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Department of Electrical & Computer

Engineering Technology

EET 3086C – Circuit Analysis

Laboratory Experiments

Masood Ejaz

EET 3086C – Circuit Analysis Valencia College

2

Experiment # 1

DC Measurements of a Resistive Circuit and Proof of Thevenin Theorem

Prelab: Solve the circuits theoretically (steps 1, 2, and 3) and then perform PSpice simulations

to fill out appropriate tables under procedure section.

Objective: To build a resistive circuit and its Thevenin equivalent to prove their equivalency for

the load.

Procedure:

1. Build the following resistive circuit on the breadboard and measure the indicated variables

Figure 1: Resistive Circuit for Step 1

VR4 IR3 VR6 IR6

Theory

Simulation

Lab

2. Suppose your load is comprised of resistors R4, R5, and R6. Draw the Thevenin equivalent

circuit and then build it on the breadboard. Measure load current and load voltage and

compare them to the corresponding values that you obtained in step 1 to show the

equivalency of both the circuits for this load (Note: if exact value of RTH is not available, use

the closest value or make a series combination of resistors to get to the closest value)

VTH = _____________________________; RTH = ____________________________

R1

1.0k

R22.0k

R3

3.0k

R44.7k

R5

1.0k

R62.2k

V110 V


3

VLOAD ILOAD

Theory

Simulation

Lab

3. Now assume that load is just resistor R6. Repeat step 2.

VTH = _____________________________; RTH = ____________________________

VLOAD ILOAD

Theory

Simulation

Lab

Thevenin Circuit

Thevenin Circuit


4

Discussion: You lab report discussion should include an explanation and importance of

Thevenin theorem and explanation of your Thevenin equivalent circuits. If there is any

discrepancy in your results, make sure to discuss that too.


5

Experiment # 2

Transient Response of RC and RL Circuits

Prelab: Perform lab simulation using PSpice. Also, find the response equations as being asked in

the lab and fill out the corresponding tables to compare simulated and theoretical results.

Objective: To design first-order RC and RL circuits to observe their transient response

RC Circuit

Procedure:

1. For the first-order RC cicuit as shown in figure 1, derive the equations for the capacitor

voltage when input is 5V (complete or step response) and when it is 0V (source-free or

natural response).

vc(t) [step response] = ____________________________________________

vc(t) [natural response] = ____________________________________________

2. Build a first-order RC circuit as shown in figure 1. Use square wave as your input and choose

its frequency such that pulse width of the square wave (tp) is six times the time constant () of

the circuit, i.e. 6pt . It can safely be assumed that this pulse width time is long enough for

the circuit to get to its steady-state value. Remember that pulse width is half of the time

period of the square wave. Set input voltage to be 5Vp-p (high voltage = 5V, low voltage =

0V)


6

Figure 1: First-Order RC Circuit

3. Connect your oscilloscope to observe both input signal and voltage across capacitor

simultaneously. Fill out the following table with your theoretical, simulated, and observed

values from oscilloscope. Save your waveform.

vc(t) [step response] vc(t) [natural response]

Theory Simulation Lab Theory Simulation Lab

t =

t = 2

t = 3

RL Circuit

Procedure:

1. A first-order RL circuit is shown in figure 2. Derive the equations for the inductor current

when input is 5V (complete or step response) and when it is 0V (source-free or natural

response).

iL(t) [step response] = ____________________________________________

iL(t) [natural response] = ____________________________________________

C1

10n

R1

1k

R2

2k

R3

2k

V1

TD = 0

TF = 1p

V1 = 0

TR = 1p

V2 = 5V

0


7

Figure # 2: First-Order RL Circuit

2. Build the circuit from figure 2. Use square wave as your input and choose its frequency such

that pulse width of the square wave (tp) is six times the time constant () of the circuit, i.e.

6pt . It can safely be assumed that this pulse width time is long enough for the circuit to

get to its steady-state value. Remember that pulse width is half of the time period of the

square wave. Set input voltage to be 5Vp-p (high voltage = 5V, low voltage = 0V)

3. Observe the current passing through the inductor. For hands-on, measure the voltage across

R3 on the oscilloscope and calculate current from that. PSpice simulation can plot the current

using a current probe. Fill out the following table with your theoretical, simulated, and

observed values. Save your waveform.

iL(t) [step response] iL(t) [natural response]

Theory Simulation Lab Theory Simulation Lab

t =

t = 2

t = 3

Discussion:

Your lab report should show the derivation of the equations. Discussion should focus on the

transients in RL and RC circuits. Also discuss about discrepancies between lab and expected

results. Discuss why it is important to study transient analysis of RL and RC circuits, i.e. their

practical implication.

L1

1mH

R1

100

R2

100

R3

100

V1

TD = 0

TF = 1p

V1 = 0

TR = 1p

V2 = 5V

0


8

Experiment # 3

Transient Response of RLC Circuits

Prelab: Solve circuits theoretically and perform simulation using PSpice. Write down your

prelab calculations and observations as required in the following procedure.

Objective: To design two different RLC circuits to study the response characteristics.

Procedure:

4. For the first RLC circuit as shown in figure 1, calculate the values for neper frequency ()

and resonant frequency (o). Determine the type of damping and calculate the root(s) of the

characteristic equation.

Figure # 1: First RLC Circuit

Neper

Frequency ()

Resonant

Frequency (o)

Damping Type s1 s2

5. Assume that input is a square wave with values from 0 to 5V with level zero representing

source-free circuit and 5V representing step circuit. Perform the analysis to calculate the

capacitor voltage for both step and source-free circuits.

vc(t) (step) = _____________________________________________________________

vc(t) (source-free) = _______________________________________________________

6. Simulate your circuit with PSpice. Take pulse width (half of the time period) of the square

wave to be around six times the time constant (reciprocal of the dominant neper frequency,

C

10nF

L

100mH

R21k

R1

1k

V1

TD = 0

TF = 1p

V1 = 0V

TR = 1p

V2 = 5V

0


9

i.e. dominant root). Observe the voltage across capacitor. Make sure to keep your simulation

interval small enough to have a smooth graph.

7. Use MATLAB to plot the step and source-free responses from your expressions of capacitor

voltage (one plot will be preferred else plot separately). Compare your plot with the

simulated results to check the accuracy of your derived expressions. Fill out the following

table. Make sure to put the simulated and MATLAB plots in your lab report.

Step Response Source-free Response

First Peak

Time

First Peak

Value

(positive

or

negative)

Steady-

State

Value

First Peak

Time

First Peak

Value

(positive or

negative)

Steady-

State

Value

Simulation

MATLAB

8. Build your circuit on bench and observe capacitor voltage to fill out the following table.

Compare your results with the simulated and theoretical responses for validation.


First Peak

Time

First Peak

Value

(positive or

negative)

Steady-

State

Value

First Peak

Time

First Peak

Value

(positive or

negative)

Steady-

State

Value

Bench

9. Now, for the second RLC circuit as shown in figure 2, calculate the values for neper

frequency () and resonant frequency (o). Determine the type of damping and calculate the

root(s) of the characteristic equation.

Neper

Frequency ()

Resonant

Frequency (o)

Damping Type s1 s2


10

Figure # 2: Second RLC Circuit

10. Assume that input is a square wave with values from 0 to 5V with level zero representing

source-free circuit and 5V representing step circuit. Perform the analysis to calculate the

voltage across R2 for both step and source-free circuits.

VR2(t) (step) = _____________________________________________________________

VR2(t) (source-free) = _______________________________________________________

11. Simulate your circuit with PSpice. Take pulse width (half of the time period) of the square

wave to be around six times the time constant (reciprocal of the dominant neper frequency,

i.e. dominant root). Observe the voltage across capacitor. Make sure to keep your simulation

interval small enough to have a smooth graph.

12. Use MATLAB to plot the step and source-free responses from your expressions of the

voltage across R2 (one plot will be preferred else plot separately). Compare your plot with

the simulated results to check the accuracy of your derived expressions. Fill out the following

table. Make sure to put the simulated and MATLAB plots in your lab report.


First Peak

Time

First Peak

Value

(positive

or

negative)

Steady-

State

Value

First Peak

Time

First Peak

Value

(positive or

negative)

Steady-

State

Value

Simulation

MATLAB

C1

100nF

L1

100mH

R11k

R22k

V1

TD = 0

TF = 1p

V1 = 0V

TR = 1p

V2 = 5VR3

3k

0


11

13. Build your circuit on bench (if required) and observe voltage across R2 to fill out the

following table. Compare your results with the simulated and theoretical responses for

validation.


First Peak

Time

First Peak

Value

(positive or

negative)

Steady-

State

Value

First Peak

Time

First Peak

Value

(positive or

negative)

Steady-

State

Value

Bench

Discussion:

Your lab report discussion should focus on the transients in RLC circuits. Discuss different types

of damping, effect of neper (), resonant (o), and natural resonant (d) on the circuit response,

and practical implication of this study. Compare your theoretical, simulated, and lab results and

discuss if there are any discrepancies.


12

Experiment # 4

Sinusoidal Response of an RLC Circuit

Prelab: Solve circuit theoretically and perform simulation using PSpice. Write down your prelab

calculations and observations as required in the following procedure.

Objective: To observe amplitude and phase change in an RLC circuit under a sinusoidal forcing

function.

Procedure:

1. Solve for the voltage expressions across inductor and capacitor in figure 1

Figure 1: RLC Circuit for the Experiment

VL(j) = __________; vL(t) = _________________________________________________

Vc(j) = __________; vc(t) = _________________________________________________

2. Simulate the circuit in PSpice and observe waveforms across source, capacitor, and inductor.

Fill out the following table with the observed values from the simulated results.

VL(peak) (Volt) Phase angle L(degree) VC(peak) (Volt) Phase angle C(degree)

Vs

5 V

100kHz

0Deg

L1330uH

R1

100

R2

510

R31.0k

R4

1.0k

C11.0nF


13

Note:

(i) To measure phase angle of VL and VC from the simulation and oscilloscope, measure the

time difference between the zero-crossing of your source waveform and the respective

voltage waveforms using cursors (figure 2). Let this time be t, then using the following

relationship, phase angle for each of the waveform can easily be found,

360T

t

where T is the time period of each waveform (constant as long as f is constant), and is

the phase angle.

(ii) When you use PSpice to simulate your circuit, make sure to use fourth or fifth cycle of

your voltage waveforms to measure peak voltage and phase angle, i.e. when voltages are

settled down to their steady-state. From the simulation, you will see that for the first

couple of cycles, vLand vC will still be in the process of settling down to their steady-state.

Figure 2: Measurement of t from simulation

t


14

3. Build circuit on the breadboard and repeat step 2. Fill out the following table with your lab

results

VL(peak) (Volt) Phase angle L(degree) VC(peak) (Volt) Phase angle C(degree)

4. Show the phasor relationship of the three voltages using phasor diagram

Discussion:

Your discussion should encompass the importance of sinusoidal analysis as well as reason to

perform analysis in complex frequency domain versus time domain. You should also discuss the

concept of lagging waveforms versus leading waveforms and effect of the inclusion of capacitors

and inductors in the sinusoidal circuits.

Exercise:

Make Thevenin equivalent of your circuit assuming load to be C1. Find load voltage and load

current and show their phasor relationship.


15

Experiment # 5

Analysis of Series RLC Band-pass Filter

Prelab: Solve circuit theoretically and perform simulation using PSpice (AC sweep with both

linear and logarithmic sweep type). Write down your prelab calculations and observations as

required in the following procedure.

Objective: To observe the frequency response of a series RLC bandpass filter or series resonant

circuit

Procedure:

1. For the bandpass filter design shown in figure 1, let resonant frequency fo be 159.15 KHz and

required bandwidth is approximately 15.915 KHz. Complete the design by calculating the

following quantities:

Inductance L Capacitance C Quality factor Q Lower cut-off f1 Upper cut-off f2

Figure 1: Series RLC Band-pass filter

2. Fill out the following table from your calculated and simulated values. Note that the input

sinusoidal source has 5Vp output.

Calculated Simulated

VR (fo)

VR (f1)

VR (f2)

Vin

5Vac

0Vdc

0

+

Vout

-

C1L1

R1

10k


16

3. From your simulation, figure out the upper and lower frequencies corresponding to 10% of

the maximum output and write them down. These will be considered as stop-band

frequencies

flower_10% = _________________________; fupper_10% = _________________________

4. Build circuit on the bench and fill out the following table with your observations.

Hz Volt

fo v(fo)

f1 v(f1)

f2 v(f1)

flower_10% v(flower_10%)

fupper_10% v(fupper_10%)

5. From your observations, draw a rough sketch of frequency response of the circuit (vR vs. f)

Discussion: In your lab report, discuss band-pass filter, its equations, its practical applications,

and discrepancies between theoretical, simulated and lab results and their possible explanation.


17

Exercises:

(i) Derive circuit equations to find out flower_10% and fupper_10%

(ii) Create two MATLAB programs to calculate different parameters for series band-pass

filter as follows:

Program 1 should be a function based on this lab, i.e., given the center frequency,

required bandwidth, and resistor value, it should calculate values for inductor and

capacitor, upper and lower cut-off frequency and quality factor. Further, it should also

plot the frequency response of the circuit. Plot should be properly labeled.

Program 2 should be a function that calculates center frequency, quality factor,

bandwidth, upper, and lower cut-off frequencies based on the input values of resistor,

capacitor and inductor. Plot the frequency response of the circuit and properly label your

plot.

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