Safety Precautions

• Refer to the departmental  and university  safety regulations.  Report to the lab demonstrators immediately in case of any irregularities.

• In the rare event of electric shock, one should be removed from the source and the current should be shut down immediately.

• Before touching any circuit elements, ensure that it is not connected to high voltages. We only need to deal with voltages below 20 V in this course.

• When using the DC power supply, dial the voltages to zero before switching it and before connecting the circuit. Double check your circuit before dialing up the voltage from zero.

• Electrolytic capacitors CANNOT be connected to a reverse voltage.

Acknowledgment – This version is largely based on the lab reports before this semester.

I. OBJECTIVES

1. To measure time-varying voltages using an analog oscilloscope.

2. To study the amplitude response of an RC circuit as a function of frequency.

3. To study the phase response of an RC circuit as a function of frequency.

II. EQUIPMENT

1. Signal generator SG (Model: )

2. Real-time Analog Oscilloscope OSC (Model: )

3. Digital Multimeter (Model: ________________________________)

4. BNC cable

5. Solderless breadboard

6. Components: Resistor R=1 kΩ; Capacitor C= 0.l  μF.

Check: Using the multimeter to verify the values of R=             and C =             .

The correct mode is needed for measuring C.

III. BACKGROUND

An AC voltage is a sinusoid with a period T. For RC circuit, the characteristic time is RC according to Chapter 8. When the AC voltage drives the RC circuit, the behavior depends on the comparison of T and RC.

•   If T >> RC, then the capacitor behaves as an open-circuit.

•   If T << RC, then the capacitor behaves as an short-circuit.

The resultant circuit can be applied as a low-pass filter, where only signals at low frequencies can pass through. Here, RC = sec so we expect interesting transition to appear when the frequency crosses (2πRC)-1 = Hz.

IV. PROCEDURES (Items with # can be done after the lab)

First write down the names/SID of your group members, the venue, and the seat number.

(A) Sinusoidal Signal Measurements

0. Look at OSC carefully. It has 10 horizontal divisions and 8 vertical divisions, right?

1. To begin with, prepare OSC for measuring the signals as follows:

(a) Power/CRT Panels: Turn on the cathode ray (i.e. electron beam). Adjust beam intensity and focus knobs.

(b) Vertical Panel: Choose VERT MODE = CH1 for seeing only CH1.

(c) CH1 Subpanel: VOLT/DIV = 0.5 V/div. Select “DC” to avoid internal filtering. (d) Horizontal panel: MAIN TIME/DIV to 1 ms/div. Ignore the delay options.

(e) Trigger Panel (top):

• Source = CH1; Coupling = AUTO

• Hold Off = minimized (i.e. pushed in and fully counter-clockwise)

• MAIN kept at MAIN mode (i.e. not the MIX, DELAY, or XY modes)

• Position ~ 12-o’clock (i.e. default position for horizontally centering)

All of the three small red-knobs for VAR are for the purposes of fine measurements only. Push them in to avoid unwanted magnification. Turn them clockwise fully for locking to calibrated measurements.

Follow the steps above carefully. Then, take a picture of OSC for record. 1

2. Connect the SG directly to CH1 of OSC. Use the multimeter to verify that the casing of SG and OSC are both shorted.

3. Before enabling the output of SG,

(a) sine wave,

(b) frequency f = 0.2 kHz, and

(c) peak-to-peak amplitude V1pp ~2.5 V by:

•   tuning to the nine-o’clock position (Topward SG) or

•   setting amplitude of ~2.5 V (Rigol SG)

The rest of SG should be left at the default of: No attenuation (i.e. 0 dB without pushing) and zero-offset (Topward SG) or Offset =0 and Phase = 0 (Rigol SG)

Take a picture of SG for record.

#4. The expected signal V1(t) is shown below. Write down its mathematical formula.

Fig. 1. Signal from SG V1(t) expected mathematically.

Fig. 2. Signal from SG V1(t) as expected experimentally.

5. Enable the output of SG, do the following to yield the expected experimental signal (as illustrated in Fig. 2):

(a) Tune CH1 position so that the sine function is vertically centered

(b) Check the zero by momentarily switching from DC to GND (and back to DC).

(c) Tune trigger level (top) so that the trace starting from zero with a positive slope. Note here that triggering is very important in providing OSC with a reference starting time for each repetition.

Carefully obtain the exact trace in Fig. 2. Then, take a clear picture for record.

6. Experimentally, record:

Total number of horizontal divisions for one full cycle X = 5 div.

Total number of vertical divisions from the minimum to maximum Y= div.

#7. Calculate using the above:

The measured V1pp = Y × 0.5 V/div. = Volts

The measured period T =X × 1 ms/div. = seconds

These values in bold have been adopted in step A1(c) and A1(d).

#8. Does the answer obey T = 1/f? What is the relative error? Provide an explanation if there are errors.

(B) Input-Output Measurements

In the following circuit, SG provides V1(t) as the input and the voltage V2(t) across the capacitor is regarded as the output.

Fig. 3. The input V1(t)  from  SG  and  output V2(t) across the capacitor.

Fig. 4. Expected input V1(t) and V2(t). Period of T and time shift of ∆t.

Both V1  and V2 are expected to have the same period T. However, the output V2  is expected to have a smaller amplitude and a time shift of ∆t.

1. Build the above RC circuit, including the connection to SG and OSC via two BNC cables. Check that the shielding of the BNC cables (i.e. usually linked to the black alligator clip) are correctly connected to the node at the bottom in Fig. 3.

2. On OSC, switch to showing CH2 as follows:

(a) Vertical Panel: Choose VERT MODE = CH2 for seeing only CH2.

(b) CH2 Subpanel: VOLT/DIV =0.5 V/div. Select “DC” that stands for no internal filtering.

(c) Tune CH2 position so that the sine function is vertically centered.

(d) Check the zero by momentarily switching from DC to GND (and back to DC).   Other Panels: No change. The trigger should NOT be changed. It should continue to be based on CH1.

The trace should look like Fig. 5(a). Take a clear picture for record.

Fig. 5. (a) CH2 only and (b) CH1 & CH2 that are very close to each other.

3. On OSC, switch to showing both CH1 and CH2 by setting VERT MODE = DUAL.

The traces are very close to each other (Fig. 5(b)). Take a picture for record.

4. Keep VOLT/DIV for both CH1 and CH2 as 0.5 V/div. Fill out Table I. Only the boxes in gray have to be completed during the lab session.

Table I Basic Data points at 200 Hz, 2 kHz, 20 kHz, and 200 kHz

Take pictures for the time trace for each case.   Examples are shown below Fig.6.

Fig. 6. CH1 & CH2 at different frequencies.

5. As an option, more data points can be taken for Tables II and III.

Table II Additional data points at 400 Hz, 4 kHz, 40 kHz, and 400 kHz

Table III Additional data points at 700 Hz, 7 kHz, 70 kHz, and 700 kHz

#6. From the experimental data,

(a) plot the V2pp/V1pp versus f

(b) plot the ϕ versus f

Mark on both plots fc = 1/(2πRC) as the characteristic frequency determined by the RC time.

V. DISCUSSIONS

1.   As bonus, set SG to 500 Hz with a square wave. Then determine the RC time constant from OSC. Example of the time trace is shown in Fig. 7 .

Fig. 7. CH2 obtained from a square-wave input at 500 Hz.

2. Comment on the physical reason for the low-frequency and high-frequency behaviors of CH2. Then, suggest one application of the RC circuit.

VI. REFERENCES

•    "Modern Instrumentation and  Measurement Techniques" by Helfrick, A.D. and Cooper, W.D.: Chapter 7, Sections 1, 2, 4, and 10.1.

•   "Electronic Instrumentation and Measurements" by Bell, D. A. Chapter 11, Sections 1-4 and 6.

VII. Instructions for Preparing the Formal Report:

The  following  serves  as  a  rough  guideline  for  formal  report.  More  professional guidelines would be necessary in the future.

1.   Format: At least 9 pages, single-spaced, 12-points Times New Romans (PDF).

2.   DO NOT JUST HAND IN THIS DOCUMENT!!! No part of the formal report can contain sentences in this document.

3.   The procedural steps should be expressed in passive voice and in past tense. (e.g. The time scale of the oscilloscope was set to 1 ms/div.)

4.   Figures: Must include labeled axes, units, legends, and caption.

5.   Tables: Must include units, legends, and caption

6.   Content:

•   Title of the report

•   Name of all group members

•   Date, time, and venue

•   Objective,   Background,    Procedure   and    Results,   Discussions.   They correspond to Sections I-V of this document.

•   Add a conclusion (and a reference list if necessary)

7.   Checking: The items marked by (*) have to be included.