / P1]
Therefore the voltage gain is expressed as:
voltage gain_dB = 10 log_10 [V2 / V1]^2 = 20 log _10 [V2 / V1]

The experiment asks you to measure the input and output voltage with an oscilloscope at several frequencies and then plot the logarithmic gain. You also measure the phase.

PROCEDURE

  1. Before making any connections and measurements, use the nominal values of the available resistor and capacitor to calculate the theoretical "break frequency". Verify that you are predicting a filter circuit that "breaks" between 600 Hz and 6 kHz.
    w_B = 2 pi f_B = 1/RC
  2. Connect the RC filter circuit to the function generator and oscilloscope as shown:
  3. With a sine wave input from the function generator, measure the input and the output voltages as a function of frequency. Take data both above and below and at the predicted break frequency. Use the dual channels of the oscilloscope for these measurements. Then calculate the voltage gain, V2/V1.
    _______f________V2_out_______V1_in____________Gain=V2/V1________________
  4. Graph your experimental values on a log scale. Both gain and frequency should be plotted as logarithms. Also plot your theoretically predicted values. Compare your experimental vs. theoretical results.
  5. Next, use the scope to look at the relative phase of the input and output voltages. Measure the phase shift at the break frequency. What is the phase shift as 100 Hz? What is it at 100 kHz?
  6. Use your DMM (digital multi-meter) as an AC voltmeter to measure the voltage drops across the resistor alone, the voltage across the capacitor, and the input. The max frequency you should do this at is 1 kHz because the DMM's frequency response is limited! Does the arithmetic sum of the resistor and the capacitor voltages equal the input voltage? Draw a "phasor" diagram to explain why.
  7. From this same phasor diagram, find the phase angle between the input and the output. Verify the phase with the scope.

    8. FINAL QUALITATIVE OBSERVATIONS

  8. Reconnect the circuit as shown:

    and observe the input and output voltage on the dual trace scope. Note the frequency at which the output/input = 0.707. Make a rough sketch of the gain vs. frequency of this circuit. This circuit is called a "high-pass" filter.

References