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PRACTICAL WORK BOOK
For Academic Session 20_ _
NETWORK ANALYSIS ( 203147 )
2012 pattern
For
S.E. (Electrical Engineering)
Department of Electrical Engineering
(University of Pune)
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SHREE RAMCHANDRA COLLEGE OF ENGG. LONIKAND (096)
DEPT. : ELECTRICAL ENGG. NETWORK ANALYSIS ( 203147 ) SEM. : II (SE)
TITLE: INSTRUCTIONS
Do’s and Don’ts in Laboratory (for students):
1. Do not handle any equipment before reading the instructions/Instruction manuals.
2. Apply proper voltage to the circuit as given in the procedure.
3. Check CRO probe before connecting it.
4. Strictly observe the instructions given by the teacher/Lab Instructor.
Guidelines to write your observation book (for students):
1. Experiment Title, Aim, Apparatus, Procedure should be right side.
2. Circuit diagrams, Model graphs, Observations table, Calculations table should be left side.
3. Theoretical and model calculations can be any side as per your convenience.
4. Result and Conclusion should always be at the end.
5. You all are advised to leave sufficient no of pages between experiments for theoretical or
model calculations purpose.
After successful performance of all practical’s following process will be done
Quiz on the subject.
Conduction of Viva-Voce Examination.
Evaluation and Marking Systems
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SHREE RAMCHANDRA COLLEGE OF ENGG. LONIKAND (096)
DEPT. : ELECTRICAL ENGG. NETWORK ANALYSIS ( 203147 ) SEM. : II (SE)
TITLE: LIST OF EXPERIMENTS
Any four experiments from the first five of the following and any four experiments from rest
of the list. (Minimum four experiments should be based on simulation software
PSPICE/MATLAB along with hardware verification)
1. Verification of Superposition theorem in A.C. circuits.
2. Verification of Thevenin’s theorem in A.C. circuits.
3. Verification of Reciprocity theorem in A.C. circuits.
4. Verification of Millmans’ theorem.
5. Verification of Maximum Power Transfer theorem in A.C. circuits.
6. Determination of time response of R-C circuit to a step D.C. voltage input. (Charging and
discharging of a capacitor through a resistor)
7. Determination of time response of R-L circuit to a step D.C. voltage input. (Rise and decay
of current in an inductive circuit)
8. Determination of time response of R-L-C series circuit to a step D.C. voltage input.
9. Determination of parameter of Two Port Network.
10. Determination of Resonance of R-L-C Parallel circuit
11. Determination of Resonance, Bandwidth and Q factor of R-L-C series circuit.
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SHREE RAMCHANDRA COLLEGE OF ENGG. LONIKAND (096)
DEPT. : ELECTRICAL ENGG. NETWORK ANALYSIS ( 203147 ) SEM. : II (SE)
EXPERIMENT NO. : SRCOE/ELECT/NA/01 PAGE:__-__ DATE: EXPERIMENT TITLE: SUPERPOSITION THEOREM
AIM: Verification of Superposition Theorem in A.C. circuits.
APPRATUS:
Sr. No Name of the Equipment Specification Quantity
1 Superposition circuit kit
2 Ammeter
3 Voltmeter
4 Connecting wires
SUPERPOSITION THEOREM STATEMENT
The Superposition Theorem can be used to analyze multi-source AC linear bilateral
networks. It may be stated as follows.
In any multisource (containing initial condition energy sources of emf or current source)
complex network consisting of linear bilateral elements, the responses (loop current or node
voltage) caused by the individual sources of the network may be found by determining the
algebraic sum of the response (current) at that element while considering the effect of
individual source. The other ideal voltage sources are replaced by its internal resistance (or
by a short circuit) and ideal current sources in the network are replaced open circuit across
the terminals. This theorem is valid only for linear systems.
PROOF OF SUPERPOSITION THEOREM:
- Find the current through Z3 by using Superposition Theorem
Z1
1' 2'
21
Z2
Z3 I3 V2V1
Figure No. 1.1
Solution :
Step 1: Considering source V1 acting independently and short-circuiting the other sources
(V2) or replace by internal impedances to measure current through I1’
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Z1
1' 2'
21
Z2
V1 Z3 I1'
Figure No. 1.2
I1 is current supplied by V1
I1’ is current through Z3
Step 2: Considering source V2 and short-circuiting the source V1 to measure current through
I2’
Z1
1' 2'
21
Z2
Z3 I2' V2
Figure No. 1.3
I2 is current supplied by V2
I2’ is current through Z3
Step 3: By using superposition theorem current through
I3 is current flowing through load impedance
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PROCEDURE:
Superposition Theorem:
1. Connect the circuit as shown in fig (1.1)
2. Set the Variac for rated voltage.
3. Make the supply voltage V2 short-circuited and apply V1 as shown in fig (1.2) and note
down the current through load impedance as .
4. Make the supply voltageV1 short-circuited and apply V2 as shown in fig (1.3) and note
down the current through load impedance as .
5. Now connect the V1 and V2 source to note down current through load impedance Z3 and
verify that theoretically and practically which proves Superposition theorem.
OBSERVATION TABLE:
Z1= ; Z2= ; Z3=
Sr.
No.
V1 = V; V2 = 0V V2 = V; V1 = 0V V1 = V; V2 =
I1’ (mA) I2’ (mA) I3 = I1’ + I2’ (mA)
Practical Theoretical Practical Theoretical Practical Theoretical
THEORETICAL CALCULATION:
CONCLUSION:
EXERCISE:
1. Prove Superposition theorem to find current through Z3 for the given circuit in figure
no. 1.4 and 1.5 practically and theoretically.
V2
18V
1' 2'
21
I3
Z2
2.2KΩZ1
1KΩ
Z3
10KΩV1
8.48V
V2
10 V
1' 2'
21
I3
Z2
125Z1
125
Z3
300V1
90 V
Figure No. 1.4 Figure No. 1.5
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SHREE RAMCHANDRA COLLEGE OF ENGG. LONIKAND (096)
DEPT. : ELECTRICAL ENGG. NETWORK ANALYSIS ( 203147 ) SEM. : II (SE)
EXPERIMENT NO. : SRCOE/ELECT/NA/02 PAGE:__-__ DATE:__:__:__
EXPERIMENT TITLE: RECIPROCITY THEOREM.
AIM: To study Verification of Reciprocity Theorem in A.C. circuits.
APPRATUS:
Sr. No Name of the Equipment Specification Quantity
1 Experimental kit
2 Variac
3 Connecting wires
4 Ammeter
5 Voltmeter
RECIPROCITY THEOREM STATEMENT
The reciprocity theorem states that in any linear, bilateral network consisting of single source
V1, gives the ratio of voltage V1 introduce in one loop to the current I in other loop is same as
the ratio obtain if the positive of V1 and I are interchanged in the network. The response at
any branch (or) transformation ratio is same even after interchanging the sources is V1 / I1 =
V1 / I2. A network that obeys reciprocity theorem is known as reciprocal network.
Before interchanging the source
Z1
1' 2'
21
Z2
Z3V1 I1
Figure No. 2.1
Apply KVL to loop 1
Apply KVL to loop 2
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I1 and I2 will get
Obtain ratio of voltage source V1 in loop 1 and current in loop 2
When is adding in loop 1 and current in loop 2
Step 2: When is adding in loop 2 and find current in loop 1
After interchanging the source
Z1
I2
1' 2'
21
Z2
Z3Vs
A
Figure No. 2.2
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Loop 1 abca
Loop2 bcb
Hence, we observe from equation 1 and 2 and current in loop1 . The ratio of
and
is
same.
This proves the reciprocity theorem.
PROCEDURE:
Reciprocity Theorem:
1. Connect the circuit as shown in fig (2.1).
2. Note down the ammeter reading as
3. Now interchange the source and ammeter as in fig (2.2).
4. Note down the ammeter reading as
5. Now verify that
=
theoretically and practically which proves reciprocity theorem.
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OBSERVATION TABLE:
Z1= ; Z2= ; Z3=
Sr. No. When V1 is acting in loop 1 and current in
loop 2 (V1= Volts)
When V1 is acting in loop 2 and current in
loop 1(V1= Volts)
Practical values Theoretical values Practical values Theoretical values
(mA)
(Ω) (mA)
(Ω) (mA)
(Ω) (mA)
(Ω)
THEORETICAL CALCULATION:
CONCLUSION:
EXERCISE:
Prove Reciprocity theorem for the given circuit in figure no. 2.3
I2
Z1
125
1' 2'
21
Z2
600
Z3
300Vs A
Figure No. 2.3
I2
Z1
27
1' 2'
21
Z2
27
Z3
56Vs A
Ω Ω
Ω
Figure No. 2.4
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SHREE RAMCHANDRA COLLEGE OF ENGG. LONIKAND (096)
DEPT. : ELECTRICAL ENGG. NETWORK ANALYSIS ( 203147 ) SEM. : II (SE)
EXPERIMENT NO. : SRCOE/ELECT/NA/03 PAGE:__-__ Date :
EXPERIMENT TITLE: THEVENIN’S THEOREM
AIM: To Study Verification of Thevenin’s Theorem in A.C. Circuits.
APPRATUS:
Sr. No Name of the Equipment Specification Quantity
1 Experimental kit
2 Digital Multimeter
3 Variac/ regulated power supply
4 Connecting wires
5 Ammeter
6 Voltmeter
THEVENIN’S THEOREM OVERVIEW
Thevenin’s Theorem will be examined for the AC case. While the theorem is applicable to
any number of voltage and current sources, this exercise will only examine single source
circuits for the sake of simplicity. The Thevenin’s source voltage and Thevenin’s impedance
will be determined experimentally and compared to theoretically. The Thevenin’s impedance
is found by replacing all sources with their internal impedance and then applying appropriate
series-parallel impedance simplification rules.
THEVENIN’S THEOREM STATEMENT
Thevenin’s Theorem states that any two terminal linear bilateral networks composed of
energy sources, and impedances can be replaced by an equivalent two terminal network
consisting of an independent voltage source Vth in series with an impedance Zth. Where,
thevenin’s voltage Vth is the open circuit voltage between the load terminals and Zth is the
impedance measured between the terminals with all the energy sources replaced by their
internal impedances.
It is a method for reduction of complex circuit into a simple one.
It reduces the need for repeated solution of the same sets of equations.
PROOF OF THEVENIN’S THEOREM:
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Z1= R+jxL
ZL =
R-
jxC
1' 2'
21
Z2
= R
+j(xL
-xC
)
V1
Figure No. 3.1
V1 ZL
1' 2'
21
Z1
Z2
ILA
Figure No. 3.2
Z1
1' 2'
21
Z2
V1I1 I2
Z3
Z4
ZL
Step 1: Remove ZL
Z1
1' 2'
21
Z2
V1I1 I2
Figure No. 3.3
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Z1
1' 2'
21
Z2
V1I1 I2
Z3
Z4
ZL
Step 2: Find voltage between terminal 2-2’ i.e
Vth
V1
1' 2'
21
Z1
Z2
Figure No. 3.4
Z1
1' 2'
21
Z2
V1I1 I2
Z3
Z4
Vth
Apply KCL for closed loop cabc
Step 3: Find the impedance between terminal 2-2’, Zth
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Z1
1' 2'
21
Z2
ZthV1= 0
Figure No. 3.5
Z1
1' 2'
21
Z2
V1=
0V
I1 I2
Z3
Z4
Zth
Step 4: Figure No. 3.2 is replaced and connect ZL
Vth ZL
IL’
1' 2'
21
Zth
A
Figure No. 3.6
By using Thevenin’s theorem current through ZL
PROCEDURE:
THEVENIN’S THEOREM:
1. Connections are made as per the circuit shown in fig (3.2).
2. Set the Variac and apply the voltage to V1 and note down the current IL flowing through
the load.
3. Connect the circuit as shown in fig (3.3 & 3.4) by open circuiting the load resistance.
Apply the voltage and note down the reading of voltmeter as Vth.
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4. Connect the circuit as shown in fig (3.5), measure the effective resistance Zth with the help
of a multimeter, by short-circuiting the voltage source.
5. Connect the Thevenin’s equivalent circuit as shown fig (3.6) note down the load current
IL’.
6. Thevenin’s theorem can be verified by checking that the currents IL and IL’ are equal.
OBSERVATION TABLE:
Z1= ; Z2= ; Z3= ; Z4= ; ZL=
Vs
Volts
Theoretical values Practical values
IL (mA) Vth (Volts) Zth (Ω) IL’(mA) IL(mA) Vth(Volts) Zth(Ω) IL’(mA)
THEORETICAL CALCULATIONS:
CONCLUSION:
EXERCISE :
1. Find current through 600 ohm by using Thevenin’s theorem shown in fig .
ZL
600
1' 2'
21
Z1
125
Z2
300V1
110
2. Find the current through the 15kΩ resistor (ZL) in the circuit using Thevenin’s th'm.
ZL
15kΩ
Z3
5.1kΩ
1' 2'
21
Z 1
2.2 kΩ
Z2
1kΩV1
110Z 4
10kΩ
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SHREE RAMCHANDRA COLLEGE OF ENGG. LONIKAND (096)
DEPT. : ELECTRICAL ENGG. NETWORK ANALYSIS ( 203147 ) SEM. : II (SE)
EXPERIMENT NO. : SRCOE/ELECT/NA/04 PAGE:__-__ Date :
EXPERIMENT TITLE: MILLMAN’S THEOREM
AIM: To study Verification of Millman’s Theorem in A.C. circuits.
APPRATUS:
Sr. No Name of the Equipment Specification Quantity
1 Circuit Board
2 Digital Multimeter
3 Variac/ regulated power supply
4 Connecting wires
5 Ammeter
6 Voltmeter
MILLMAN’S THEOREM STATEMENT:
If n voltage sources V1, V2, ...,Vn having internal impedances ( or series impedances) Z1,
Z2,... Zn respectively are connected in parallel then these sources may be replaced by a single
voltage source Vm having internal series impedance Zm, where, Vm and Zm are given by
VnV1
Zn
1 ' 2'
21
Z1 Z2 Z3
V2 V3
Figure No. 4.1
Zm
2'
2
Vm
Figure No. 4.2
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And
Where, are the admittances
Zm
2 '
2
Figure No. 4.3
Corresponding to the impedances
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Z1
V1
Z1I1
Figure No. 4.4
Z2
V2
I2 Z2
Figure No. 4.5
Zn
Vn
In Zn
Figure No. 4.6
In Z1I1 I2 I3 ZnZ2 Z3
Figure No. 4.7
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PROCEDURE:
1. Do the connection as per circuit diagram.
2. .
3. .
4. .
5. .
OBSERVATION TABLE:
Sr. No. Practical values (mA) Theoretical values
(mA)
THEORETICAL CALCULATION:
CONCLUSION:
EXERCISE
1. Using Millman’s theorem find the current and voltage in resistor Z4 in the given
network
VnV
51
Z4
5
1 ' 2'
21
Z
5 1 Z
22 Z
103
V
4V2
I3
1A
Figure No.4.8
2. Using Millman’s Theorem find the current through 56 Ω in the given circuit.
Vn
4.42VV2
20 V
Z
27Ω
12
2' 1'
Z
15 Ω3
Z
56ΩZ
10 Ω2
V1
8.84 V
2
Figure No.4.9
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SHREE RAMCHANDRA COLLEGE OF ENGG. LONIKAND (096)
DEPT. : ELECTRICAL ENGG. NETWORK ANALYSIS ( 203147 ) SEM. : II (SE)
EXPERIMENT NO. : SRCOE/ELECT/NA/05 PAGE:__-__ Date :
EXPERIMENT TITLE: TWO PORT NETWORK PARAMETERS
AIM: To Determine the Parameters of Two Port Network’s.
APPRATUS:
Sr. No Name of the Equipment Specification Quantity
1 Two port network kit
2 Digital Multimeter
3 Variac/ regulated power supply
4 Connecting wires
5 Ammeter
6 Voltmeter
THEORY:
A two-port network has two terminals name as 1-1’ to which source is connected (driving
energy/input port) and 2-2’ is connected to load (output port), four variables as shown in
figure. These are the voltages and currents at the input and output ports, namely V1, I1 and
V2, I2. To describe relationship between ports voltages and currents, two linear equations are
required. From this, two are independent and two are dependent variables.
V1 V2
I1
I1 I2
I2
2- port
network
Port 1 Port 2
1'
1 2
2'
Figure No.5.1
We will further see Z-parameter, Y-parameter and ABCD parameter
Z-Parameter: Z parameters are called impedance parameters. The parameters Z22 are defined
only when the current in one of the ports is zero i.e. one of the port is open circuited. Hence,
Z-parameters are open circuited parameters. By expressing V1 and V2 (dependent variables)
in terms of I1 and I2 (independent variables)
In matrix form
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From the above equations, either we can find out Z-parameters by input terminals or output
terminals are open circuited (assigning values of the independent variables as zero) called
open circuited impedance (ohms).
Z12 I2
Z11
V1
I1
Z22
Z21 I1
I2
V2
Figure No. 5.2
0 .... input impedance
0 .... forward transfer impedance
0 .... reverse transfer impedance
0 .... output impedance
Y-Parameter: These parameters are called admittance parameters. By expressing V1 and V2
(independent variables) in terms of I1 and I2 (dependent variables) given as
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From the above equations, we can find out Y-parameters either input or output port are short
circuiting by assigning values of the independent variables as zero. These are called short
circuit admittance parameters (Siemens).
y12 V2
y11
V1
I1
Y21 V1
y22
V2
I2
Figure No. 5.3
0 .... input admittance
ABCD Parameter: These are transmission parameters and are used for analysis of
transmission system where input port is referred as sending end and output port is referred as
receiving end. By expressing V1 and I1 (input port/ dependent variables) in terms of V2 and I2
output port (independent variables).
V1 V2
I1
I1 I2
I2
2- port
network
Port 1 Port 2
1'
1 2
2'
Figure No. 5.3
Considering, the current entering in both the ports and is positive. The indicates that is
leaving the port 2.
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ABCD matrix is a transfer matrix of the network. These parameters are measured by open
circuit and short circuit test on the output port (By assigning values of the independent
variables as zero).
A = open circuit voltage gain
B = short circuit transfer parameter
C = open circuit reverse transfer parameter
D = short circuit reverse current gain
PROCEDURE :-
1. Connect dc power supply Va = 5V at port 1-1’ and keep output port open circuited i.e.
.
2. Measure the current I1 by connecting mill ammeter in series with R1 and voltage V2 across
R4 by Multimeter.
3. From these values of V1, V2, I1 and I2 (I2 = 0) find input driving point impedance where V1
= Va. i.e. Z11 = V1 / I1 at I2 = 0 &
Find forward transfer impedance i.e. Z21 = V2 / I2 at I2 = 0.
4. Connect dc power supply Vb = 5V at port 2-2’ and keep input port open circuited i.e. I1 = 0.
5. Measure the current I2 by connecting milliammeter in series with supply and voltage V1
across R3 by multimeter.
6. From this value of V2, V1, I2 and I1 (I1=0) find output driving point impedance that is Z22 =
V2 / I2 at I1 = 0 & Z12 = V1 / I2 at I1 = 0.
7. Calculate Z-parameters theoretically. These values should be approximately equal to the
practical values of Z-parameters.
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OBSERVATION TABLE:
I2 = 0 I1 = 0
Practical values Theoretical values Practical values Theoretical values
V1 V1
V2 V2
I1 I2
Z11 Z12
Z21 Z22
V2 = 0 V1 = 0
I1 I1
I2 I2
V1 V1
Y11 Y11
Y21 Y21
THEORETICAL CALCULATION:
CONCLUSION:
EXERCISE :
1. Find the Z. Y, and ABCD parameter for the given circuit.
'
V2
Z
100
a
1' 2'
21
Z
100
c
Z
50b
V1
I1 I2
Figure No. 5.4
'
Z
2.2kΩ
1' 2'
21
Z
1kΩ
Z560Ω
V1
10 V
I1 I
AA
V2
8 V
Z
560Ω
Z
2.2kΩ
Figure No. 5.5
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SHREE RAMCHANDRA COLLEGE OF ENGG. LONIKAND (096)
DEPT. : ELECTRICAL ENGG. NETWORK ANALYSIS ( 203147 ) SEM : II (SE)
EXPERIMENT NO. : SRCOE/ELECT/NA/__ PAGE:__-__ Date :
EXPERIMENT TITLE: RESONANCE OF RLC CIRCUIT
AIM: To Determine Resonance, Resonant frequency, Quality factor and Bandwidth of the
RLC circuit.
APPARATUS:
Sr. No Name of the Equipment Specification Quantity
1 Two port network kit
2 Digital Multimeter
3 Variac/ regulated power supply
4 Connecting wires
5 Ammeter
6 Voltmeter
CIRCUIT DIAGRAM :
Vin
R
C
i
Vo
L
Figure No. 6.1
THEORY:
In series RLC circuit Impedance , Current And, Phase angle
Ф= . We know that both and are the function of frequency f. When
f is varied both and get varied.
If the frequency of the signal fed to such a series circuit is increased from minimum, the
inductive reactance (XL= 2πfL) increases linearly and the capacitive reactance ( = 1/2πfC)
decreases exponentially. At resonant frequency fr, - Net reactance , X = 0 (i.e., XL=Xc) -
Impedance of the circuit is minimum, purely resistive and is equal to R - Current I through
the circuit is maximum and equal to V/R - Circuit current , I is in phase with the applied
voltage V (i.e. phase angle Ф = 0). At this particular resonant frequency, a circuit is in series
resonance. Resonance occurs at that frequency when,
Therefore
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BW of series RLC circuit: At series resonance frequency, current is maximum and
impedance is minimum. The power consumption in a circuit is proportional to square of the
current as . Therefore, at series resonance current is maximum and power is also
maximum Pm. The half power occurs at the frequencies for which amplitude of the voltage
across the resistor becomes equal to of the maximum. For frequency above and below
resonant frequency fr, f1 and f2 are frequencies at which the circuit current is 0.707 times the
maximum current, Imax or the 3dB points.
Bandwidth: The difference between the half power frequency f1 and f2 at which power is
half of its maximum is called bandwidth of the series RLC circuit. Therefore from above figs
Out of two half-power frequencies, the f2 is upper cut off frequency and f1 is lower cut off
frequency. The current in series RLC circuit as
At resonance,
At half power,
Equating eq 1 and 2
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From the equation 3 we can find two values of half power frequency which are and
corresponding to f1 and f2
Equation 7 shows that resonant frequency is geometric mean of the two half power frequency
is
Subtracting equation 5 from equation 4 we get,
Quality Factor: It is the ratio of energy stored in the oscillating resonator to the energy
dissipated per cycle by damping processes. It is dimensionless parameter. It determines the
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qualitative behaviour of simple damped circuit. The quality factor of RLC series circuit is the
voltage magnification in the circuit at resonance is
Therefore, the quality factor is
It indicates the selectivity or sharpness of the tuning of a series circuit.
It gives correct indication of the selectivity of such series RLC circuit, which are used
in many circuits.
A system with low Q < ½, is said to be overdamped
A system with high Q > ½, is said to be underdamped
A system with intermediate Q = ½ is said to be critically damped
The quality factor increases with decreasing R
The bandwidth decreases with decreasing R
PROCEDURE:
1. Connect function generator to the CRO and set the output voltage 10Vpp at 1kHz. as
shown in circuit diagram.
2. Apply the input voltage to series resonance circuit as shown in fig. and observe output
voltage on CRO.
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3. Increase the function generator output signal frequency from minimum say 10 Hz to a
maximum signal frequency of 100KHz in decade steps (10, 20, 30…..100, 200,…..1000,
2000…..10k, 20k……., 100kHz). Note the corresponding output voltage.
4. For applied signal frequency measure current with the help of milliammeter.
5. Calculate the gain in dB and theoretical frequency using
6. Plot the graph of frequency v/s Gain, find the frequency on the graph at which gain is
maximum, this frequency is known as resonant frequency and this should be approximately
to the theoretical frequency calculated in step 5.
OBSERVATION TABLE:
Sr.
No.
Frequency
(Hz)
Output Voltage
(Vo)
Current (mA) Gain(dB) = 20log(Vo/Vin)
10Hz
20
1kHz
100kHz
Nature of Graph
frequency
lo
10/.707BW= f2-f1
f1 f0 f2
Ga
in
Figure No.
THEORETICAL CALCULATION:
CONCLUSION:
Exercise :
L1=10mH C1=0.047microfarad R1= 4.7kohm
L2= 47mH C2=0.1microfarad R2=2.2ohm
NETWORK ANALYSIS (NA)
S.R.C.O.E, LONIKAND PUNE Page
SHREE RAMCHANDRA COLLEGE OF ENGG. LONIKAND (096)
DEPT. : ELECTRICAL ENGG. NETWORK ANALYSIS ( 203147 ) SEM. : II (SE)
EXPERIMENT NO. : SRCOE/ELECT/NA/__ PAGE:__-__ Date : EXPERIMENT TITLE: RESONANCE OF RLC PARALLEL CIRCUIT
AIM: To Determine Resonance of RLC Parallel Circuit.
APPARATUS:
Sr. No Name of the Equipment Specification Quantity
1 Two port network kit
2 Digital Multimeter
3 Variac/ regulated power supply
4 Connecting wires
5 Ammeter
6 Voltmeter
CIRCUIT DIAGRAM:
S
V
R L
i
Cic
Figure No. 7.1
THEORY:
A parallel circuit like the one that is illustrated in Fig. No. is said to be under resonance
when the resultant current drawn by it and the line voltage across it’s terminal are in phase.
The frequency at which this happens is known as resonant frequency. Consider a commonly
used tank circuit for easy simplification.
Inductive reactance of the coil
Capacitive reactance of the coil
Impedance of the coil
NETWORK ANALYSIS (NA)
S.R.C.O.E, LONIKAND PUNE Page
Ω
Current in an inductive branch
Phase angle between &
Current in the capacitive branch
The resultant is obtained from the phasor addition of and . If F of such a value that =
then, the resultant current I is minimum L= and in phase with the supply
voltage as shown in figure is said to be in response and the frequency at which this happens is
known as resonance frequency.
The expression for the resonant frequency for the circuit under consider
If fr is the resonant frequency then
If R is small then,
NETWORK ANALYSIS (NA)
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Hence, it should be noted that at resonance, the susceptances of both the parallel branches are
equal and net susceptances of the whole circuit is always zero.
Dynamic Impedances :
At resonance, the resultant current is given by
From equation 2
Putting this value in above equation, we get
The term at the denominator in the above equation is known as the equivalent dynamic
impedance of parallel circuit under resonance of obvious corresponding result is minimum.
Purely resistive as the parallel circuit under resonance offer’s maximum impedance to current
of one particular circuit may be used in ratio or electric circuits to filter out or rejected the
circuit of the desired frequency.
Q-factor of parallel circuit:
Parallel resonance is often refers to as current resonance because even through very little
current is known from supply by the parallel circuit under resonance.
Now from equation 5 the line current drawn from the supply at resonance it given by
The current in the inductive branch is given by
The ratio of current circulating between the two parallel branches to the line current drawn
from the supply is called current magnification. Therefore, from the above equation we have,
NETWORK ANALYSIS (NA)
S.R.C.O.E, LONIKAND PUNE Page
Alternatively,
It is the same as that for series resonance circuit
OBSERVATION TABLE:
Sr. No. Parameter Value
1. Resonant frequency (fr)
2. Quality factor
Nature of graph:
ФL
Ic s
inФ
L
CONCLUSION:
EXERCISE:
NETWORK ANALYSIS (NA)
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NETWORK ANALYSIS (NA)
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SHREE RAMCHANDRA COLLEGE OF ENGG. LONIKAND (096)
DEPT. : ELECTRICAL ENGG. NETWORK ANALYSIS ( 203147 ) SEM. : II (SE)
EXPERIMENT NO. : SRCOE/ELECT/NA/__ PAGE:__-__ Date : EXPERIMENT TITLE: TIME RESPONSE OF RL SERIES CIRCUIT
AIM: Determination of Time Response of series RL circuit to step DC input voltage (rise
and decay of current in an inductive circuit)
EQUIPMENTS REQUIRED:
1. MATLAB SOFTWARE
CIRCUIT DIAGRAM:
S
V
R
Li
Figure No. .1
THEORY
Consider a RL series circuit shown in figure .1 with S is closed at t=0. Kirchoff’s law gives
the differential equation for the circuit
Taking Laplace transform
The initial condition specified by the last equation is as the inductance is unfluxed,
=0 thus above equation is as
Where and are unknown coefficients. As the first step, simplify the equation by putting
all terms over a common denominator.
Equating coefficients to obtain set of linear algebraic equations
NETWORK ANALYSIS (NA)
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From the above equations we get the ,
] , t
The final solution gives a transform into the sum of reversed separate parts is known as
loading of partial fraction expansion.
PROGRAM :
V = 100;
R =.0100;
L=0.10
Lamda =L/R;
Im = V/R;
t=0:01:100
i=Im*(1-exp(-t / lamda)); % rise in current
iL = Im*exp(-t / lamda ); % decay in current
plot (t,i,t,iL);
xlabel(‘time(t) in sec’);
ylabel(‘current in ampere’);
title(determination of time response of RL circuit for step D.C. voltage ( rise and decay of
current in an inductive circuit’).
Nature of graph:
NETWORK ANALYSIS (NA)
S.R.C.O.E, LONIKAND PUNE Page
PROCEDURE :
1. Connect the circuit as shown in figure no.
CONCLUSION :
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SHREE RAMCHANDRA COLLEGE OF ENGG. LONIKAND (096)
DEPT. : ELECTRICAL ENGG. NETWORK ANALYSIS ( 203147 ) SEM : II (SE)
EXPERIMENT NO. : SRCOE/ELECT/NA/0 PAGE:__-__ Date : EXPERIMENT TITLE: TIME RESPONSE OF RC SERIES CIRCUIT
AIM: Determination of Time Response of RC circuit to step DC input voltage (charging and
discharging of Capacitor).
EQUIPMENTS REQUIRED:
1. MATLAB SOFTWARE
CIRCUIT DAIGRAM:
S
V
R
C
i
Figure No. .1
THEORY:
NETWORK ANALYSIS (NA)
S.R.C.O.E, LONIKAND PUNE Page
PROGRAM:
V = 100;
R = 100000;
C = 100E-6;
Lamda =R*C;
t=0:.1:100
Vc = V*(1-exp(-t / lamda));
Vr = V*exp(-t / lamda );
plot (t, Vc, t, Vr);
xlabel(‘time(t) in sec’);
ylabel(‘voltage in Volts’);
title(‘determination of time response of RC circuit for step D.C. voltage’)
NETWORK ANALYSIS (NA)
S.R.C.O.E, LONIKAND PUNE Page
SHREE RAMCHANDRA COLLEGE OF ENGG. LONIKAND (096)
DEPT. : ELECTRICAL ENGG. NETWORK ANALYSIS ( 203147 ) SEM. : II (SE)
EXPERIMENT NO. : SRCOE/ELECT/NA/__ PAGE:__-__ Date :
EXPERIMENT TITLE: TIME RESPONSE OF RLC SERIES CIRCUIT.
AIM: Determination of Time Response of series RLC circuit to step DC voltage.
EQUIPMENTS REQUIRED:
1. MATLAB SOFTWARE
CIRCUIT DIAGRAM:
V
R
L
C
Figure No .1
THEORY:
Taking Laplace transform
Multiply by s/L to num and den,
Nature of graph
CONCLUSION :