Lab 3 – AC Circuit Tools

Contents

Exercise 3.1: Measurement of the Circuit Component Values ........................................... 2

Exercise 3.2: Measurement of Component and Circuit Impedance Z ................................ 2

Exercise 3.3: Testing an RC Circuit with the Function Generator and Oscilloscope ......... 4

Exercise 3.4: The Gain/Phase Bode Plot of the RC Circuit ................................................ 8

Multisim Challenge: Determine the Bode Plot of an RC circuit. ..................................... 11

Figure 3.0Scope SFP showing two channel capability

Many electronic circuits contain alternating current (AC). Designing good circuits requires tools

to measure components, impedance values, and tools to display circuit properties. With good AC

tools and minimal circuit knowledge, you can modify any circuit to achieve optimal response.

Goal: This lab introduces the NI ELVIS II tools for AC circuits: a digital multimeter, function

generator, oscilloscope, impedance analyzer, and Bode analyzer.

Required Soft Front Panels (SFPs)

Digital Multimeter using Ohmmeter/Capacitance (DMM[Ω/C])

Function Generator (FGEN)

Oscilloscope (Scope)

Impedance Analyzer (Imped)

Bode Analyzer (Bode)

Required Components

1 kΩ resistor R (brown, black, red)

1 µF capacitor C

Exercise 3.1: Measurement of the Circuit Component Values

Complete the following steps to obtain the values of the circuit components:

1. Launch the NI ELVIS II Instrument Strip.

2. Select Digital Multimeter.

3. Connect test leads to the DMM (VΩ. ) and (COM).

4. Use DMM[Ω] to measure the resistor, R.

5. Use DMM[C] to measure the capacitor, C.

6. Fill in the following chart:

Resistor R _________________ kΩ (1 kΩ nominal)

Capacitor C _________________ µF (1 µF nominal)

7. Close the DMM.

End of Exercise 3.1

Exercise 3.2: Measurement of Component and Circuit Impedance Z

For a resistor, the impedance is the same as the DC resistance. You can represent it on a 2D plot

as a line along the x-axis, which is often called the real component. For a capacitor, the

impedance (or more specifically, the reactance), XC is imaginary, depends on frequency, and is

represented as a line along the y-axis of a 2D plot. It is called the imaginary component.

Mathematically, the reactance of a capacitor is represented by:

XC = 1/jωC

where ω is the angular frequency (measured in radians/sec) and j is a symbol used to represent

an imaginary number. The impedance of an RC circuit in series is the sum of these two

components where R is the resistive (real) component and XC is the reactive (imaginary)

component.

Z = R + XC = R + 1/jωC Ω

Impedance can also be represented as a phasor vector on a polar plot with:

Magnitude = √ (R2 + XC

2)

and

Phase θ = tan-1

(XC / R)

A resistor has a phasor along the real (x) axis. A capacitor has a phasor along the negative

imaginary (y) axis. Recall from complex algebra that

1/j = -j.

Complete the following steps to visualize this phasor in real time:

1. Select Impedance Analyzer (Imped) from the NI ELVIS II Instrument Launcher

strip.

Figure 3.1. Phasor Vector for an RC circuit at 1000 Hz

2. Place your components on the NI ELVIS II protoboard.

3. Connect jumpers from Impedance Analyzer DUT+ and DUT- to the nominal 1 kΩ

resistor.

4. Turn on power to the NI ELVIS II protoboard and click on Run.

5. Verify that the resistor phasor is along the real axis and its Phase is zero.

6. Connect the Impedance jumpers to the capacitor.

7. Verify that the capacitor phasor is along the negative imaginary axis and its Phase is

270 or -90 degrees.

8. The default measurement frequency is 1000 Hz. Adjust the frequency value and

observe that the reactance (length of the phasor) gets smaller when you increase the

frequency and larger when you decrease the frequency. Recall |Xc| = 1/ωC.

9. Connect the Impedance jumpers across the capacitor and resistor in series. The phasor

has now both a real and imaginary component.

10. Change the measurement frequency from 100, to 500, to 1000, to 1500 Hz and watch

the phasor move.

11. Adjust the frequency until the magnitude of the reactance |Xc| equals the magnitude

of the resistor, R. At this special frequency, the phasor phase reads 315 or -45

degrees.

12. What is the magnitude of the phasor ____________?

Answer: about |R| 1.41

13. Close the Impedance Analyzer window.

End of Exercise 3.2

Exercise 3.3: Testing an RC Circuit with the Function Generator and Oscilloscope

Complete the following steps to build and test the RC circuit.

1. On the workstation protoboard, build a voltage divider circuit, using a 1 µF capacitor

and a 1.0 kΩ resistor.

2. Connect the RC circuit inputs to function generator [FGEN] and [Ground] pin sockets

on the protoboard. It is important that the function generator is connected to the

capacitor and the resistor is connected to the ground, and not the other way around.

This will be explained later.

Figure 3.2. Real RC componets connected to the FGEN

The power supply for an AC circuit is often a function generator. Use it to test your RC circuit.

3. From the NI ELVIS II Instrument Launcher strip, select FGEN icon.

Figure 3.3. FGEN front panel

The FGEN SFP has controls, which can do the following:

- select the waveform type (sine, triangle, or square)

- set the frequency by rotating the Frequency dial or entering the frequency into a text

box [Hz]

- select the waveform amplitude and any offset using the Amplitude and DC Offset

controls

Function Generator real controls (Frequency) and (Amplitude) are also available on the right side

of the NI ELVIS II workstation. As with the variable power supply, you can enable manual

control by clicking on the Manual Mode box [ ]. A green LED on the right side of the

workstation comes on to indicate manual control. The Frequency and Amplitude knobs are now

active and the virtual controls are grayed out on the NI-ELVISmx Function Generator window.

Note: The Function Generator also provides some special operations such as signal modulation

(AM or FM) or frequency sweeping.

4. Set the Function Generator to Sine wave, 2000 Hz, 2 Vpk-pk. Click on Run.

You can use the Scope SFP to visualize and analyze the voltage signals of the RC circuit.

5. From the NI ELVIS II Instrument Launcher strip, select the Scope icon.

Figure 3.4. Sine wave displayed on the Scope front panel

The scope instrument SFP is similar to most oscilloscopes, but the NI ELVIS II oscilloscope can

automatically connect inputs to a variety of sources, features built-in AC measurements and

waveform cursors, and can easily log a waveform pattern.

6. Connect wires from the BNC 1 pin-outs on the left side of the protoboard across the 1

kΩ resistor in your RC circuit. Connect the CH0 BNC port on the left side of the NI

ELVIS II workstation to the BNC 1 port on the left side of the protoboard. Apply

power to the protoboard and click on the oscilloscope [Run] button.

7. You see a sine wave on the oscilloscope. Set the controls as follows:

- Scale CH0 500 mV/div

- Coupling CH0 AC

- Time base 500 µs/div

- Trigger (Edge), Source (Chan 0 Source), Level (V) (0.1)

Check out the Channel 0 measurements RMS: Freq: and Vpk-pk: at the bottom of the waveform

screen. You can activate cursors to measure time-related parameters such as period, duty cycle,

and time intervals.

8. Play with the FGEN controls (virtual or real) and observe the changes on the

oscilloscope window.

9. Connect another set of wires from BNC2 to the Function Generator SYNC pin socket

and GROUND on the protoboard. Don’t forget to connect the BNC2 port to Scope

CH1 with a BNC cable. SYNC is a TTL 5 V signal often used for triggering.

10. Click the Scope CH1 enable box [ ]. You see a new signal (blue in color) and at TTL

levels. For reference, see the oscilloscope picture at the start of this lab, Figure 3.4.

11. The RC circuit is a passive highpass filter with a low-frequency cutoff point near 160

Hz. You can visualize the filter parameters using the FGEN Sweep Frequency

feature. Set the oscilloscope at the above settings. Set the FGEN controls to the

following:

- Start Frequency 5 Hz

- Stop Frequency 5 kHz

- Step 50 Hz

Click on the Function Generator [Stop] button and then click on the [Sweep] button

Note: If the order of the capacitor and resistor is switched, then the circuit will be a

low pass filter. This is why it was important to connect the function generator to the

capacitor and not the resistor..

12. Observe how the filtered signal CH 0 changes with respect to the SYNC CH 1 signal

in both amplitude and phase as the frequency is swept.

At low frequencies, the signal CH 0 is smaller in amplitude and not in phase with the

SYNC signal. At higher frequencies, the amplitude is close to the function generator

amplitude and the two signals are in phase.

13. Close the Function Generator and Oscilloscope windows.

End of Exercise 3.3

Exercise 3.4: The Gain/Phase Bode Plot of the RC Circuit

A Bode plot defines in a very real graphical format the frequency characteristics of an AC

circuit. Amplitude response is plotted as the circuit gain measured in decibels as a function of log

frequency. Phase response is plotted as the phase difference between the input and output signals

on a linear scale as a function of log frequency.

Complete the following steps to build an RC circuit and measure the gain and phase Bode plots

of the circuit. Be sure to connect the function generator to the capacitor and not the resistor as

this will change the functionality of the circuit.

1. From the NI ELVIS II Instrument Launcher strip, select Bode icon.

With the Bode Analyzer, you can scan over a range of frequencies – from a start frequency to a

stop frequency in steps of ∆f. You can also set the amplitude of the test sine wave. The Bode

Analyzer uses the function generator SFP to generate the test waveform. You must connect

FGEN output sockets to your test circuit and to AI 1+ and Ground AI 1-. The output of the

circuit under test goes to AI 0+ and Ground. You can find more information by clicking the

HELP button on the lower right corner of the Bode Analyzer window.

2. Rebuild the RC circuit on the NI ELVIS protoboard, similar to the following circuit and

make the connections as described above.

Figure 3.5. RC componenst connections for Bode Measurements

3. Verify that your circuit is connected as above. Turn on the protoboard power and click on

the [Run] button.

Figure 3.6. Bode Analyzer front panel measurements of an RC circuit

4. Click on the [ ] Cursors On box. You can step through your measured data points and

view the magnitude and phase at each frequency measured.

5. Note the frequency where the signal amplitude has fallen to -3 dB. The phase at this point

should read approximately 45 degrees. This frequency is called the lowpass cutoff point.

6. Both the oscilloscope and the Bode analyzer SFPs have a Log button. When activated,

the data presented on the graphs is written to a text file on your hard drive. You can now

read this data for further analysis with Excel, LabVIEW, NI DIAdem, or some other

analysis or plotting program.

7. Click on the [Log] button and save your data set.

View an example data set like the one below when you click the Log button after a frequency

scan.

End of Exercise 3.4

Multisim Challenge: Determine the Bode Plot of an RC circuit.

Verify that the Bode plot as predicted with NI Multisim is a good representation of the real Bode

plot found in Exercise 3.4.

1. Launch the Multisim program RC.

2. Double-click the Bode icon to bring up the Bode results window.

3. Run the program to get a feel for the shape of the Bode plots.

4. Ensure the scales are set to the same as in Exercise 3.4.

5. Double-click, in turn, the Resistor and the Capacitor and enter the component values

found in Exercise 3.1.

6. Run the program a second time.

Figure 3.7. Amplitude versus log Frequency of a Multisim RC Circuit

7. On completion, click on the [Save] button. This saves the Multisim Bode plot data as

an Excel file.

8. Overlay, in Excel, your data set from Multisim with the data set taken in Exercise 3.4

for the real circuit on NI ELVIS II.

This exercise demonstrates how you can compare a circuit designed with Multisim with the real

circuit built on NI ELVIS II.