Multisimnetworks Lab Manual
-
Upload
chaitanya-jambotkar -
Category
Documents
-
view
5 -
download
0
description
Transcript of Multisimnetworks Lab Manual
-
Department of Electrical and Electronics Engineering
MULTISIM / NETWORKS
Laboratory Manual
GOKARAJU RANGARAJU INSTITUTE OF ENGINEERING AND TECHNOLOGY
(Autonomous Institute under JNTU Hyderabad)
-
MULTISIM / NETWORKS LAB
GRIET/EEE 2
CERTIFICATE
This is to certify that it is a bonafide record of practical work done in the Multisim/Networks Laboratory in I sem of II year during the year
2011-2012 Name: Roll No: Branch: Signature of staff member
-
MULTISIM / NETWORKS LAB
GRIET/EEE 3
Contents
1.Thevenins Theorem.
2. Nortons Theorem
3. Maximum Power Transfer Theorem.
4. Superposition and Reciprocity Theorems.
5. Z and Y parameters.
6. Transmission and Hybrid Parameters.
7. Compensation and Millimans Theorems.
8. Series Resonance
9.Parallel Resonance.
10. Locus of Current Vector in an R-L Circuit
11. Locus of Current Vector in an R-C Circuit
12Measurement of 3-phase power by two wattmeter method for unbalanced loads.
13. Measurement of Active and Reactive power by star and delta connected balanced loads.
-
MULTISIM / NETWORKS LAB
GRIET/EEE 4
1. Thevenins Theorem
Aim:
1. To construct a circuit and verify Thevenins Theorem for the given circuit.
Apparatus Required:
1. Voltmeter
2. Resistances
3. Bread board
4. Ammeter
5. DC voltage source
Theory:
Thevenins Theorem:
This theorem states that a network composed of lumped, linear circuit elements may , for the
purposes of analysis of external circuit or terminal behaviour, be replaced by a voltage source
V(s) in series with a single impedance.
Thevenins theorem simplifies the method of finding current through any specified branch. For this
purpose we have to find two things:
1. Thevenins Resistance Rth
2. Thevenins Voltage Vth
-
MULTISIM / NETWORKS LAB
GRIET/EEE 5
Circuit Diagram:
Theoretical Calculations:
To find current through 1k ohm resistor using Thevenins theorem:
1) To find Thevenins resistance (Rth) across 1k ohm resistor:
R1
2.2k
R2
2.2k
0
1
Rth = (2.2* 2.2)*106/ (2.2+2.2)(10)
3= 1.1k ohm
2) To find Thevenins voltage (Vth) across 1k ohm resistor:
R1
2.2k
R2
2.2k
1
V110 V
2
00
I=10/4.4*10
3 =2.27mA
-
MULTISIM / NETWORKS LAB
GRIET/EEE 6
Applying KVL,
-10 + (2.2*103*2.27*10
-3) +Vth =0
Vth=5.006V Thevenins equivalent circuit is:
R1
1.1k
V15.006 V
2
0
1
Finding current through 1k ohm resistor using Thevenins theorem,
R1
1.1k
R2
1k
V15.006 V
2
0 0
3
It=5.006/ (2.1*103) = 2.38 mA
Current through 1k ohm resistor is 2.38mA.
Hence Thevenins theorem is verified.
Procedure:
A) Thevenins procedure
1. Remove the resistor R5.4. Remove the voltage source and short the terminals 2, 4.
5. Resistance measured between 1, 3 is Thevenins resistance.
6. Thevenin equivalent circuit is obtained by connecting Vth and Rth in series.
7. Connect the resistance 1K in series with Thevenin equivalent circuit and measure current across the load
8. Verify the current measured in Thevenin equivalent circuit and original circuit.
Observations:
Thevenins Voltage (Vth) =
-
MULTISIM / NETWORKS LAB
GRIET/EEE 7
Thevenins Resistance (Rth) =
Load Current (IL) =
Multisim Results:
Thevenins Voltage (Vth) =
Thevenins Resistance (Rth) =
Load Current (IL) =
Theoretical Calculations to be done by Students:
-
MULTISIM / NETWORKS LAB
GRIET/EEE 8
Result:
1. Thevenins theorem is verified.
-
MULTISIM / NETWORKS LAB
GRIET/EEE 9
2. Nortons Theorem
Aim:
To construct a circuit and verify Nortons Theorem for the given circuit.
Apparatus Required:
1. Voltmeter
2. Resistances
3. Bread board
4. Ammeter
5. DC voltage source
Theory:
Nortons Theorem:
Any linear circuit containing several energy sources and resistance can be replaced by a single constant generator in
parallel with a single resistor.
Circuit diagram:
R1
100
R2
150
R351
V110 V
1
3
2
-
MULTISIM / NETWORKS LAB
GRIET/EEE 10
Nortons procedure:
1. Remove the resistance R2.
2. Insert an ammeter across the open terminals.
3. Measure the resistance between the terminals replacing 10v DC source with a short let us say this equals
Rn (Nortons resistance)
4. Construct an equivalent circuit and verify the current across the load in both circuits.
Theoretical calculations:
R1
100
R2
150
R351
V110 V
1
3
2
STEP 1:
Finding R equivalent:
To find R
R1
100
R251
0
1
-
MULTISIM / NETWORKS LAB
GRIET/EEE 11
Req= (100*51)/151
=33.77ohm
STEP 2:
To find IN:
R1
100
R251
V110 V
1 4
Since there is a short circuit path across R2, so current will not pass through R2, R2 can be neglected.
IN=10/100=0.1A
I10.1 A
R133.77 R2
150
1
2
I150= (0.1)*(33.77/33.77+150)
=0.0183A
Observations:
Nortons Current (IN) =
-
MULTISIM / NETWORKS LAB
GRIET/EEE 12
Nortons Resistance (RN) =
Load Current (IL) =
Multisim Results:
Nortons Current (IN) =
Nortons Resistance (RN) =
Load Current (IL) =
Theoretical Calculations to be done by Students:
-
MULTISIM / NETWORKS LAB
GRIET/EEE 13
Result:
Nortons theorem is verified.
-
MULTISIM / NETWORKS LAB
GRIET/EEE 14
-
MULTISIM / NETWORKS LAB
GRIET/EEE 15
3. Maximum Power Transfer Theorem
Aim:
1. To construct a circuit and verify Maximum Power transfer Theorem for the given circuit.
Apparatus Required:
1. Voltmeter
2. Resistances
3. Bread board
4. Ammeter
5. DC voltage source
Theory:
Maximum Power transfer theorem:
Maximum power transfer theorem states that the power delivered from a source to a load is maximum when source
resistance equals load resistance.
Circuit Diagram:
V110 V
R1
2.2k
RL
R32.2k
1 a
0
Procedure:
Maximum Power transfer theorem
-
MULTISIM / NETWORKS LAB
GRIET/EEE 16
1. Construct the circuit.
2. Connect the circuit with different loads.
3. Note down the power delivered to load and voltage.
4. Verify the resistance at which maximum power is delivered is equal to R1.
Observations:
For Maximum power transfer:
S.No V(volts) I(mA) Power delivered
To load VI
R(load) V2/4RL
1. 2.381 2.381 5.66m 1k
2. 2.5 2.273 5.68m 1.1k 5.68
3. 3.33 1.515 5.04m 2.2k
4. 1.687 3.012 5.08m 2.2k
5. 0.417 4.167 1.73m 100
6. 4.051 0.863 3.49m 4.7k
Maximum power transfer calculations:
Load current= I= VS / (RN + RL)
-
MULTISIM / NETWORKS LAB
GRIET/EEE 17
P= Power delivered to load = (VS / (RN + RL)) 2 RL
Maximum power transferred = V2/4RL
STEP1:
To find equivalent resistance across ab (Rab)
1.Rab is found out by shorting the voltage source and calculating resistance across a&b.
Rab= ((2.2K)//(2.2k))/94.4k)
=1.1k
STEP 2:
Finding VTH
1. VTH is the voltage across a&b.
V210 V
R5
2.2k
R62.2k
2
4
0
R2
2.2k
R42.2k
3
0
-
MULTISIM / NETWORKS LAB
GRIET/EEE 18
Voltage across ab is VTH
Current through 2.2k=10/ (2.2+2.2) k
=2.27mA
VTH= (2.2k)*(2.27m)
=5V
Therefore, VTH=5V
Maximum power transfer occurs when RL=Rab=1.1K
Power transferred = (VTH*VTH)/ (4*RL)
=25/ (4*1.1k)
=0.00568W.
Also, V*I= (2.5)*(2.2727m)
=0.00568W
Therefore VI= (VTH*VTH)/ (4*RL)
Hence maximum power transfer theorem is verified.
Theoretical calculations to be done by students:
-
MULTISIM / NETWORKS LAB
GRIET/EEE 19
-
MULTISIM / NETWORKS LAB
GRIET/EEE 20
Result:
Maximum power transfer theorem is verified.
-
MULTISIM / NETWORKS LAB
GRIET/EEE 21
-
MULTISIM / NETWORKS LAB
GRIET/EEE 22
4. Super position Theorem and Reciprocity Theorem.
Aim:
1. To construct a circuit and verify Super position Theorem for the given circuit.
2. To construct a circuit and verify Reciprocity Theorem for the given circuit.
Theory: A) Super position Theorem:
In any linear network containing two or more sources response in any element is equal to the algebraic
sum of responses caused by individual sources acting while the other sources are inoperative.
The word inoperative means a voltage source is replaced by a short circuit while the current source
replaced by open circuit.
B) Reciprocity Theorem:
In a circuit having several branches, if a source of voltage V produces a current I in another branch, the
same current I will flow in the first branch if voltage source is put in the second branch. That means
voltage source and ammeter can be interchanged but the ammeter reading will remain unaltered.
Circuit Diagram:
A) Super position Theorem:
.
B) Reciprocity Theorem:
R1
2.2k
R2
4.7k
R3 3.3k
V1 10 V
1
V2 8 V
10
0
2
-
MULTISIM / NETWORKS LAB
GRIET/EEE 23
R13.3k
R2
2.2k
R31.0k
R4
10k
R54.7k
V110 V
2 3
4
0
U1DC 1e-0090.099m A
+
-
5
6
Procedure:
Superposition:
1. First measure the current through R5 due to source V1 while source V2 is replaced with short circuit. Let
this current be Iv1.
2. Next measure current through R5 due to source V2 while source V1 is replaced with short circuit.
3. Let this current be Iv2.
4. Now let both sources be in place. The current through R5 is measured once again. Let this current be I.
5. Verify whether I= Iv1+Iv2.
Reciprocity:
1. Construct the circuit given.
2. Measure the current in the R5.
3. Now replace ammeter with voltage source and voltage source with ammeter measure the current in R3.
4. Compare both readings.
-
MULTISIM / NETWORKS LAB
GRIET/EEE 24
Observations:
1) Superposition theorem:
V1
(volts)
V2
(volts)
R1
(ohms)
R2
(ohms)
R3
(ohms)
I1
(mA)
I2
(mA)
I3.3k
=
I3.3k
(mA)
10 2 2.2k 4.7k 3.3k 1.4194 0.5316 1.951
2) Reciprocity Theorem Experiment:
R1
(kohms)
R2
(kohms)
R3
(kohms)
R4
(kohms)
R5
(kohms)
Vs
(volts)
I
(mA)
I
(mA)
Vs/I
(kohms)
Vs/I
(kohms)
3.3 2.2 1 10 4.7 10 0.09 0.09 111.11 111.111
Theoretical calculations:
1) Superposition theorem:
-
MULTISIM / NETWORKS LAB
GRIET/EEE 25
Consider 10V D.C. voltage source and replace 8V D.C. voltage source with short circuit.
R1
2.2k
R2
4.7k
R33.3k
V110 V
1
U2DC 1e-0091.419m A
+
-
4
2
0
Total resistance, RT = (4.7k||3.3k) +2.2k
=4.139 kohms.
Total current, I = 10 / RT
=10 / 4.139
=2.416 mA.
The current through 3.3kohm resistor is,
I= I x 4.7k / (4.7k + 3.3k)
= 2.416 x 4.7 / 8k
R1
2.2k
R2
4.7k
R3 3.3k
V1 10 V
1
V2 8 V
10
0
2
-
MULTISIM / NETWORKS LAB
GRIET/EEE 26
= 1.4194 mA.
Now, consider 8V D.C. voltage source and replace 10V D.C. voltage source by short circuit.
R42.2k
R53.3k
R6
4.7k
V28 V
5
U1DC 1e-0090.531m A
+
-
7
0
8
Total resistance, RT = (2.2k || 3.3k) + 4.7k
= 6.02 kohms.
Total current, I = 8 / 6.02k
= 1.3289 mA.
The current through 3.3kohm is,
I2 = 1.3289mA x 2.2k / 5.5k
= 0.5316 mA.
Therefore, the total current passing through 3.3kohm
I3.3k = I1 + I2
=1.4194 + 0.5316
= 1.951 mA.
Now consider both the voltage sources,
V
-
MULTISIM / NETWORKS LAB
GRIET/EEE 27
V310 V V4
8 V
R7
2.2k
R83.3k
R9
4.7kU3DC 1e-0091.950m A
+
-
3 9
11
6
0
Applying nodal analysis,
(V 10)/2.2k + V/3.3k + (V-8)/4.7k =0
Therefore, V = 6.4388V.
The current through 3.3kohm resistor is,
I3.3k = V / 3.3k
= 6.4388 / 3.3k
= 1.9512mA.
HENCE PROVED.
2) Reciprocity theorem:
V
-
MULTISIM / NETWORKS LAB
GRIET/EEE 28
Applying nodal analysis,
V /5.5k + V/1k + (V 10)/14.7k =0
V = 0.54V.
The current I in the 3.3kohm resistor branch is,
I = V / 5.5k = 0.54/5.5k =0.09mA.
Now, the reciprocal circuit to the above circuit is,
V
R1 3.3k
R2
2.2k
R3 1.0k
R4
10k
R5 4.7k
V1 10 V
2 3
4
0
U1 DC 1e-009 0.099m A
+
-
5
6
-
MULTISIM / NETWORKS LAB
GRIET/EEE 29
U1DC 1e-0090.099m A
+
-
V110 V
R13.3k
R2
2.2k
R31.0k
R4
10k
R54.7k
1
2 3
46
0
Applying nodal analysis,
(V 10) / 5.5k + V / 1k + V / 14.7k =0
V = 1.45V.
The current I in the branch is,
I = V / R = 1.45 / 14.7k = 0.09mA.
HENCE PROVED.
Bread Board Results:
1) Superposition theorem:
V1
(volts)
V2
(volts)
R1
(kohms)
R2
(kohms)
R3
(kohms)
I1
(mA)
I2
(mA)
I3.3k
=
I3.3k
(mA)
10 8 2.2k 4.7k 3.3k 1.42 0.5 1.92
-
MULTISIM / NETWORKS LAB
GRIET/EEE 30
2) Reciprocity theorem:
Vs
(volts)
I
(mA)
I
(mA)
Vs / I
(kohms)
Vs / I
(kohms)
10 0.1 0.1 100 100
Multisim Results:
1) Superposition theorem:
V1
(volts)
V2
(volts)
R1
(kohms)
R2
(kohms)
R3
(kohms)
I1
(mA)
I2
(mA)
I3.3k = I3.3k
(mA)
10 8 2.2 4.7 3.3 1.419 0.531 1.95
2) Reciprocity theorem:
Vs
(volts)
I
(mA)
I
(mA)
Vs / I
(kohms)
Vs / I
(kohms)
10 0.099 0.099 101.01 101.01
Theoretical Calculations to be done by Students:
-
MULTISIM / NETWORKS LAB
GRIET/EEE 31
-
MULTISIM / NETWORKS LAB
GRIET/EEE 32
-
MULTISIM / NETWORKS LAB
GRIET/EEE 33
-
MULTISIM / NETWORKS LAB
GRIET/EEE 34
Result:
1. Superposition theorem is verified for the given circuit.
2. Reciprocity Theorem is verified for the given circuit.
-
MULTISIM / NETWORKS LAB
GRIET/EEE 35
5. Z and Y Parameters
Aim:
To find z & y parameters of a given two port network.
Apparatus:
1. DC voltage source.
2. Resisters. (100, 47, 220, 680, 560).
3. Voltmeter.
4. Ammeter.
5. Breadboard.
Theory:
Networks having two terminals designated as input terminals and two terminals designated as output terminals are
called Two Port Networks. The set of input terminals is called INPUT PORT and the set of output terminals is
called OUTPUT PORT.
A two port network is described by V1, I1, V2, I2 and their inter relations are expressed by
Z parameters normally used in power systems.
Y parameters normally used in power systems.
ABCD parameters used in transmission lines.
H parameters electronics.
Z parameters
V1= Z11I1+Z12I2
V2= Z21I1+Z22I2
Y parameters
I1= Y11V1+Y12V2
I2= Y21V1+Y22V2
-
MULTISIM / NETWORKS LAB
GRIET/EEE 36
Circuit diagram:
R1
100
R2220
R3
47
R4
680
R5
560
V110 V
V210 V
1 2
3
5
6 0
Pocedure:
Determination of Z parameters
1. Connect a DC voltage source of 5v to the input and measure the current I1. Since I2 =0.
2. Using the same circuit we can determine Z21. For this value we have to measure V2
3. Note that even if a voltmeter is connected at the output there is no current at outputs as voltmeter has a very high
resistance. As I2 =0.
4. To determine Z12, I1must be zero. So do not connect anything at the input.
5. Connect a DC voltage source of 5V at the output and measure the voltage v1 since I1 = 0.
6. Using same circuit we can determine Z22. Since I1 = 0.
Determination of Y parameters
1. To determine Y11, V2 should be zero. So short the output terminals and measure input current
and input voltage. As V2 = 0
2. Using the same circuit we can determine Y21, Measure the short circuit current I2. As V2 =0.
3. To determine Y21, V1 should be zero. So short the terminals through an ammeter
-
MULTISIM / NETWORKS LAB
GRIET/EEE 37
4. Determine Y22, as V1 = 0, I2 = Y22V2
Theoretical calculations:
Z Parameters:
V1= Z11I1+Z12I2
V2= Z21I1+Z22I2
Step1: Open the output terminals.
V310 V
R6
100
R7220
R8
47
R9
560
R10
680
U1
DC 1e-009
0.011 A+ -
4
7
8
9
0
U2DC 10M2.500 V
+
-
11
12
I2=0A
I1=10/ (100+220+560) =0.01136A
V2=0.01136x220=2.42v
Z11=V1/I1=880
Z21=V2/I1=220
Step2: open the input terminals.
-
MULTISIM / NETWORKS LAB
GRIET/EEE 38
V310 V
R6
100
R7220
R8
47
R9
560
R10
680
9
0
U2DC 10M2.323 V
+
-
4
7
U1DC 1e-0090.011 A
+
-
8
10
11
I1=0A
V2=10V
I2=10/ (47+220+680)=0.0105567A
V1=0.01055x220=2.323V
Z12=V1/I2=220
Z22=V2/I2=947
Z21=Z12
Y Parameters:
I1= Y11V1+Y12V2
I2= Y21V1+Y22V2
Step1: Short the output terminals.
V310 V
R6
100
R7220
R8
47
R9
560
R10
680
9
0
U1DC 1e-0090.012 A
+
-
4
7
8
U2DC 1e-0092.803m A
+
-
10
11
V2=0V
V1=10V
-
MULTISIM / NETWORKS LAB
GRIET/EEE 39
Req = [(470+680)||220]+660=828.8
I1=10 / (828.8) =0.012A
I2= - (0.012x220)/ (220+727) = -0.0027A
Y11=I1/V1=0.0012mohs
Y21=I2/V1= -0.00027mohs
Step2: Short the input terminals.
V310 V
R6
100
R7220
R8
47
R9
560
R10
680
9
0
U1DC 1e-0090.011 A
+
-
8
10
11
U2
DC 1e-009
2.803m A+-
4
7
V1=0v
V2=10v
Req = [(100+560) ||220] +47+680
=892
I2= (10/892) =0.0112A
I1= - (0.0112x220) / (220+660) = -0.0028A
Y12=I1/V2= -0.00028mohs
Y22=I2/V2=0.000112mohs
Y12=Y21
Observations:
Z parameters:
-
MULTISIM / NETWORKS LAB
GRIET/EEE 40
V1(v) V2(v) I1(m A) I2(m A) Z11 (k ) Z21(k )
10.02 2.48 11.5 0 0.87 0.21
8 2.02 9.2 0 0.87 0.21
V1(v) V2(v) I1(m A) I2(m A) Z12 (k ) Z22(k )
2.3 10.02 0 10.6 0.22 0.96
2.75 12 0 12.5 0.22 0.96
Y Parameters
V1(V) V2(V) I1(m A) I2(m A) Y11(m mohs) Y21(m mohs)
10.02 0 12.4 - 2.8 1.2 -0.28
8 0 9.66 - 2.25 1.2 -0.28
V1(V) V2(V) I1(m A) I2(m A) Y12(m mohs) Y22(m mohs)
0 10.02 -2.8 11.4 -0.28 1.1
0 12 -3.4 13.9 -0.28 1.1
-
MULTISIM / NETWORKS LAB
GRIET/EEE 41
Using multisim: Z parameters:
V1(v) V2(v) I1(m A) I2(m A) Z11 (k ) Z21(k )
10 2.5 11.364 0 0.87 0.21
8 2 9.652 0 0.82 0.21
V1(v) V2(v) I1(m A) I2(m A) Z12 (k ) Z22(k )
2.323 10 0 10.56 0.219 0.95
2.78 12 0 12.67 0.219 0.95
Y Parameters
V1(v) V2(v) I1(m A) I2(m A) Y11(m mohs) Y21(m mohs)
10 0 12 2.802 1.2 0.28
8 0 9.652 2.22 1.2 0.28
V1(V) V2(V) I1(m A) I2(m A) Y12(m mohs) Y22(m mohs)
-
MULTISIM / NETWORKS LAB
GRIET/EEE 42
0 10 2.803 11 0.28 1.1
0 12 3.363 13 0.28 1.1
Theoretical Calculations to be done by Students:
-
MULTISIM / NETWORKS LAB
GRIET/EEE 43
-
MULTISIM / NETWORKS LAB
GRIET/EEE 44
-
MULTISIM / NETWORKS LAB
GRIET/EEE 45
Result:
Z and Y parameters are found for the given 2-port network.
-
MULTISIM / NETWORKS LAB
GRIET/EEE 46
6. Transmission and Hybrid Parameters.
Aim:
To find out the Transmission and Hybrid parameters of the given two port network.
Apparatus Required:
1. DC Voltage source.
2. Resistors.
3. Voltmeter.
4. Ammeter.
Theory: Networks having two terminals designated as input terminals and two terminals designated as output
terminals are called TWO PORT NETWORKS. The set of input terminals is called INPUT PORT and the set of
output terminals is called OUTPUT PORT.
A two port network is described by V1, I1, V2, I2 and their inter relations are expressed by
Z parameters normally used in power systems.
Y parameters normally used in power systems.
ABCD parameters used in transmission lines.
H parameters used in electronics.
Hybrid parameters:
V1=h11I1+h12V2
I2=h21I1+h22V2
Transmission parameters:
V1=AV2+BI2
I1=CV2+DI2
Procedure:
Hybrid parameters:
-
MULTISIM / NETWORKS LAB
GRIET/EEE 47
1. Input voltage V1 and output current are taken as dependent variables; these parameters are called Hybrid
Parameters.
2. Keeping the input terminals open I1 = 0 so V1 = h12V2
3. Using the same circuit h22 can be measured, as I1= 0, I2 = h22V2
4. To determine h12 output terminals are shorted through an ammeter as V2 = 0, V1 = h11I1
5. Same circuit can be used to determine h21 also V2 =0, I2 = h21I1
Transmission parameters:
1. A = V1/V2 is measured when receiving end is open circuited.
2. C = I1/V2 is also measured when receiving end is open circuited.
3. B = V1/ I2 is measured when receiving end is shorted.
4. D = I1/I2 is measured when receiving end is shorted.
Circuit Diagram:
Theoretical Calculations:
Hybrid parameters:
-
MULTISIM / NETWORKS LAB
GRIET/EEE 48
To determine the h parameters first short circuit output terminal
V1= 10V V2= 0
Req= [47||560] +100
=143.36 ohm
I1= 10/143.36= 0.06975A
I2= - (0.6975x560)/560+47
= -0.06435amps
h11=V1/I1 = 143.369
h21= I2/I1=-0.06435/0.06975= - 0.9225A
Now open input terminals
V1
12 V
R1
100
R2
47
R3560
1
U1DC 10M0.000 V
+
-
4
U2DC 1e-0090.000 A
+
-
2
3
0
V2=12V I1=0
-
MULTISIM / NETWORKS LAB
GRIET/EEE 49
I2= 12/607 = 0.0197A
v1= 560x0.0197= 11.070V
h12 =V1/V2 = 11.07/12 = 0.922
h22= I2/V2 = 0.0197/12 = 0.00164 mho
h12= - h21
Transmission parameters:
Open the output terminals:
I1= 10/660 = 0.015A
I2= 0A
V1= 10V
V2= 0.015x560
= 8.48V
A= V1/V2 = 10/8.48 = 1.179
C= I1/V2= 0.015/8.48 = 0.00176 mohs
Now short the output terminals
-
MULTISIM / NETWORKS LAB
GRIET/EEE 50
V1=10V V2=0V
Req = 146.36
I1= 10/143.36 = 0.06995A
I2= (- 0.0699x560)\ (560+47) = - 0.06434A
B= V1/I2 = 10/0.06434 = -155.423ohms
D = I1/I2 = 0.06975/0.06434 = - 1.0841
AD-BC= (1.179x1.0841)-(155.4x0.00176)
=1
Observations:
Hybrid parameters:
V1(v) V2(v) I1(mA) I2(mA) h12 h22( m mho)
11.06 12.02 0 19.28 0.92 1.6
10.15 11.01 0 18.5 0.92 1.6
-
MULTISIM / NETWORKS LAB
GRIET/EEE 51
V1(v) V2(v) I1(mA) I2(mA)
h11 ohm h21
10.02 0 69.8 -64.5 143.5 -0.92
5.01 0 34.5 -32.0 143.5 -0.92
Transmission parameters:
V1(v) V2(v) I1(mA) I2(mA) A C(m mohs)
10 8.49 15.3 0 1.178 1.8
5.01 4.25 7.6 0 1.178 1.8
V1(v) V2(v) I1(mA) I2(mA) B (mohms) D
10.01 0 69.8 -64.3 -0.155 -1.1
5.01 0 34.5 -32.0 -0.156 -1.1
Using Multisim:
Hybrid parameters:
V1(v) V2(v) I1(mA) I2(mA) h12 h22( m mho)
-
MULTISIM / NETWORKS LAB
GRIET/EEE 52
11.07 12 0 19.76 0.92 1.6
10.14 11 0 18 0.92 1.6
V1(v) V2(v) I1(mA) I2(mA)
h11 ohm h21
10 0 69.75 -64.35 143.5 -0.92
5 0 35 -32.0 143.5 -0.92
Transmission parameters:
V1(v) V2(v) I1(mA) I2(mA) A C(m mohs)
10 8.48 15.15 0 1.178 1.8
5 4.242 7.576 0 1.178 1.8
V1(v) V2(v) I1(mA) I2(mA) B (mohms) D
10 0 69.75 -64.35 -0.155 -1.1
5 0 35 -32.0 -0.156 -1.1
-
MULTISIM / NETWORKS LAB
GRIET/EEE 53
Theoretical Calculations to be done by Students:
-
MULTISIM / NETWORKS LAB
GRIET/EEE 54
-
MULTISIM / NETWORKS LAB
GRIET/EEE 55
-
MULTISIM / NETWORKS LAB
GRIET/EEE 56
Result:
Hybrid parameters, transmission parameters for the given circuit are determined.
-
MULTISIM / NETWORKS LAB
GRIET/EEE 57
7. Compensation and Millimans Theorems.
Aim:
1. Verify compensation theorem for a given network.
2. Verify Millimans theorem for a given network.
Apparatus Required:
1. Voltmeter
2. Resistances
3. Bread board
4. Ammeter
5. DC voltage source
Theory:
1) Compensation Theorem:
It states that in any linear bilateral network, any element can be replaced by voltage source of magnitude equal to
current through the element multiplied by value of element provides currents and voltages in another part
of circuit remain unaltered.
Consider the network as shown in figure.
-
MULTISIM / NETWORKS LAB
GRIET/EEE 58
In the above circuit, the resistance R, can be replaced by a voltage source at value
IR
2) Millimans Theorem: Millimans theorem states that in any linear active bilateral network consisting of no of voltage sources which are in
parallel and are in series with their internal resistances then this entire system of circuit can be replaced by a single voltage source in series with a single resistance.
Let us consider the circuit shown below consisting of no of voltage sources V1,V2,V3............Vn are in series with
their internal resistances r1,r2,r3..........rn can be reduced into a single circuit with a voltage source V and the
resistance R as shown in the figure b.
Fig (a)
-
MULTISIM / NETWORKS LAB
GRIET/EEE 59
fig (b)
Circuit Diagram:
1) Compensation Theorem:
R1
3.3k
R2
2.2k
R31k
V112 V
1 3
0
Fig (1)
R1
3.3k
R2
2.2k
R31k
V112 V
1 3
R41.1k
0
2
Fig (2)
-
MULTISIM / NETWORKS LAB
GRIET/EEE 60
R1
3.3k
R2
2.2k
R31k
3 R41.1k
2
V11.03 V
1
0
Fig (3)
2) Millimans Theorem:
V110 V
V212 V
R1100
R2470
R356023
1
0
Fig (4)
Procedure:
1) Compensation Theorem:
1. Consruct the circuit as shown in figure.
2. Note the ammeter reading I1
3. Modify the circuit in fig (1) as fig (2) and replace R2 with R2+R and voltage source
V=I1-R.
4. Note the ammeter reading I2
5. Construct the circuit as in fig (3) and note the ammeter reading I3
-
MULTISIM / NETWORKS LAB
GRIET/EEE 61
6. Tabulate the above readings by repeating the experiment for 5 sets of resistor values.
2) Milimans Theorem:
1. Connect the circuit as shown in fig (a).
2. An ammeter is connected in series with the load resistance R3 and the corresponding load current I1 (IL) is
determined.
3. The circuit is reduced into the equivalent form of thevenins voltage with a resistor of Rth.
4. Now the current across the load is measured as Il.
5. If the currents Il & Il are equal then the millimans theorem is verified.
Observations:
1. Compensation theorem:
Theoretical Calculations:
From fig (1):
R1
3.3k
R21k
R3
2.2k
13
0
Req = (3.3+0.688)*1000
= 3.98 k ohms
I = V/R = 12/3.98k
= 3.009 mA
I1 = I (1/1+2.2)
= 3.009*(1/3.2)
= 0.94 mA
-
MULTISIM / NETWORKS LAB
GRIET/EEE 62
To find I2 add R =1k ohm
From fig (2):
Req = ((3.3*1/1+3.3)+3.3)*1000
= (0.767+3.3)*1000
= 4.067 k ohms
I = V/R
= 12/4.067*1000
= 2.95 mA
I2 = I (1/1+3.3)
= 2.95 * 0.233
= .686 mA
I = I1 I2
= 0.94 0.686
= 0.253 mA
VERIFICATION:
From fig (3):
V = I *R
= 0.94*1.1
=1.03 volts
Req = (((2.2+1.1)1/2.2+1.1+1)+3.3)*1000
= (3.3/4.3)+3.3
= 4.067 k ohms
I = V/R
-
MULTISIM / NETWORKS LAB
GRIET/EEE 63
= 1.03/4.067
= 0.253 mA
Both currents are equal
Hence compensation theorem is verified.
Bread board results:
Multisim Results:
V R1 R2 R3 I1
(A)
R V=I1.R I2 (A) I3 (A) I1-I2
(A)
12
12
12
3.3k
1k
560
2.2k
3.3k
100
1k
2.2k
100
0.941
2.069m
9.836m
1.1k
1.1k
470
0.99
2.276
4.622
0.686
1.622m
2.776m
0.255
0.446
7.057
0.255
0.447
7.060
12
12
100
2.2k
560
1k
470
560
0.015
1.683m
100
100
1.5
0.168
13m
1.575m
2.02m
0.109
2m
0.108
V R1 R2 R3 I1
(A)
R V=I1.R I2 (A) I3 (A) I1-I2
(A)
-
MULTISIM / NETWORKS LAB
GRIET/EEE 64
2. Millimans theorem:
Theoretical calculations:
From fig (4):
Applying K.C.L,
(V-10)/100 + (V-12)/470 +V/560 = 0
V(1/100 + 1/470 + 1/560) = (10/100 +12/470)
V(0.01 + 0.002 + 0.002) = 0.1+0.026
V(0.014) = 0.126
V = 9 volts
I = V/R
= 9/560
= 0.016A
12
12
12
3.3k
1k
560
2.2k
3.3k
100
1k
2.2k
100
0.941
2.069m
9.836m
1.1k
1.1k
470
0.99
2.276
4.622
0.686
1.622m
2.776m
0.255
0.446
7.057
0.255
0.447
7.060
12
12
100
2.2k
560
1k
470
560
0.015
1.683m
100
100
1.5
0.168
13m
1.575m
2.02m
0.109
2m
0.108
-
MULTISIM / NETWORKS LAB
GRIET/EEE 65
Using millimans theorem,
R=1/ (G1+G2)
= 1/ ((1/100) + (1/470))
= 1/ (0.01+0.002)
= 83.3 ohms
V= (V1G1 +V2G2)/ (G1+G2)
= ((10/100) + (12/470))/ (0.012)
= 0.126/0.012
= 10.5 volts
R283.3
R3560
V110.5 V
1
2
3 I = V/Req
= 10.5/ (83.3+560)
= 0.016A
Both currents are equal, Hence millimans theorem is verified.
Breadboard results:
-
MULTISIM / NETWORKS LAB
GRIET/EEE 66
V1
(V)
V2
(V)
R1 R2 R3 I
(mA)
I
(mA)
V
(V)
R
10 12 100 470 560 16.2 16.1 10.5 82.46
Multisim results:
V1
(V)
V2
(V)
R1 R2 R3 I
(A)
I
(A)
V
(V)
R
10 12 100 470 560 0.016 0.016 10.5 82.46
Theoretical Calculations to be done by Students:
-
MULTISIM / NETWORKS LAB
GRIET/EEE 67
-
MULTISIM / NETWORKS LAB
GRIET/EEE 68
-
MULTISIM / NETWORKS LAB
GRIET/EEE 69
-
MULTISIM / NETWORKS LAB
GRIET/EEE 70
Result:
1. Compensation Theorem is verified. 2. Millimans Theorem is verified.
-
MULTISIM / NETWORKS LAB
GRIET/EEE 71
8. Series Resonance
Aim:
1. To observe the resonance and calculate resonant frequency, band width, quality factor in series resonance
circuit.
Apparatus Required:
1. AC voltage source.
2. Resistor.
3. Inductor.
4. Capacitor.
5. Voltmeter
Theory:
Series Resonance:
As the frequency is varied in a RLC circuit maximum current is observed at a particular frequency. This
phenomenon is called series resonance. Also referred to as current resonance. Z
Circuit Diagram:
A) Series Resonance:
R1
100
L1
10mH V1
4 V
50 Hz
0Deg C1 .100u
U1
DC 10M
0.000 V + -
U2
DC 10M
0.000 V + -
U3 DC 10M 0.000 V
+
-
1 2 3
0
-
MULTISIM / NETWORKS LAB
GRIET/EEE 72
Procedure:
A) Series Resonance:
1. Connect resistor, inductor and capacitor in series.
2. Using the formula.
r=1/ (2LC)
Calculate resonant frequency.
3. Note down current through the circuit, Voltage across (VR ), Voltage across Inductor (VL),Voltage across
capacitor (Vc)
4. Plot the graph Current Vs Frequency and Impedance Z Vs Frequency.
5. Plot the graph VRVs Frequency, VLVs Frequency and VCVs frequency.
6. From the graph note down the frequency at which Vc is maximum (Fc), the frequency at which Vr is maximum
(Fr) and the frequency at which Vl is maximum (Fl).
It is observed that Vc becomes maximum at a frequency lower than the resonant frequency and Vl becomes
maximum at a frequency more than the resonant frequency.
7. Frequency at which Vc becomes maximum can be calculated using the formula.
c=1/2 ((1/LC)-(R*R/2L)) 1/2
Frequency at which Vl becomes maximum can be calculated using the formula.
l=1/2 ((1/LC)-(R*R*C*C)/2)1/2
Verify with observed values.
8. On the graph current Vs frequency, note down the maximum current.Calaculate 70.7% of this current and draw a
horizontal line corresponding to this value on the graph. Note down the values at which this horizontal line
intersects the curve (f1 and f2).
9. The average of frequencies f2-f1 is called Band Width (BW).
10. fr/BW is known as Q (quality factor).
-
MULTISIM / NETWORKS LAB
GRIET/EEE 73
Calculate Q using Q=BW/fr and also Q=Xlr/R
=2frl/R Where Xlr is reactance of inductor at resonant frequency.
11. Voltage across capacitor =IXc=V/rCR=VrL/R=QV.
Calculate the ratio of voltage across Capacitor to applied voltage. Observe that ratio (amplification) is
=Q.High Q coils are sometimes used to produce high voltages.
-
MULTISIM / NETWORKS LAB
GRIET/EEE 74
OBSERVATION:-
S.NO: FREQUENCY
(hz)
APPLIED
VOLTAGE
Va(volts)
Vr (volts) VL (volts) Vc (volts) CURRENT (I)
(amps)
1 50 4 3.8 0.12 1.21 0.038
2 100 4 3.96 0.24 0.65 0.0389
3 150 4 4 0.38 0.43 0.039
4 159.2 4 4 0.4 0.396 0.04
Practical
Values
Multisim
Values
1
2
3
4
-
MULTISIM / NETWORKS LAB
GRIET/EEE 75
GRAPHS:-
CURRENT~FREQUENCY :-
-
MULTISIM / NETWORKS LAB
GRIET/EEE 76
CAPACITOR VOLTAGE~FREQUENCY:-
INDUCTOR VOLTAGE~FREQUENCY:-
-
MULTISIM / NETWORKS LAB
GRIET/EEE 77
-
MULTISIM / NETWORKS LAB
GRIET/EEE 78
-
MULTISIM / NETWORKS LAB
GRIET/EEE 79
-
MULTISIM / NETWORKS LAB
GRIET/EEE 80
-
MULTISIM / NETWORKS LAB
GRIET/EEE 81
RESULT:-
1. Resonant frequency=159.2 Hz
2. Band Width=1575 Hz
3. Quality Factor=0.101
-
MULTISIM / NETWORKS LAB
GRIET/EEE 82
9. Parallel Resonance
Aim:
To observe the resonance and calculate resonant frequency, band width, quality factor in parallel resonance
circuit
Apparatus Required:
1. AC voltage source.
2. Resistor.
3. Inductor.
4. Capacitor.
5. Voltmeter
Theory:
Parallel Resonance:
As the frequency is varied in a RLC circuit maximum voltage is observed at a particular frequency. This
phenomenon is called Parallel resonance. Also referred to as voltage resonance.
Circuit Diagram:
Parallel Resonance
-
MULTISIM / NETWORKS LAB
GRIET/EEE 83
R110k
R2
100
L110mH
C110uF
XMM1
XMM2
2
V2
10 Vrms
50 Hz
0
1
3
Procedure:
Parallel Resonance:
1. Connect a voltmeter across the parallel combination and note down voltage as frequency is gradually increased.
You will note that voltage will be maximum at a certain frequency. This frequency is known as resonant frequency.
Note down the voltage across series resistor.
2. Note down the maximum value of voltage and mark a horizontal line at 0.707 times Vmax. At the points of
intersection mark f1 & f2 known as half power frequencies.
S.NO FREQUENCY
(HZ)
APPLIED
VOLTAGE
(Va)volts
Vr
(volts)
Vout
(volts)
I=Vr/r
(AMPS)
Z=V/I
(ohms)
1
2
3
4
5
503
550
450
350
300
10
10
10
10
10
1.515
4.52
5.315
8.963
9.467
8.485
7.657
7.271
3.806
2.764
0.01515
0.0452
0.05315
0.08963
0.09467
560.066
169.402
136.8
42.463
29.196
-
MULTISIM / NETWORKS LAB
GRIET/EEE 84
CALCULATIONS:
Fr = (1/ (2lc))
=1/ (2*10*10*10-9)
Fr =503.292 hz
Xl=j31.16
Xc=-j31.162.
3. Draw the curves
Vout Vs frequency
I Vs frequency
Z Vs frequency.
4. Calculate Half power frequencies f1 and f2 using the formula.
1=-1/2RC+ [(1/2RC) 2 +1/LC] 1/2 (Lower Half power Frequency)
2=1/2RC+ [(1/2RC) 2 +1/LC] 1/2 (Upper Half power Frequency).
5. Band Width = 2- 1=1/RC.
f2-f1=1/2RC.
Quality Factor=rRC.
Observations:
S.NO FREQUENCY
(HZ)
APPLIED
VOLTAGE
(Va)volts
Vr
(volts)
Vout
(volts)
I=Vr/r
(AMPS)
Z=V/I
(ohms)
-
MULTISIM / NETWORKS LAB
GRIET/EEE 85
1
2
3
4
5
-
MULTISIM / NETWORKS LAB
GRIET/EEE 86
-
MULTISIM / NETWORKS LAB
GRIET/EEE 87
-
MULTISIM / NETWORKS LAB
GRIET/EEE 88
-
MULTISIM / NETWORKS LAB
GRIET/EEE 89
-
MULTISIM / NETWORKS LAB
GRIET/EEE 90
-
MULTISIM / NETWORKS LAB
GRIET/EEE 91
-
MULTISIM / NETWORKS LAB
GRIET/EEE 92
-
MULTISIM / NETWORKS LAB
GRIET/EEE 93
RESULT:
Parallel Resonance is verified
-
MULTISIM / NETWORKS LAB
GRIET/EEE 94
10. LOCUS OF CURRENT VECTOR IN AN R-L CIRCUIT
CONTENT:
In this experiment you will learn that current vector leads the applied voltage and the tip of the current vector describes a semi circle when one of the components (R or L) is
varied from zero to infinity.
CIRCUIT 1:An RL circuit is shown below:
v
current I =--------
R+jXL
V(R+JXL) V.R jVXL
-------------------- = ---------- + -------------
R2+XL
2 R
2+XL
2 R
2+XL
2
Z=( R2+XL
2)
1/2
-
MULTISIM / NETWORKS LAB
GRIET/EEE 95
VR jVXL
SO I= ----- + --------- =Ix+jIy say
Z2 Z
2
Two cases arises:
a) Keep XL constant and vary R (different resistors used) b) Keep R constant and vary Xl (different inductors used )
In either case tip of the current vector describes a semi circle.
PROCEDURE:
CIRCUIT 1:
-
MULTISIM / NETWORKS LAB
GRIET/EEE 96
These are three methods to draw the locus
METHOD 1:
Using a multimeter in AC voltage range, note down voltage applied, voltage across resistor and voltage across capacitor. Keeping resistor constant and for various values of
capacitor, note down meter readings and fill up the following table:
Keeping C constant, use values of R and note down Vapplied, Vr and VL producing a table
similar to above.
S.No Vapplied Vr VL
1
2
3
4
5
-
MULTISIM / NETWORKS LAB
GRIET/EEE 97
For each set of readings a triangle can be constructed using a compass as shown. All the points
such as A, B etc., lie on a semi circle.
METHOD 2:
Connect oscilloscope channel 1 and channel 2 as shown in circuit 1.
The wave forms are as shown below when the oscilloscope is kept in dual mode.
-
MULTISIM / NETWORKS LAB
GRIET/EEE 98
The time delay between the two waves is t. T is the period. Both t and T are noted for each value
of capacitor. The angle between the two wave forms is
a = t*360/T
Measure also magnitudes Va and Vl from the oscilloscope. Draw the triangle as shown. Different
triangles can be constructed for different values of capacitor. Tips of all such triangles fall on a
semi circle.
METHOD 3:
-
MULTISIM / NETWORKS LAB
GRIET/EEE 99
Third method uses Lissazous figure to measure angle between the applied voltage and voltage across resistor Vr.
By making connections as above, channel 1 displays the applied voltage and channel 2 displays
the voltage across the resistance.
If we select dual-trace option Va and Vr are displayed simultaneously and the time lag between
the two can be measured and converted to angle.
If we select XY option we can display the Lissazous figure and angle can be obtained using the
formula
Y1 X1
Sina = ----- = ------
Y2 X2
-
MULTISIM / NETWORKS LAB
GRIET/EEE 100
AB is marked proportional to applied voltage. Using a protractor mark a line at an angle mark a
to AB. Mark the magnitude of voltage across resistance on this line to get the point P, join PB.
Using several values of resistor R repeat the experiment. It can be observed that for each resistor
value a different location for point P is obtained. It is also observed that all the points P1, P2,
P3. Fall on a semi circle.
-
MULTISIM / NETWORKS LAB
GRIET/EEE 101
Take reading as shown below
S.NO Vr Vs X1 X2 Y1 Y2 sina=Y1/Y2 a
1 4 2.2 2 2.2 3.6 4 0.9089 65.39
2 4 2 1.8 2 3.6 4 0.8995 64.1
3 4 1.6 1.6 1.6 3.6 4 1 90
4 4 0.6 1 1.2 3.8 4 0.8332 56.43
NOTE:
All the above three methods can be used to obtain the locus of current vector in the case where
capacitor value is kept unchanged and various values of resistors are used.
Also note that the current vector in this experiment is actually represented by voltage across the
resistor to scale.
-
MULTISIM / NETWORKS LAB
GRIET/EEE 102
-
MULTISIM / NETWORKS LAB
GRIET/EEE 103
11. LOCUS OF CURRENT VECTOR IN AN R-C CIRCUIT
CONTENT:
In this experiment you will learn that current vector leads the applied voltage and the tip of the current vector describes a semi circle when one of the components (R or C) is
varied from zero to infinity.
CIRCUIT 1:
An RC circuit is shown below:
V
current I =--------
R+jXc
V(R+JXc) V.R jVXc
-------------------- = ---------- + -------------
R2+Xc
2 R
2+Xc
2 R
2+Xc
2
Z=( R2+Xc
2)
1/2
-
MULTISIM / NETWORKS LAB
GRIET/EEE 104
VR jVXc
SO I= ----- + --------- =Ix+jIy say
Z2 Z
2
Two cases arise:
a) Keep Xc constant and vary R (different resistors used) b) Keep R constant and vary Xl (different capacitors used )
In either case tip of the current vector describes a semi circle.
PROCEDURE:
CIRCUIT 1:
-
MULTISIM / NETWORKS LAB
GRIET/EEE 105
These are three methods to draw the locus
METHOD 1:
Using a multimeter in AC voltage range, note down voltage applied, voltage across resistor and voltage across capacitor. Keeping resistor constant and for various values of
capacitor, note down meter readings and fill up the following table:
S.No Vapplied Vr Vc
1
2
3
4
5
Keeping C constant, use values of R and note down Vapplied, Vr and Vc producing a table
similar to above.
For each set of readings a triangle can be constructed using a compass as shown. All the points
such as A, B etc., lie on a semi circle.
-
MULTISIM / NETWORKS LAB
GRIET/EEE 106
METHOD 2:
Connect oscilloscope channel 1 and channel 2 as shown in circuit 1.
The wave forms are as shown below when the oscilloscope is kept in dual mode.
The time delay between the two waves is t. T is the period. Both t and T are noted for each value
of capacitor. The angle between the two wave forms is
a = t*360/T
-
MULTISIM / NETWORKS LAB
GRIET/EEE 107
Measure also magnitudes Va and Vl from the oscilloscope. Draw the triangle as shown. Different
triangles can be constructed for different values of capacitor. Tips of all such triangles fall on a
semi circle.
METHOD 3: Third method uses Lissazous figure to measure angle between the applied
voltage and voltage across resistor Vr.
By making connections as above, channel 1 displays the applied voltage and channel 2 displays
the voltage across the resistance.
If we select dual-trace option Va and Vr are displayed simultaneously and the time lag between
the two can be measured and converted to angle.
If we select XY option we can display the Lissazous figure and angle can be obtained using the
formula
Y1 X1
Sina = ----- = ------
Y2 X2
-
MULTISIM / NETWORKS LAB
GRIET/EEE 108
AB is marked proportional to applied voltage. Using a protractor mark a line at an angle mark a
to AB. Mark the magnitude of voltage across resistance on this line to get the point P, join PB.
Using several values of resistor R repeat the experiment. It can be observed that for each resistor
value a different location for point P is obtained. It is also observed that all the points P1, P2,
P3. Fall on a semi circle.
-
MULTISIM / NETWORKS LAB
GRIET/EEE 109
Take reading as shown below
S.NO Vr Vs X1 X2 Y1 Y2 sina=Y1/Y2 A
1 4 2.2 2 2.2 3.6 4 0.9089 65.39
2 4 2 1.8 2 3.6 4 0.8995 64.1
3 4 1.6 1.6 1.6 3.6 4 1 90
4 4 0.6 1 1.2 3.8 4 0.8332 56.43
NOTE:
All the above three methods can be used to obtain the locus of current vector in the case where
capacitor value is kept unchanged and various values of resistors are used.
Also note that the current vector in this experiment is actually represented by voltage across the
resistor to scale.
-
MULTISIM / NETWORKS LAB
GRIET/EEE 110
-
MULTISIM / NETWORKS LAB
GRIET/EEE 111
12.Measurement of 3-phase power by two wattmeter method for
unbalanced loads.
Objective:
Measurement of power by 2-wattmeters for unbalanced loads in a 3- phase circuit.
Apparatus:
32 Amps, 3 pole Fuse Switch
0 -300 W, U.P.F. Wattmeters
0 10 A, Ammeter
0-300 V, Voltmeter
Theory:
In a 3-phase, 3-wire system, power can be measured using two wattmeters for balance and
unbalanced loads and also for star, delta type loads. This can be verified by measuring the power
consumed in each phase. In this circuit, the pressures coils are connected between two phase
such that one of the line is coinciding for both the meters.
P1 + P2 = 3 VPh IPh COS
Power factor Cos = Cos (tan-1
3 ((P1 P2)/ (P1 +P2)))
Circuit diagram:
-
MULTISIM / NETWORKS LAB
GRIET/EEE 112
Observations:
Type of Load
(W)
W1
W
W2
W
I1
Ma
I2
mA
Vph
Volts
W1+
W2
KW
P
KW
R1=R2=R3=1K
R1+L1=1K+40m
R1+C1=1K+1uf
52.908
52.904
4.757
52.908
52.904
4.757
230.018
229.99
68.9
230.018
229.99
68.94
-
MULTISIM / NETWORKS LAB
GRIET/EEE 113
FOR UNNBALANCED LOADS:
TYPE OF LOAD
W1(W)
W2(W)
I1
(mA
I2
(mA
Vph
(V)
W1+W2
(W)
P
(KW)
R1=560,
R2=1K,
R3=220
R1+L1=560+1m,
R2+L2=1K+10m
R3+L3=220+20m
R1+C1=560+1uf
R2+C2=1K+1uf
R3+C3=220+10uf
2.832
94.746
2.832
77.802
240.393
77.802
594.456
410.746
594.456
71.169
1.045
71.169
TYPE OF LOAD
W1(W)
W2(W)
I1
(mA
I2
(mA
Vph
(V)
W1+W2
(W)
P
(KW)
-
MULTISIM / NETWORKS LAB
GRIET/EEE 114
-
MULTISIM / NETWORKS LAB
GRIET/EEE 115
Result:
Three Phase Power Measured by two wattmeter method for unbalanced load is
13. Measurement of Active and Reactive power by star and delta connected
balanced loads.
Objective:
Measurement of active and reactive power using 1-wattmeter at different R, L & C loads.
Apparatus:
Hardware: Name of the apparatus Quantity
32 Amps, 3 pole Fuse Switch 1 No
0 -300 W, U.P.F. Wattmeters 1 No
0 10 A, A.C Ammeter 1 No
0-300 V, A.C Voltmeter 1 No
-
MULTISIM / NETWORKS LAB
GRIET/EEE 116
Theory:
The active power is obtained by taking the integration of function between a particular time intervals
from t1 to t2
t2
P = 1/ (t2- t1) P (t) dt
t1
By integrating the instantaneous power over one cycle, we get average power.
The average power dissipated is
Pav = Veff[ Ieff cos]
From impedance triangle,
Cos = R/Z
Substituting, we get
Reactive Power Pr = Veff[ Ieff sin]
Active power measurement:
-
MULTISIM / NETWORKS LAB
GRIET/EEE 117
Reactive power measurement:
-
MULTISIM / NETWORKS LAB
GRIET/EEE 118
Procedure:
a) Connect the circuit as shown in the circuit diagram.
b) Keep all the toggle switches in ON condition.
c) Switch on equal loads on each phase i.e. balanced load must be maintained with different
load combinations.
d) Connect the ammeter in R-Phase and then switch OFF the toggle switch connected across
the ammeter symbol.
e) Connect the pressure coil of the wattmeter across R-Y phase and current coil in R-phase
to measure active power.
Observations:
Load: Balanced load
Active Power:
-
MULTISIM / NETWORKS LAB
GRIET/EEE 119
Type of load Vph
(Volts)
Il
(mA)
Pph
(Watts)
Pactual
P=3*Pph
(Watts)
Cos
=P/( 3VlIl )
R=10k 120.009 11.992 1.439 4.296 0.986
R-10k
C=1F
120.009 11.432 1.302 3.906 0.949
L=1mH
F
120.009 100 12 36 0.999
Reactive Power:
Type of the
load
Vph
(Volts)
Il
(mA)
Pph
(Var)
Pactual
P=3*Pph
(Var)
Cos
=P/( 3VlIl )
R=10k 120.009 11.992 4.150 12.45 0.9612
R-10k
C=1F
120.009 11.432 1.602 4.806 0.389
L=1Mh
F
120.009 99.647 9.4 28.287 0.788
-
MULTISIM / NETWORKS LAB
GRIET/EEE 120
Result: Active and Reactive powers were measured using 1-wattmeter at R, L and C Loads.
-
MULTISIM / NETWORKS LAB
GRIET/EEE 121
-
MULTISIM / NETWORKS LAB
GRIET/EEE 122
-
MULTISIM / NETWORKS LAB
GRIET/EEE 123
-
MULTISIM / NETWORKS LAB
GRIET/EEE 124
-
MULTISIM / NETWORKS LAB
GRIET/EEE 125
-
MULTISIM / NETWORKS LAB
GRIET/EEE 126
-
MULTISIM / NETWORKS LAB
GRIET/EEE 127
-
MULTISIM / NETWORKS LAB
GRIET/EEE 128
-
MULTISIM / NETWORKS LAB
GRIET/EEE 129
-
MULTISIM / NETWORKS LAB
GRIET/EEE 130