Chapter 7
AC Analysis

m7.3 Phase-Shift Circuits

Figure m7.3 shows a phase-shift circuit based on op amps.

1. Write the general expression for the magnitude of V_out with frequency taken as a variable. Hint: View the circuit as the cascade of two standard op-amp circuits.
2. Write the general expression for the phase of V_out with frequency taken as a variable.
3. Set C = 0.1 μF and set all resistors to 1.0 kΩ. Determine the frequency in Hz at which V_out and V_in share the same magnitude. What is the phase shift at this frequency?

NI Multisim Measurements

Enter the circuit of Figure m7.3 with the component values listed in Part 3 of the problem statement. Use the AC voltage source for V_in with unit amplitude and frequency set to the value you calculated in Part 3. Use interactive analysis and the oscilloscope to measure the the magnitude and phase of V_out.

Additional helpful tips:

• Use the AC_VOLTAGE source. Set the “Voltage (Pk)” to 1 and “Frequency (F)” to the value you found in Part 3.
• IMPORTANT: As a practical matter, connect a 100 kΩ resistor in parallel with the capacitor to prevent the output of the first-stage circuit from saturating.
• Connect Simulate → Instruments → Oscilloscope so that you can view V_in and V_out at the same time.
• Use oscilloscope cursors to measure magnitude and phase with the technique described in Appendix F.

NI myDAQ Measurements

Construct the circuit of Figure m7.3 with the component values listed in Part 3 of the problem statement. Use the NI ELVISmx Function Generator to create the sinusoidal voltage source on AO0; set its frequency to the value you calculated in Part 3. Use the NI ELVISmx Oscilloscope to measure the node voltages V_in and V_out.

Additional helpful tips:

• The function generator amplitude control uses “peak-to-peak” units. The amplitude of a sinusoid is one-half of its peak-to-peak value.
• IMPORTANT: As a practical matter, connect a 100 kΩ resistor in parallel with the capacitor to prevent the output of the first-stage circuit from saturating.
• Use oscilloscope cursors to measure magnitude a phase with the technique described in Appendix F.