Find the Thevenin equivalent impedances and non-ideal sources for various
circuits.
Pre-lab preparation:
Assume the following components are available to build your experiment:
Resistors: 1.2 k 2.4 k
Capacitors: .15 µF 2.5 µF
Calculate the Thevenin equivalent impedance across the side, face, and
diagonal of the resistive cube shown in Fig. 1 below.
Calculate the Thevenin equivalent impedance of the infinite ladder circuit
shown in Fig. 2. Calculate the impedance if the ladder has only 2, 3, or 4
R-2R stages.
Calculate the equivalent non-ideal voltage source for the 3-stage D/A
converter shown in Fig. 3 when the input is "6".
Simulate the circuit shown in Fig. 4 and plot the output voltage (magnitude
and phase) from 1 Hz to 100 kHz.
Extra Credit (10%) Simulate the circuit shown in Fig. 5 and plot
the output voltage (magnitude and phase) from 1 Hz to 100 kHz. Compute the
Thevenin equivalent non-ideal voltage source for the circuit at 100 Hz.
Experiment:
Complete the following tasks:
Construct the circuit shown in Fig. 1 and measure the impedance across EACH
side, face, and diagonal of the resistive cube (Hint: there should be 28
measurements total).
Take out each individual resistor from the cube and measure its
resistance value separately.
Construct the circuit shown in Fig. 2 with two R-2R stages and measure the
input impedance. Repeat the measurement for circuits with 1 - 7 stages and
measure the input impedance of each. Let R = 1 k Ohm.
Measure the value of each resistor in the ladder separately and record its
location in the 9-stage ladder network.
Construct the circuit shown in Fig. 3 for the 3-stage D/A converter. Let
R = 1 k Ohm. Measure the open circuit voltage and the short circuit current
when the input is "4" and the voltage source is 5 volts. Repeat the voltage and
current measurements for inputs of "1" and "2". Measure the input impedance.
Construct the circuit shown in Fig. 4 and measure the output voltage
(magnitude and phase) from 1 Hz to 100 kHz. Normalize the result to the input
signal. Use the "waveform math" menu to display the input (channel 1) vs the
output (channel 4). Print the result.
Extra Credit (10%) Construct the circuit shown in Fig. 5 and find
the frequency where the output voltage is a maximum. Find the equivalent
non-ideal voltage source at this frequency. Measure the output voltage
magnitude at frequencies up to 100 times higher and lower than the optimal
frequency.
Post-lab analysis:
Generate a lab report following the sample report available on the Web page.
Mention any difficulties encountered during the lab. Describe any results that
were unexpected and try to account for the origin of these results (i.e.
explain what happened).
IN ADDITION, respond to the following questions/instructions:
What is the average value and standard deviation of the resistances in the
cube (a) according to the cube measurements and (b) according to the direct
measurements of the resistances?
Plot the value of the input impedance of the R-2R ladder as a function of
the number of stages. Estimate the asymptotic value of the ladder as the number
of stages gets very large. Compare the results with the calculations (plot on
the same curve) and compute the average value and standard deviation of the
ladder resistors.
Use the measurements to compute the Thevenin equivalent non-ideal voltage
source for all three input cases.
Use the measurements to compute the Thevenin equivalent source if the
input were "6" (show your work). Compare this to the value that you calculated.
Plot the results of the measurements with the circuit in Fig. 4 and compare
the results to the simulations. Explain any discrepancies that you find.
Interpret the plot containing the "waveform math".
If you did the extra credit, compare the simulations with the experimental
results for the circuit in Fig. 5.