Chapter 7
AC Analysis

m7.2 Equivalent Circuits

For the circuit in Fig. m7.2:

1. Determine the Thévenin equivalent circuit at terminals (a,b) using the open-circuit/short-circuit method. Show the Thévenin impedance as a resistor in series with a single reactive element (capacitor or inductor) and determine the values of all components in the equivalent circuit. The sinusoidal source V_S= 3 V and f = 500 Hz frequency. Component values are: R₁ = 90 Ω, R₂ = 100 Ω, C = 1.0 μF, and L = 33 mH.
2. Repeat with the source frequency increased to 1100 Hz.
3. Does the circuit seem to “change its personality” with different source frequencies? Explain your answer.

NI Multisim Measurements

1. Enter the circuit of Figure m7.2 with an AC_VOLTAGE source. Set its “AC Analysis Magnitude” to 3 volts and leave the “AC Analysis Phase” at its default zero value. Run a Simulate → Analyses → Single Frequency AC Analysis to measure the open-circuit voltage magnitude and phase. Next, connect a 0.1 Ω resistor across the terminal pair A-B to approximate a short circuit and then measure the magnitude and phase of the short-circuit current through this small resistor. Calculate the Thévenin voltage and Thévenin impedance from these measurements.
2. Repeat to obtain the open-circuit voltage and short-circuit current at 1100 Hz.

Additional helpful tips:

• Name the net connected to Terminal A to make it easier to find in the AC Analysis “Outputs” tab.
• Choose “Magnitude/Phase” for the “Complex number format” option.

NI myDAQ Measurements

1. Construct the circuit of Figure m7.2; do not include resistor R₁ as this device simply models the finite winding resistance of the physical inductor. Build an op amp voltage follower to strengthen the current drive of AO0 and use the voltage follower output as V_S. Create the sinusoidal voltage with the NI ELVISmx Function Generator. Measure the open-circuit voltage magnitude and phase, taking the source voltage V_S as the phase reference. Connect a 10 Ω resistor across the terminal pair A-B to approximate a short circuit. Measure the voltage across this resistor and divide by its measured resistance to obtain the short-circuit current magnitude and phase. Calculate the Thévenin voltage and Thévenin impedance from these measurements.
2. Repeat to obtain the open-circuit voltage and short-circuit current at 1100 Hz.

Additional helpful tips:

• The function generator sets it amplitude in terms of “peak-to-peak” voltage; this is twice the amplitude of the sinusoid. Adjust this voltage to yield a sinusoid with a 3-volt amplitude.
• Use the NI ELVISmx Oscilloscope to display V_S on AI0 and the voltage at Terminal A on AI1.
• The oscilloscope “Display Measurements” panel under the waveform display measures the peak-to-peak voltage of the waveforms. Set the timebase to display at least two cycles to ensure that the measurement is accurate. Display even more cycles to improve the accuracy and stability of the measurement.
• You may also use the cursors to measure the amplitude (peak value).
• Refer to Appendix F to learn how to measure amplitude and phase of a sinusoidal waveform.