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Method of Circuit Analysis

Objectives

To gain the practical understanding of electrical circuits and solve circuit parameters byusing Nodal and Mesh Analysis

To gain experience in basic functionality of Oscilloscopes and Function Generators

Resources

E&CE 140 at learn.uwaterloo.ca

Part A: Mesh and Nodal Analysis

Nodal Analysis

The main purpose of nodal analysis is to find the voltage at each node with respect to areference, in the electrical circuit. To do so, KCL equation is written for each node in the circuit

in terms of the voltages at each node.

For example, the circuit shown in figure 1 has five nodes; one of them is the ground or

reference (zero voltage), and nodes 1, 2, 3 and 4 with voltages V1, V2, V3 and V4 respectively.

Figure 1: Sample circuit for Mesh and Nodal analysis

Out of the 4 nodal voltages, V1 and V4 are known because they are connected to voltage sources.This leaves us with 2 unknown voltages V2 and V3, which means that to solve this circuit we

have to write KCL equations at nodes 2 and 3.

KCL at node 2: (V2 – V1)/ R 1 + (V2 – 0)/ R 2 + (V2 – V3)/ R 3 = 0

KCL at node 3: (V3 – V2)/ R 3 + (V3 – 0)/ R 4 + (V3 – V4)/ R 5 = 0

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Mesh Analysis

The main purpose of mesh analysis is to find the currents in each mesh in the circuit. To do so,

KVL equation is written for each mesh in the circuit in terms of the currents in each mesh.

For example, the circuit in figure 1 has three meshes, which means we have three unknowns

I1, I2 and I3, which also means we have to write three KVL equations, one for each mesh.

KVL Mesh 1: -V1 + I1. R 1 + (I1 – I2).R 2 = 0

KVL Mesh 2: (I2 – I1).R 2 + I2. R 3 + (I2 – I3).R 4 = 0

KVL Mesh 3: (I3 – I2).R 4 + I3. R 5 + V4 = 0

We now have a system of 3 equations and 3 unknowns that we can solve.

Prelab Exercise

For the circuit shown in Figure 1, let V1 = 15V, V4 = 24V, R 1 = R 3 = R 4 = 20kΩ and

R 2 = R 5 = 10kΩ.

o Use the nodal analysis method to find the voltages V2 and V3.

o Find the mesh currents to calculate mesh currents I1, I2 and I3.

o Use the results from previous steps to calculate the currents in each resistor R 1 to

R 5. Please indicate the direction of current in each resistor ( right, left, up and

down)

Procedure (45 mins)

Build the circuit shown in figure below

V4

V1

R1 R3 R5

R2 R4

20kΩ 20kΩ 10kΩ

10kΩ 20kΩ

24V

20V

Ground

1 2 3

Figure 2: Nodal & mesh analysis

15V

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Use the Digital Multimeter to measure the voltages at nodes 2, 3.

Use the Digital Multimeter to measure the currents going through all resistors.

Report

1. Compare your measurements with the results from Exercise 3 in pre-lab section.

Part B Oscilloscopes and Function Generator

Prelab Exercise

1. Explain the difference between RMS (Vrms), Peak (Vpk) and Peak-to-Peak (Vp-p) Voltages.

2. Considering the Agilent 33220A function generator, state two methods for modifying the

signal amplitudea) First method?

b) Second method?

c) Can these methods be used to change the signal frequency?

Refer to the Lab handout guide for the Agilent 33220A function generator to answer the

following question:

3. The output termination is set to 50Ω, and the frequency set to 1 kHz sine wave. The

generator displays a voltage set to 8Vp- p and is connected to a 50 Ω load;

a) Determine the actual peak to peak voltage measured at the load.

b)

If the output termination is then reset to Hi Z while the 50 Ω load still connected, what

will be the value of the voltage displayed on the screen of the generator and what is the

measured voltage at the load?

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Procedure (1 hr)

Oscil loscope Basics

a) Turn the oscilloscope on. (Some front panel diagrams of the oscilloscope are included on

the last two pages). Locate and press the Default Setup button (DSO-X 2002A).

b) Adjust the voltage scale control (Y-axis) to 500mV per division. Adjust the time scale

control (X-axis) to 200µs per division.

c) Connect channel 1 to the function generator output via breadboard. Connect channel 2

across the 2kohm resistor (as shown in figure 3).

d) Create a voltage divider as shown in figure 3 by connecting a 2kohm and 1kohm resistor

in series. Connect the Agilent 33220A function generator to the circuit using the BNC

cable.

e) Adjust the Agilent 33220A function generator as follows:

o

Turn ON the function generator;

o Using the system menu, set the output termination to HI Z (press Utility select

output setup, select HIZ and press done );

o Set the output signal to be sinusoidal signal;

o Set the frequency to 1kHz;

o Set the output voltage amplitude to 2 Vp-p (this is the value that should be

displayed on the function generator display).

AC

Function

generator

(Agilent

33220A)

Oscilloscope

channel 2

Oscilloscope

channel 1

R1

R2

1kΩ

2kΩ

Figure 3: Voltage divider using Oscilloscope

f) Press Run/Stop button on the oscilloscope and adjust the intensity of the oscilloscope grid

by accessing the Display Menu (display button), then selecting the Intensity (Grid softkey for DSO5012A) soft key and using the entry knob to adjust the intensity such that

the grid lines are clearly visible. Using the grid, estimate the peak to peak voltage for

channel 1 and 2. (You can adjust the position of the signal on screen for easier reading).

Capture (save) the image for recording your data. See instructions for capturing

oscilloscope images in the appendix of this lab manual.

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g) Using the cursors, measure the peak to peak voltage and period of the signal for channel

1 and 2. (For using cursors press the cursor button on the oscilloscope, select Y from the

screen. Select Y1 and Y2 and adjust the cursors using the knob. ΔY on the screen

displays the difference between Y1 and Y2).

h) Press the Ch 1 vertical scale knob to select fine vertical adjustment (for DSO5012A

press channel 1 and select fine soft key) and adjust using the vertical knob to determine

the minimum voltage per division settings that can be used to measure this signal? To get

correct measurements, the displayed signal should not be clipped on the oscilloscope

screen. (Note: you can adjust the vertical offset to move the reference level up or down as

needed). Capture the scope image, insert it into your data file and deselect fine vertical

adjustment after the measurement is made. Repeat this step for Ch2.

i) Determine the minimum time division scale that you can use to measure the signal period

using the cursors (To obtain the correct measurements, at least one complete cycle should

be displayed on the oscilloscope screen). Capture the image from the oscilloscope, insert

it into your data file and deselect the fine horizontal adjustment after the measurementis made.

Report

1. What is the advantage of using the cursor measurements over the grid measurements?

Function Generator

ACFunction generator

(Agilent 33220A)Oscilloscope

R1 R2100Ω 100Ω

Ground

Figure 4: Output termination test

a) With the function generator turned off, connect the circuit shown in Figure 4. Connect the

Agilent function generator and the oscilloscope to the circuit on the breadboard. b) Adjust the Agilent 33220A function generator as follows:

Turn ON the function generator;

Using the system menu, set the output termination to 50Ω (press Utility select output

setup, select 50 ohms and press done);

Set the output signal to be sinusoidal signal;

Set the frequency to 1kHz;

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Set the output voltage amplitude to 8 Vp-p (this is the value that should be displayed on

the function generator display)

c)

In the oscilloscope, set the voltage (vertical) scale to 5v/div and set the time (horizontal)scale to 200 µsec/div. Record the peak to peak voltage measured with the oscilloscope. You

can use the measure button in the “Measure” to obtain the peak to peak voltage displayed on

the right edge of the display screen. Normally we will be using the Cursors function for

measurements in this lab.

d) Disconnect the 50 Ω load connected:

What is the displayed voltage of the function generator? What is the measured peak to peak

voltage at the output on your oscilloscope?

e) Reconnect the 50 Ω load, Set the output termination to Hi Z:

What is the displayed voltage of the function generator? What is the measured peak to peakvoltage at the output on your oscilloscope?

f) Disconnect the 50 Ω load: What is the displayed voltage on the generator? What is the

measured peak to peak voltage on the oscilloscope?

Report

1. Why is the measured peak to peak voltage different from the displayed voltage at the function

generator for d and e?

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Figure 5. Oscilloscope front control panel DSO-X 2002A

Figure 7. Horizontal Controls

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Appendix

Capturing Oscilloscope Images

Before You Start:. ALWAY BACKUP YOUR FILES REGULARLY THROUGHOUT THE LAB!!

How to Capture:

Using a USB memory stick

1) Place memory stick in the USB port on the front panel

2)

Press the [Save/Recall] key.

3)

In the Save/Recall Menu, press Save.

4) In the Save Trace and Setup Menu, press Format, then, turn the Entry knobto select 8- bit Bitmap image (*.bmp).

5) Press the Save to softkey and use the Entry knob to select USB stick tonavigate to the save location.

6) The default name will be 1 for the first file, 2 for the second and so on

7) Press the Settings softkey.

8)

Select Invert Grat with appropriate softkey. 9)

Confirm That the Palette softkey is set to Color.

10) Finally, press the Press to save softkey.

A message indicating whether the save was successful is displayed.