Equipment:
List all the equipment used in this experiment.

Components:
List all the components used in this experiment.

Objectives:

• Use Tektronix Model 2213 to measure Phase Difference
• Use Tektronix Model 2213 to measure AC Voltage
• Create and explain a simple ac impedance model
• Speculate the possible source of errors
• Find the thevenin equivalent of an AC circuit

Tektronix 2213 oscilloscope can also be used to measure phase  indirectly.  From the class notes you should be able to transfrom any circuit from time domain to its phasor domain.  Read the textbook on page 382 (section 8.2) for more information.

(PreLab) A. Design

1. Design a series circuit that has a voltage source (Vs), one capacitor (C1= 820 pF Capacitor) and one resistor(Rp) connected in series.
2. Draw this test circuit and annotate it as Figure #1
3. Derive a general equation that will yield the magnitude and phase of a voltage across Rp.  Assume voltage source,

Vs = A /_0.  Vs is assumed to have a zero phase, f=0 because it is the reference voltage.  A is the amplitude of Vs.
4. Label this equation - "Equation 1 - Equation for finding Magnitude and Phase of V_Rp"
5. Substitute Rp = 3.3K , 6.8 K, 15 K, 22K, 33K, 47K, 68K, 110K, 220K and 470K Ohms and find the corresponding  Magnitude and Phase of each Rp value given.  Use C1 = 820 pF, Amplitude =16V and f = 10KHz.
6. Put all the data in Data Table 1A - "Magnitude/Phase Calculation"

B. Measurement of Phase Difference on Oscilloscope

1. Read Keithley 2213 manuals throughly on phase measurement section (page 20).  The manual can be obtained HERE.

[Hint] You will not be able to measure phase difference directly from the oscilloscope.
2. Set up HP 8116A to the folowing specifications.

POWER          1(ON)
MODE             NORM
WAVEFORM  depress a button that has sine wave above it.
FREQ               use the range and vernier switch to select 10 kHz
DTY                 50%
AMP                16.0 V
OFS                  0V
 
3. Connect the function generator output to channel 1 of the scope and connect the other side of the BNC T to a second BNC coaxial cable.  The other end of BNC coaxial cable is connected to alligator adapter.
4. The alligator adapter is connected to Vs of Figure #1.
5. Voltage across Rp of Figure #1  is connected to Channel #2 of the oscilloscope.  Use BNC cable and alligator adapter to do this.
6. Set front panel of the oscilloscope for dual trace operation.  You will be able to see input signal from function generator on CH1 and the output voltage across Rp of Figure #1 on CH2 on the same screen.
7. Put Rp = 3.3 KOhm on the circuit of Figure #1.
8. Measure the Phase difference between signals of CH1 and CH2.
9. Put the Phase difference values in Data Table 1B - "Phase Difference Measurement"

Repeat step 7-9 for  Rp = 6.8 K, 15 K, 22K, 33K, 47K, 68K, 110K, 220K and 470K Ohms.

2. - AC Thevenin Analysis

In this section the concept of AC thevenin circuit is explored.  The concept of AC Thevenin is similar to DC Thevenin except that the circuit is in phasor domain.  A circuit that contains R, L and C components are given below.  You are asked to analyze the circuit to find Vth, Zth and Isc.

                                                        Figure 2
 

1. The nominal (ideal) values of R, C, L and Vs is given below.  Record these nominal value in Data Table 2.

R1 = R2 = R3 = 270 Ohm
C1 = 0.01 uF
C2 = 0.001 uF
L1 = 1000 uH
L2 = 10000 uH
Vs = 2 Vpp @ 50.39 kHz + 5 %
2. Use Philips PM6304 Programmable Automatic RCL Meter to obtain measured values of R1, R2, R3, C1,C2, L1 and L2.  You have to go to the TA room (Room 304) to get the measurement pad and manual for PM6304.  Record the measured values in Data Table 2.
3. (PreLab) Derive a general equation to find Thevenin Voltage (Vth), Thevenin Impedance (Zth) and Short Circuit Current (Isc) with respect to terminal A and B.  Assume R3 is connected between terminal A and B.
4. Analyze the circuit to find Vth,Isc and Zth.  Use the measured values of R, C and L in the circuit.  Put the results in Data Table 2.
5. Draw the thevenin equivalent circuit for Figure 2.  Label it as Figure 2B - "Thevenin Equivalent of Figure 2"

1. Build the circuit of Figure 2.
2. Measure the thevenin voltage (Voltage across terminal A and B).
3. Measure the Zth (thevenin impedance).
4. Measure Isc (short circuit current).
5. Put the measured results in Data Table 2.
6. Compare the measured data to the results in section 2.

1. Why measured values have to be used for R,L and C in the Thevenin analysis of Figure 2?
2. Determine the accuracy of your measurement data compare to your calculation data.  What are the percentage of errors?