The circuit of Figure 7.5 operates at 1 kHz. Determine the node voltages VAand VB.
Use these component values:
• R1 = 4.7kΩ, R2 = 3.3kΩ and R3 = 2.2kΩ
• C1 = 0.047 µF and C2 = 0.1 µF
• V1= 96 0◦V and V2= 36 − 90◦V
Figure 7.5: Circuit for Problem 7.4
NI Multisim Measurements
Enter the circuit of Figure 7.5 and run an AC analysis to measure the voltage magnitude and phase of VAand VB.
More specifically:
• Use the AC VOLTAGE source. Set the “AC Analysis Magnitude” and
“AC Analysis Phase” values according to the specified voltage source values.
• Set up an Simulate → Analyses → AC Analysis to sweep the fre-quency over a range that includes 1 kHz; use a “Linear” sweep type with “Vertical Scale” set to “Linear.”
7.4. PHASOR-DOMAIN ANALYSIS TECHNIQUES (7-9) 103
• Use the “Grapher View” cursors to measure the voltage magnitude and phase at 1 kHz.
NI Multisim video tutorials:
• Measure frequency response with AC Analysis:
http://youtu.be/tgCPDBtRcso
• Find the maximum value of trace in Grapher View:
http://youtu.be/MzYK60mfh2Y
NI myDAQ Measurements
Construct the circuit of Figure 7.5 on the preceding page. Use the NI ELVISmx Arbitrary Waveform Generator to create the sinusoidal voltage sources; use AO0to create V1and AO1 to create V2. Use the NI ELVISmx Oscilloscope to measure the node voltages VAand VB. Take V1as the reference voltage when measuring phase.
Additional helpful tips:
• Set the Arbitrary Waveform Generator sampling rate to its maximum value of 200 kHz.
• Create a single period of a unit-amplitude 1 kHz sinusoid for each output channel. Adjust the phase of the AO1 channel to match the phase of V2.
• Set the “Gain” controls of the Arbitrary Waveform Generator to match the magnitudes of the specified voltage sources.
• Refer to Appendix F to learn how to use the oscilloscope to measure magnitude and phase.
NI myDAQ video tutorials:
• Arbitrary Waveform Generator (ARB):
http://decibel.ni.com/content/docs/DOC-12941
• Oscilloscope:
http://decibel.ni.com/content/docs/DOC-12942
Chapter 8
AC Power
8.1 Periodic Waveforms (8-1)
Merriam-Webster defines a rectifier as a “device for converting alternating current into direct current.” A half-wave rectifier does so by setting the ative portion of the waveform to zero. A full-wave rectifier negates the neg-ative portion of the waveform, effectively reflecting it to its positive equiv-alent.
1. Plot the half-wave rectifier output and full-wave rectifier output for each of the three standard waveforms shown in Figure 8.1 on page 109.
2. Determine the general expressions for the (a) average value and (b) rms value for each of the six rectified waveforms.
3. Evaluate your expressions for average and rms values for Vm= 10volts and T = 10 ms.
NI Multisim Measurements
1. Create the half-wave rectified and full-wave rectified versions of the three standard waveforms of Figure 8.1 on page 109 using the follow-ing approach:
• Create the unrectified original waveform with the Function Gen-erator,
• Connect a wire to the + terminal of the function generator and double-click to terminate the wire in “empty space” without con-necting to any other terminal. Display the net names to deter-mine the number of this net. Connect the Common terminal to ground.
• Place the ABM VOLTAGE source, ground its negative terminal, and enter the function positive(v(n)) (where n is the net number of the wire connected to the function generator output) to make the ABM source create the half-wave rectified version of the function generator waveform,
• Place another ABM source (also with its negative terminal grounded) with the absolute value function abs(v(n)) to create the full-wave rectified full-waveform, and
• Place an SPDT switch (single-pole double-throw) to conveniently connect one ABM source or the other to the oscilloscope to dis-play the rectified waveform.
2. Place a Measurement Probe to display the average value and rms value of the rectified waveform. Determine the average and rms val-ues of each of the rectified waveforms.
Additional tips:
• The “Analog Behavior Modeling” (ABM) voltage source “senses” the voltage of net n with the function v(n). The connection between the function generator and the ABM source does not appear visually.
• The Multisim User Manual describes a wide variety of functions that can be used by the ABM source. Visit ni.com/manuals and enter
“Multisim User Manual” into the search box. See the “Mathematical Expressions” section of Chapter 7.
• Set up theSimulate → Instruments → Measurement Probeto display V(dc)for average value and V(rms) for rms value.
8.1. PERIODIC WAVEFORMS (8-1) 107
NI Multisim video tutorials:
• Display and change net names:
http://youtu.be/0iZ-ph9pJjE
• Measure RMS and average value with a measurement probe:
http://youtu.be/OnK-Unld17E
• Set the digits of precision of a measurement probe:
http://youtu.be/GRO60XLgzHg
• ABM (Analog Behavioral Model) voltage source:
http://youtu.be/8pPynWRwhO4
NI myDAQ Measurements
1. Create the half-wave rectified and full-wave rectified versions of the three standard waveforms of Figure 8.1 on page 109 with the arbitrary waveform generator on AO0; use 200 kS/s for the sampling rate. Dis-play this signal on the oscilloscope using AI0. Extract the average value of the waveform using the RC circuit shown in Figure 8.2 on page 110 and display the output of this circuit on AI1.
2. Read the average value of the rectified waveform using either the cur-sor value or the “RMS” indicator below the waveform display for AI1.
Read the “RMS” indicator for AI0 to measure the rms value of the rectified waveform. Display at least two periods of the waveform to ensure accuracy of the “RMS” indicator.
Additional helpful tips:
• Set both channels of the oscilloscope to the same volts per division.
In this way the RC circuit output (average value) overlays the recti-fied waveform and you can visually see how the average value tends toward the effective center of the waveform.
• IMPORTANT: Be sure to observe proper polarity for the electrolytic capacitor. The capacitor may mark the negative lead rather than the positive lead.
NI myDAQ video tutorials:
• Arbitrary Waveform Generator (ARB):
http://decibel.ni.com/content/docs/DOC-12941
• Oscilloscope:
http://decibel.ni.com/content/docs/DOC-12942
8.1. PERIODIC WAVEFORMS (8-1) 109
Figure 8.1: Waveforms for Problem 8.1
Figure 8.2: RC circuit to extract average value of a waveform.