EEEN311 Electric Circuits Theory

Experiments

2018/2019 Academic Session

Electrical Circuit Theory Page 1

I. Network analysis technique

In the practical of this year, we will validate experimentally some of the network analysis

techniques discussed in EEEN221 course. Students are encouraged to simulate the different

exercises they prepared for the labs. Simulation permits to confirm the theoretical results

before coming to the lab session. I recommend you an interesting and free software to

simulate electrical circuits available here. Many tutorials about PSpice are available on Orcad

website and on internet. You can also use Multisim or Proteus where needed. See me if you

need personal copy of these Software.

For this experiment, you need resistors, ammeter, voltmeter or multimeter and a DC

source. Students have to choose the correct resistances using the colour code.

1. Thevenin theorem and maximum power transfer

The Thevenin theorem permits the simplification of networks composed of linear

components to a voltage source and its internal resistance (or impedance).

10 Ω 4.7 Ω A

+ 10 10 Ω 4.7 Ω

−↑

B

10 Ω Fig. 1: DC network A

4.7 Ω

+ 10 10 Ω 4.7 Ω ↑

−↑ B

Fig. 2: measure of the Thevenin (open circuit) voltage

10 Ω 4.7 Ω A

10 Ω 4.7 Ω

B

Fig. 3: measure of the Thevenin resistance

Electrical Circuit Theory Page 2

First overshoot (%)Determine the overshoot of the circuit given by 89:2;<==> = 6? @A ∗

@A

Deduce the damping coefficient ) of the circuit using the relationship between the first

overshoot and ) shown on Fig. 7. Compare it to the theoretical values when 100Ω is

replaced by + 23. Conclude.

100

80

60

40

20

0

0 0.2 0.4 0.6 0.8 1

ε

Fig. 7 First overshoot as function of damping coefficient

Determine the resonance frequency D and the quality factor of the circuit E = /&) of

the circuit. Compare these values to the theoretical one, conclude.

Replace the input by a sinusoidal signal of 2

Determine the resonance frequency (when and are in phase) varying the

frequency. The amplitude of at the resonance is called 2:;= F G:.

Measure the bandwidth of the circuit ( = 2:;= F G:/√&) and the quality factor ,

Compare to the previous values

Redo all the previous experiments for = #, = IJ # , = IJ #, = "#.

Conclude on the effect of on the output.

Electrical Circuit Theory Page 6

IV. Network in AC

For the theory part of this lab, I recommend you to use Matlab as this will make the

calculations very easy for you. Use Pspice to have an idea of the circuit outputs in practice.

For this experiment, we need a capacitor, an inductor, resistors, breadboard, a

multimeter, an oscilloscope, wires and signal generator.

1. Maximum power transfer

In DC, the conditions of maximum power transfer have been verified in the previous labs.

This exercise aims at testing the same conditions in AC at 50 01.

a. Theory

Determine the Thevenin voltage L and impedance M̅ between the terminals A and

B showing all the steps of the calculation.

Deduce the value of M̅ = + OP to guarantee the maximum power transfer.

Specify the value of and the inductor which reactance is P .

Calculate the apparent power Q̅ of the load MLLL. Deduce the active power.

Change the value of in Matlab and Pspice and show that of the active decreases

47 Ω 100 Ω A

L = 5 470 Ω XO3.18 Ω MLLL

B

Fig. 8: AC network for Thevenin theorem application

b. Experiment

Measure the Thevenin voltage L with a multimeter and its phase shift

R 5(/ = S∆> relative to the supply where ∆ is the time shift between the two

signals measurable with the oscilloscope time cursors.

Measure the Norton current TU̅ (when the capacitor is removed and output short-

circuited) and its phase shift RVW/ relative to the supply.

Deduce the phase shift R = R 5(/ X RVW/ between L and TU̅ and the Thevenin

impedance M̅ = L /TU̅ . Take R = X&. Y° for your calculations if the value you

find is very different.

Deduce the M̅ = + OP for maximum power transfer

Connect and the inductor which reactance is P . For take into account the

internal resistance of the inductor 23.

Measure the active power of the load LMLL with the multimeter and the oscilloscope.

Compare to the theoretical results. Confirm the results by using other values for M̅

Electrical Circuit Theory Page 7

VI. RLC filters

1. Series resonance

This exercise permits to find the frequency behaviour of an RLC series circuit. These

circuits are very useful in many domains of electrical engineering where they permit

separate signal at close frequencies when they are carefully designed. The selectivity of

these filters confer them a very powerful rejection capability. They bandwidth and the

quality factor can be controlled by the resistance when the frequency is fixed. For this

experiment = 100Ω, 7 = 2a0 and = 1tr.

7

LLL u

LLL LLL

Fig. 13: frequency analysis of RLC series circuit

For the theory part, use Matlab for the calculations and plotting.

For this experiment, we need a resistor, a capacitor, a breadboard, an oscilloscope and

signal generator.

a. Theory

Recall the impedance of the inductor, the capacitor and the resistor when the supply is

a sinusoidal signal at a frequency *+.

Deduce the impedance of L and C in series.

Find the voltages LLL, u and LLL as function of the frequency using the voltage division

Calculate the ratios LLL/LLL, u /LLL and LLL/LLL and their phases as a function of the

frequency as find the resonance frequency

Plot the gains b * and phases m * in log scale for the frequency varying from 1001

to 3s01

What type of filter is the RLC circuit?

Calculate the bandwidth and the quality factor ,.

Simulate the circuit with Pspice and compare the results to the theoretical values. Change

the value of and see how the bandwidth becomes.

Electrical Circuit Theory Page 11

b. Experiment

Connect the circuit of Fig. 13 and supply it with a sinusoidal signal of & amplitude.

Measure the amplitude of LLL, u and LLL and their phase shift to LLL and report in a

table for the frequency between 1001 and 1s01. Use the oscilloscope and/or the

multimeter

Plot the gains b * and phases m * as a function of the frequency. Choose correctly

the frequency step.

Determine the resonance frequency, the bandwidth and the quality factor

Compare these values to those obtained in theory

Redo the previous measurement for = 50Ω and for = 5 Ω.

Conclude

2. Parallel resonance

For this circuit, the previous values of the components are maintained.

Tu

Tu 7 LLL

Fig. 14: Parallel RLC circuit

Find the equivalent admittance of system and the ratio Tu /Tu

Plot the gains b * and phases m * in log scale for frequencies from 1001 to 1s01

What type of filter is this RLC circuit? Calculate the bandwidth and the quality factor

Measure the amplitude of Tu and its phase shift to Tu and report the values in a table

for the above range of frequency

Plot the two gains b * and phases m * as a function of the frequency.

Determine the resonance frequency, the bandwidth and the quality factor. Conclude

3. Band stop filter 7

LLL LLL

Fig. 15: Band stop filter

Answer to the same question as for RLC series circuit studied in section VI-1.

Electrical Circuit Theory Page 12

VII. Fourier series and transform

Fourier series permits to get the frequency components of periodic signals whereas the

Fourier transform is used for most of the basic non-periodic functions. In this exercise, we

focus on the square, triangular and sine signals. The supply and outputs will be analysed with

the oscilloscope. The period of all these signals is v = 0.02w.

* e

y y

Xv/2 v/2 v Xv/2 v/2 v

Fig. 17: Square signal Fig. 16: Triangular signal

++

−−

Fig. 18: RC circuit when measuring Fig. 19: RC circuit when measuring

1. Theory

What is the expression of the cut-off frequency r of these two circuits? Which type

of filter they represent?

Find the Fourier series of the square Fig. 17 and triangular functions Fig. 16

Using Parseval theorem, determine the number of harmonics required to have 90% of

the overall power of the signal. What is the corresponding frequency *x = q*+?

Find and so that the cut-off frequency is equal to *x, r = q*+.

Using the superposition theorem, find the Fourier series of the circuits of Fig. 18 and

Fig. 19 when supplied by the square and triangular signals

Deduce the Fourier transform of the output signals

Use the FFT function of Pspice to verify your theoretical results for both the supply and

the circuit outputs.

2. Experiment

a. Measures on circuit of Fig. 18

Apply the square signal to the circuit of Fig. 18

Visualize on the oscilloscope the Fourier transform the supply and the output.

Measure the amplitude and the frequency of the fundamental and the harmonics

Compare these values to the theoretical ones

Electrical Circuit Theory Page 13

Do the same experiment using the triangular signal

b. Measures on circuit of Fig. 19

Answer to the same questions using the circuits of Fig. 19

c. Filter design

Realise a filter of your choice which permits to select the fundamental of a square

and triangular signal of frequency *+ (between 2 01 and 3 01).

Explain the choice of the filter selected and the values of its parameters.

Conclude on the usefulness of filter in signal processing.

You can use Pspice first to select the right parameters before the experiment. Take into

account the components available in the Lab (see with Technicians).

Electrical Circuit Theory Page 14