ECS LAB Manual - For Students PDF
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ANURAG GROUP OF INSTITUTIONS (Formerly CVSR College of Engineering) Venkatapur (V), Ghatkesar (M), Medchal Dist.
Department of Electrical and Electronics Engineering
MANUAL FOR ELECTRICAL CIRCUITS & SIMULATION LAB II B.TECH EEE – I I SEMESTER
Dept of EEE
1
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LIST OF EXPERIMENTS 1. Verification of KCL & KVL. 2. Verification of Thevenin’s theorems. 3. Verification of Norton’s and Maximum Power Transfer Theorems. 4. Verification of Superposition theorem. 5. Verification of compensation theorem. 6. Verification of Reciprocity and
Millman’s theorems.
7. Verification of Z and Y Parameters. 8. Verification of Transmission and Hybrid parameters. 9. Simulation of Mesh Analysis. 10. Simulation Simulation of Nodal Analysis.
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1. Verification of KCL & KVL Aim: To verify KCL and KVL circuits. Apparatus:
S.No 1. 2. 3. 4. 5. 6.
Equipment
Rating
0 – 30V / 2A R 1 R 2 R 3 0 – 30 V 0 – 200 mA
Regulated power supply Resistors Voltmeter Ammeter Connecting wires Bread board
Type
Quantity
Digital
1 no 3 no 3 no 3 no As required 1 no
Digital Digital
Circuit Diagrams:KCL:+
–
A
R1 0
0-200mA 0 0 m A
+
V
0 -2
+ -2
A
–
+ 0 0 m
A A
–
R2
–
R3
KVL:R1
R2
V2 –
V1 –
0-30V
0-30V
-
V
V3
R3
–
–
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Procedure:
1) Connect the circuit as shown in the circuit diagram for kcl 2) Switch on the power supply 3) Adjust the voltage from RPS 4) Note down the ammeter readings. 5) Bring RPS to zero and switch it off. 6) Switch on the power supply and Adjust the voltage from RPS for k kvl vl 7) Note down the voltmeter readings. 8) Bring RPS to zero and switch it off the power supply.
Theoretical Calculations:For KCL: I1
R1
I3
I2 V
+ R3
R2
–
I1=I2+I3 Req
=
R1 +
I 1
I 2
I 3
Dept of EEE
=
=
=
I 1 *
I 1 *
R2 * R3 R2 V
Req
+
R3
R3 R2
+
R3
R2 R2
+
R3
4
AGI
For KVL:-
V=V1+V2+V3 R eq =R 1+R 2+R 3 eq =R I
V =
Req
V1= I* R 1 V2= I* R 2 V3= I* R 3 R1
R2
R3
V
–
Tabular Column for KCL:
I1 (mA)
I2 (mA)
I3 (mA)
Theoretical Practical
Tabular Column for KVL:
V1 (v)
V 2 (v)
V3 (v)
Theoretical Practical
Result:
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2. Verification of Thevenin’s Theorem Aim: To verify Thevenin’s Theorem for given circuit . Theory:
Thevenin’s theorem replaced a complicated circuit with a constant voltage supply and resistance in series with it. The Thevenin’s Theorem states that “Any two terminals linear bilateral DC network can be replaced r eplaced by b y an equivalent circuit cir cuit consisting of a voltage source Vth in series with all equivalent resistance Rth”. (OR)
“The current through a Load Resistor “R” connected across any two points A&B of an active network, containing Resistors and one or more sources of emf ’s ’s is obtained by dividing the Potential Differences between A&B, with R disconnected by (R+r), where ‘r’ is the resistance of the network measured between point A&B , with ‘R’ disconnected and source of emf replaced by their internal Resistances” Vth → Open circuit voltage between the terminals t erminals of network. Rth →Equivalent resistance measured between terminals. When all energy sources are replaced by their internal resistances. Apparatus: S. No 1 2 3 4 5 6 7 8
Equipment DC.RPS. Voltage source. Resistors Variable Resister Ammeter-DC Voltmeter-DC Connecting wires Bread board DRB
Range 0-30V/2A R 1 R 2 R 3 1K Ω 0-200 mA 0-30V 1.0.Sq mm
1-10KΩ
Quantity 1 3 1 1 1 As required 1 1
Circuit Diagrams: Case (i): To find load current 0-200mA A R2
R1 V
+
–
RL R3
–
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+
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Case (ii): To find Thevenin’s voltage (Vth)
R2
R1
+ V + 0-30V V R3
–
–
Case (iii): To find Thevenin’s resistance (Rth)
R2
R1
–
A +
0-200mA V + R3
–
Case (iv): To find Thevenin’s equivalent circuit A +
Rth
–
0-200mA
+ Vth
RL
–
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Procedure:
1. Connect the circuit diagram for case (i). 2. Apply the DC voltage from RPS. 3. Note down the Load current (IL) from Ammeter. 4. Now remove Load Resistor (RL) & connect a Voltmeter. As per the circuit diagram shown in case (ii) and measure the Voltage (i.e. Vth) 5. Connect the circuit diagram as shown in case (iii) and note down the ammeter and voltmeter readings. Calculate R tthh 6. After getting the Vth & Rth ,Now make a circuit as in case (iv) and applying by Vth voltage and connecting Rth & keeping Load resistance ( RL) as it is in the original circuit and measure load current ((ILth) through (RL) by connecting a ammeter in series with ( RL). 8. Compare IL & ILth and observe that the both readings are equal Tabular Column:
Thevenin’s
Case-1 IL (mA)
Theorem
Case-2
Case-3
Case-4
Vth (volts)
Rth (Ω) Rth=V/I
ILth (mA)
Theoretical Values Practical Values Conclusion:- Case-1 and Case-4 must must be equal Theoretical Calculations:Case-1 REq = [R3 ║( R 2+R L)]+ R 1 IT =V / REq I L → IT x R3 ……mA R 3+R 2+R L
R2
R1 V
+ _
RL R3
Case-2:
Measuring the Thevenin’s Voltage → ( Vth ) ( Vth ) = V *
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R3 …………..Volts (R1 + R3)
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R2
R1 V
+
Vth R3
_
Case-3:
Measuring Thevenin’s Equivalent. Resistance → ( Rth ) For given circuit, by removing supply and shorting AB ( Rth ) = (R1 ║R3) + R2
R2
R1
Rth R3
Case 4: I LTH = Vth / (Rth+ RL)……mA A Rth
+
–
0-200mA + Vth
RL
–
Precautions:
1 Reading must be taken without parallax error. 2. Measuring instruments must be handled properly. 3. All connections should be free from loose contacts Result:
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3. Verification of Norton’s Theorem. Aim: To verify Norton’s Theorem for given circuit. Theory:
It is similar to Thevenin’s Theorem , while Thevenin’s Theorem based on the idea of equivalent source of emf. Norton’s theorem is based on the idea of an equivalent current source
Norton’s theorem replaces a complicated circuit with a constant current supply and resistance in parallel with it. network work can This theorem states that “Any two terminals linear bilateral DC net
be replaced by an equivalent ckt, consisting of a current source Isc in parallel with an equivalent resistance Rth.
Any arrangement of the source of emf ‘s and the resistance can be replaced by an equivalent current source in parallel with a resistance .The current from the source is the short circuit
current in the original system , and r is the equivalent resistance of the network between it’s two terminals, when all sources of emf’s are replaced by their internal resistances. Isc → Short circuit voltage between the terminals of network. Rth → Equivalent resistance measured between terminals. When all energy sources are replaced by their internal resistances Apparatus: S. No
Dept of EEE
Equipment
Range
Qty
1
DC.RPS Voltage source.
0-30V/2A
1
2
Resistors
R 1 R 2 R 3
3
3
Load Resistor
1K Ω
1
4
Ammeter-DC
0-200 mA
1
5 6
Connecting wires Bread board
1.00 Sq.mm
As required 1
7
DRB
1-10KΩ
1
10
AGI
Circuit Diagrams: Case (i): To find load current (IL) 0-200mA A + R1 V
–
R2
+
RL R3
–
Case (ii): To find Norton’s current (IN)
R2
R1
+ V +
0-200mA R3
–
IN
–
Case (iii): To find Norton’s resistance (R N)
R2
R1
–
A +
0-200mA V
R3
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+
–
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Case (iv): To find Norton’s Equivalent Circuit
0-200mA
RN
A +
–
+ V RN
–
RL
Procedure:
1. Connect the circuit as per the circuit cir cuit diagram. 2. Apply the DC voltage from RPS. 3. Note down the Load current (IL) from Ammeter. 4. Now remove Load Resistor ( RL) & connect the circuit as shown in case (ii) & apply proper voltage, and measure the current (ie IN) 5. Connect the circuit as shown in case (iii) and apply proper voltage & note down the voltmeter and ammeter readings. Calculate the Norton resistance. 6. After getting the IN & RN ,Now connect circuit as shown in case (iv) & applying IN Current source and connecting RN & keeping Load resistance (RL) as it is in the original circuit and measure load current ((ILN) through (RL) by connecting a ammeter in series with (RL). 7. Compare IL, & ILN and observe that the both readings are equal 8. In case of Current source not available, give equivalent DC Supply voltage (ie, I N * R N)
Tabular Column:
Norton’s Theorem
Case-1 IL (mA)
Case-2
Case-3
Case-4
IN (mA)
RN (Ω) RN=V/I
ILN (mA)
Theoretical Values Practical Values Conclusion: Case-1 & Case-4 must be equal
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Theoretical Calculations:-
Case.1 (same as Thevenin’s) REq = [R3 ║ ( R 2+R L)]+ R 1] IT =V / REq R
IL→
I LN
=
I T *
…….…mA
3
R2
+
R3
+
R L
R2
R1 V
+
RL R3
_
Case-2 Measuring the Norton’s current → ( IN )
( [R ] + R 2 3 1 R Eq ………. )…….Ω mA → → It = V║/ R IN → It * R3 …………….… mA R2+R3 R Eq
R2
R1 V
+
In R3
_
Case-3 Measuring Norton’s Equivalent Resistance → ( RN ) For given circuit, by removing supply and shorting AB ( RN ) → (R 1 ║ R3) + R2
R2
R1
Rn R3
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Case.4 (same as Thevenin’s) I L → IN x
RN R N+R L
………… mA
Precautions:
1 Reading must be taken without parallax error. 2. Measuring instruments must be handled properly. 3. All connections should be free from loose contacts Result:
Dept of EEE
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3. Verification of Maximum Power Transfer Theorem Aim: To Verify Maximum Power Transfer Theorem for a given circuit Theory:
Max power will be delivered by network to the load, if the impedance of network is complex conjugate of load impedance and vice versa (or) The maximum power transfer states that “ A load will received maximum power from a linear bilateral network when its load resistance is exactly equal to the Thevenin’s resistance of network, measured looking back into the terminals of network. Apparatus: S. No 1 2 3
4 5 6
Equipment DC.RPS. Voltage source. Resistors Variable Res ister
Range 0-30V/2A R S 1-10K Ω
Quantity 1 1 1
Ammeter-DC Connecting wires Bread board
0-200 mA 1.0.Sq mm
1 As required 1
Circuit Diagram:
Procedure:
1. Connect the circuit as shown in the above figure. 2. Apply the proper voltage from RPS. 3. Now vary the load resistance (R L) in steps and note down the corresponding Ammeter Reading ( IL) milli amps 4. Tabulate the readings and find the power using formula. → Power = I2 RL 5 Draw the graph between Power and Load Resistance. Dept of EEE
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6. After plotting the graph , the Power will be Maximu Maximum m , when the L Load oad Resistance will be equal to source Resistance . Tabular Column: RL(Ω) S.NO
IL(mA) Theoretical
Practical
PL(mW) Theoretical
Practical
1 2 3 4 5 6
Model Graph:
Theoretical Calculations:-
R = (R S + R L) =.………………..Ω I = V / R =…………..…….mA Power
= (I2) RL =…..…..mW
Safety Precautions:
1. Reading must be taken without parallax error 2. Measuring instruments must be connected properly & should be free from errors 3. All connections should be free from loose contacts Result:
Dept of EEE
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4. Verification of Superposition Theorem. Aim: To verify the superposition theorem for a given circuit. Theory:
This theorem states that “The current through, or
voltage across any element in a linear
bilateral network is equal to the algebraic sum of the currents of voltages produced independently by each sources ( i.e. by getting other sources to 0). A given response in a network regulating from a number of independent sources(including initial condition source) may be computed by summing the response to each individual source with all other sources made in operative( reduced to zero voltage or zero current). This statement describes the property homogeneity in linear networks. So it is the combined properties off additivity and homogeneity off linear network. It is a result of the linear relation between current and volt in circuits having linear impedances. Apparatus: S.No 1 2 3 4 5
Equipment DC.RPS-Voltage Source Resistors Ammeter-DC
Range 0-30 Volts/2A R 1R 2R 3 0-200 milliamps
Bread board Connecting wires
1.00 sq.mm
Quantity 1 3 1 1 As required
Circuit Diagrams: Case (i): when both voltage sources are acting
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Case (ii): when one voltage source is acting and V 2 is short circuited (V2=0)
Case (iii): when one voltage source is acting and V 1 is short circuited (V1=0)
Procedure:
1. Connect the circuit as shown in case (i) 2. Adjust the voltage V1 & V2 from RPS 3. Measure the current through R3 resistor using Ammeter ie, I total. 4. Now keep the V1 voltage same & remove V2 voltage and short circuited, then measure the current through R 3 resistor , ie, I’ 5. Now keep the V 2 voltage & remove V 1 voltage and short circuited, then measure the current through R 3 resistor , ie, I ” 6. 7. 8. 9.
Verify that the I total. = I’ + I ” Tabulate the readings in the tabular column Repeat the procedure for deferent voltage values of V 1 , & V2 Compare the values Practical to Theoretical.
Theoretical Calculations: Case 1: (For measuring Itotal) When the V1 & V2 source are applied (Original circuit) V
− V1
R1
V +
R3
V +
− V2
R2
=
0
ITotal = V/R 3
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Case 2: (For measuring I’) When the V1 source is applied (V2 is zero)
R eeqq = (R 2 ║ R 3) +R 1 Ieq = V1 / R eeqq I
'
=
I eq *
R2 R2 + R3
Case 3: (For measuring I”) When the V2 source is applied (V1 is zero)
R Eq Eq = (R 1║ R3) + R 2 IEq = V2 / R Eq Eq I
''
=
R1
I eq *
2 +
R
R3
Tabular Column: Super Position Theorem
Case-1 I1 (mA)
Case-2 III (mA)
Case-3 ITotal (mA)
Theoretical Values Practical Values Safety Precautions:
1. Reading must be taken without parallax error 2. Measuring instruments must be connected properly & should be free from errors 3. All connections should be free from loose contacts Result:
Dept of EEE
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5. Verification of Compensation Theorem Aim: To verify the Compensation Theorem. Apparatus: S. No 1 2 3 4 5
Equipment DC.RPS .Voltage source. Resistors Ammeter-DC Connecting wires Bread board
Range 0-30V/2A R 1R 2R 3 0-200 mA 1.00.Sq.mm
Quantity 1 2 1 As required 1
Circuit Diagrams: Case 1:
Case 2:
Case 3:
A
R2
R1
R3
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20
–
0-200mA
Vc=I2* R
AGI
Procedure:
1. Connect the circuit as per case (i). 2. Switch ON the DC supply (RPS) and apply proper voltage from RPS 3. Note down the Ammeter reading , say it is I1 4. Now connect the circuit as per diagram .No.2 (supply to be given same as Case (i)) 5. Note down the Ammeter reading , say it is I2 6. Now connect the circuit as per diagram .No.3 (this circuit is same as Case (ii), only supply will be changed ie, V=I2x ∆R) 7. Note down the Ammeter reading , say it is I3 Now Prove that , ∆I = I1 - I2 , I2 - I1 I1 →Branch current in the original circuit.
I2 →Branch current after Branch Resistance Changed in the original
circuit. I3 →Same Branch current after compensating Voltage source the circuit.
Tabular column:
Compensation theorem
I1(mA)
I2(mA)
∆I=I1-I2(mA)
Theoretical Values Practical Values
Result:
Dept of EEE
21
AGI
6. Verification of Reciprocity Theorem Aim: To verify Reciprocity theorem for a given circuit. Theory:
Ohm’s law and Kirchoff’s laws are the fundamental tools for network analysis, while network theorems are very powerful tools for solving complicated network problems.
It is applicable only a simple sources network. The theorem states that “In any linear b ilateral network the ratio of voltage source E volts in one branch to the current I in another branch is the same as the ratio obtained if the positions of E and I are interchanged , other emf’s being removed.”. (or)
“If in any network , a porential V introduced in to any branch’A’ causes a current ‘I’ to flow in any other branch ‘B’; then the same potential ‘V’ introduced into branch ‘B’ will cause the same value of current to flow in branch ‘A’. In ther words , this law simply means that “V&I” are mutuall y interchangeable. The ratio V/I is called the transfer resistance or Impedance. Apparatus : S.No 1 2 3 4 5
Equipment DC.RPS-Voltage Source Resistors Ammeter-DC Connecting wires
Range 0-30 Volts/2A R 1R 2R 3 0-200 mA
Quantity 1 3 1
1.0 Sq.mm(single lead)
As required 1
Bread board
Circuit Diagram:Case (i):
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Case (ii):
Procedure:
1. Connect the circuit as shown in case (i) 2. Apply DC voltage from RPS as shown shown in case (i) 3. Measure the current by using Ammeter. Ammeter. 4. Now interchange the supply & Ammeter and measure the current. 5. Verify that the both current are equal equal 6. Tabulate the readings in the tabular column 7. Compare the Practical values with Theoretical values. Theoretical Calculations: Case1: (For measuring IXY)When the Voltage at AB side applied (ie,VAB)
R Eq Eq = (R 2 ║ R 3)+R 1 IEq = V1 / R Eq Eq I XY = IEq X R 3 R 2+R 3
R2
R1 V
+
IXY R3
_
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23
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Case 2: (For measuring IAB)When the Voltage at XY side applied (ie,VXY)
R Eq Eq = (R 1║ R3) +R 2 IEq = V2 / R Eq Eq IAB =
X
IEq
R 3 R 1+R 3
R2
R1
V
IAB R3
+ _
Tabular Column: Reciprocity Theorem
Case-1 IXY (mA)
Case-2 IAB (mA)
Theoretical Values Practical Values Safety Precautions:
1. Reading must be taken without parallax error 2. Measuring instruments must be connected properly & should be free from errors 3. All connections should be free from loose contacts Result:
Dept of EEE
24
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6. Verification of Millman’s Theorem Aim: To verify Millman’s Theorem for a given circuit. Theory:
This theorem is useful, when a number of voltage sources in a network need to be replaced by a single voltage source. Consider a network having V1, V2, V3 are independent voltage sources, all joined in parallel. R1, R2, R3 are impedances in series with these voltage sources. It is possible to replace all these source by a single voltage source Vm in series with an impedance Rm . Such that the voltage at the terminals and the total current delivered remain same (unchanged), even after the replacement. Appartus:
S. No 1 2 3 4
5 6 7
Equipment DC.RPS .Voltage source. Resistors Variable Resister Ammeter-DC
Range 0-30V R 1R 2R 3 1K Ω 0-200 mA
Qty 1 1 1 1
Voltmeter-DC Connecting wires Bread board
0-30V 1.0.Sq.mm
1 As required 1
Circuit Diagrams: Case 1: To find load current 0-200mA A
V1
R3
R2
R1 V2
+
+
V3
+
_
_
RL
_
Case 2: To find Millman’s voltage (Vm)
R3
R2
R1
V 0 3 0
V
_ V1 _
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V3
V2
_
_
25
AGI
Case 3: To find Millman’s resistance (Rm) 0-200mA A
_
+ +
R3
R2
R1
V
_
Millman’s Equivalent Circuit
Theoretical Calculations: Case 1:
R3
R2
R1
V3
V2
V1
V
_
_
_
− V
1
R1
+
V
RL
−V
R2
2
V +
−V 3
R3
IL=
V +
R L
=
0
V R L
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Case 2:
R2
R1
V 0 3 0
R3
V
_ V2
V1
V3 _
_
V
−V
1
R1
V +
_
−V
2
V +
R2
− V 3
R3
=
0
V=Vm
Case 3:
R3
R2
R1
Rm
1 R1
1 +
R2
1 +
R3
= Rm
Case 4:
IL=
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Vm Rm + RL
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Procedure: 1. Connect the circuit diagram for case (i). 2. Switch ON the supply and ensure that the supply should flow from the three sources. 3. Note the Ammeter reading at Load. 4. Switch OFF the supply. 5. Connect the circuit as per the case 2 and apply proper voltage to the three sources, note down the volt meter reading (Vm).
6. Connect as per the case 3Rm. and note down the voltmeter and ammeter readings. the Nowcircuit calculate the resistance 7. Now remove all the supplies & Resistors and connect only one supply ie, Vm Volts. & Equivalent Resistance ie, Rm which is calculated practically. 8. Note the Ammeter reading at Load 9. The Ammeter reading, when connected 3 sources = and when connected one sources should be equal.
Tabular Column :
Millman’s theorem
Case 1 IL(mA)
Case 2 Vm (Volts)
Case 3
Rm=V/I (Ω)
Case 4 IL(mA)
Theoretical Values Practical Values
Result:
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7. Verification of Z and Y Parameters Aim: To study and measure the Z, Y parameters for a given Two Port Passive Network.
Theory:
A port is defined as any pair of terminals into which energy is supplied, or from which energy is withdrawn or where the network variables may be measured. A two port network is a simple network, having inside a rectangular box and the network has only two pairs of accessible terminals usually one pair represents the input, and the another represents output.
In the above fig having 4 terminals have been paired into ports 1-1’ and 2-2’ Two ports containing no sources in their branch are called passive port. Two ports containing sources in their branches are called active port. The voltage and current assigned to each of the two ports. V1, I1 → input terminals V2, I2 → output terminals V1, V2, I1, I2 → are variables (2 of these are dependent variables & 2 independent variables) The Number of possible combinations generated by the four variables taken 2 at a time, t ime, is 6. Then, there are 6 possible sets of equations describing a 2 port network. For the 6 combinations, the names of the parameters are chosen to indicate dimensions (Impedance, admittance) law of consistent dimensions (Hybrid), or the principal application
of the parameter (Transmission). Name
Function Express In terms of
Open circuit Impedance
V1,V2
I1, I2
Short circuit admittance
I1, I2
V1,V2
Transmission (ABCD)
V1,I1
V2,I2
Hybrid
V1,I2
I1,V2
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Equation
V1 = Z11 I1 + Z12 I2 V2 = Z21 I1 + Z22 I2 I1 = Y11 V1 + Y12 V2 I2 = Y21 V1 + Y22 V2 V1 = AV2 - BI2 I1 = CV2 - DI2 V1 = H11 I1 + H12 V2 I2 = H21 I1 + H22 V2
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Z Parameters (Open circuit Parameters):
Z11, Z12, Z21, Z22 are called Z-parameters of 2 port network. 1) Z11 → Input Impedance where output is open circuited Z11=V1/I1 where I2=0 2) Z12 → Reverse Transfer Impedance (mutual), when input is Z12 = V1/I2 where I1=0
open circuited.
3) Z21 → Forward Impedance, when output is open circuited. Z21 = Transfer V2/I1 when I2=0 4) Z22 → Output Impedance, when input is open Z22 = V2/I2 when I1=0
circuited.
Y Parameters (Short circuit Parameters → Y11, Y12, Y21, Y22)
1) Y11 → Input Admittance wher e output is short circuited Y11=I1/V1 where V2=0 2) Y22 → Output Admittance, when input is short circuited. Y22 = I2/V2 where V1=0 3) Y12 → Reverse Transfer Admittance, when output is short circuited. Y12 = I1/V2 when V1=0 4) Y21 → Forward Transfer Admittance, when input is short circuited. Y21 = I2/V2 when V2=0
Apparatus:
S.No 1 2 3 4 5 6
Equipment
Range
DC.RPS-Voltage Source DC.RPS-Voltage Resistors Ammeter-DC Voltmeter-DC
Quantity 1 3 2 1 1
0-30 Volts/2A
R 1R 2R 3 0-200 mA 0-30 V
Bread board Connecting wires
As required
Circuit Digrams: Z parameters: Case 1:
+
A
–
0-200mA
R2
R1
+ V
+ R3
–
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V
0-30V
30
–
AGI
Case 2: R2
R1
–
A
+ 0-200mA
+ 0-30V
V V
–
R3
–
+
Procedure for Z parameters:
1) 2) 3) 4)
Connect the circuit as per case1 Keep the port 2 terminals open, i.e. (I2=0). Set desired voltage on V1 from the RPS. Measure V2 and I1, and then tabulate V1, V2, I1.
5) Calculate the parameters. Z11,Z21 6) Now open the Port1 Connect desired voltage to port 2 (I 1=0) as shown in case 2 then measure V2, V1, I2. 7) Calculate parameters Z12, Z22 Y parameters: Case 1: A + – 0-200mA
R2
R1
+ V
+
–
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0-200mA R3
31
A
–
AGI
Case 2:
–
+ 0-200mA
R2
R1
A
+
V A
+
0-200mA R3
–
–
Procedure for Y parameters
1) Connect the circuit as per case1, connect desired voltage at port1. Then short port2. Note the values of I1, I2, V1. 2) Calculate the parameters Y11,Y21 3) Connect any desired voltage at port2 and short port1 as shown in case 2 4) Then note the values of V2, I1, I2. 5) Calculate the parameters Y12,Y22 Tabular Column for ‘Z’ parameters:
Tabular Column for ‘Y’parameters:
(When I2 = 0 , Port.2 Open) Z11 = V1/ I1 : Z21 = V2/ I1
(When I/P, Port1, short circuited, V1 = 0) Y12 = I1/ V2 : Y22 = I2/ V2
V1
V2
I1
Z11
Z21
V2
5V
5V
10V
8V
12V
10V
(When I1 = 0 , Port.1 Open) Z22 = V2/ I2 : Z12 = V1/ I2 V2 V1 I2 Z22 5V 10V 12V
I1
I2
Y12
Y22
(When O/P, Port2 ,short circuited, V2 = 0) Y11 = I1/ V1 : Y21 = I2/ V1 Z12
V1 5V 8V 10V
I1
I2
Y11
Y21
Precautions: 1. Avoid loose connections. 2. Readings should be taken carefully. 3. Get your connected circuit checked by staff member.
Result:
Dept of EEE
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8. Verification of Transmission and Hybrid parameters Aim: To study and measure the Transmission & H parameters for a given two Port Passive Network. Apparatus required: S.No 1 2 3 4 5 6
Equipment DC.RPS-Voltage Source Resistors Ammeter-DC Voltmeter-DC Connecting wires Bread board
Range
Quantity
0-30 Volts/2A
1 3 2 1 As required 1
R 1R 2R 3 0-200 mA 0-30 V 1.00 sq.mm
Theory: Transmission or ABCD Parameters:
ABCD are Transmission parameters. These parameters are also known as by other name, chain parameters. In this system of parameters volt and current at port 1 are expressed in terms of volt and current at port 2. 1) A = Ratio of input volt to the output voltage when output is open circuited. A = V1/V2 when I2=0 2) B = Ratio of Input volt to output current when output is short circuited. B= -V1/I2 when V2=0. 3) C = Ratio of Input current to output voltage when output is open circuited. C = I1/V2 when I2=0. 4) D = Ratio of Input current to the output current when output is short circuited. D = -I1/I2 when V2=0. Hybrid Parameters:
1) H11=
Input Impedance with output port short circuited. H11= V1/ I1 when V2=0
2) H21 = Output admittance admittance with input port port open circuited H21 = I2/ I1 when V2=0 3) H12 = reverse voltage transfer ratio with input port open circuited. H12 = V1/ V2 when I1=0 4) H22 = Forward current gain with output port short circuited. H22 = I2/ V2 when I1=0 Dept of EEE
33
AGI
ABCD parameters: Case 1: +
A
–
R2
0-200mA R1
+ V
+
0-30V V R3
–
–
Case 2: A + – 0-200mA
R2
R1
+ V
+
–
0-200mA R3
A
–
Procedure for ABCD (Transmission)Parameters:
1. Connect the circuit as per the case 1 and apply desired voltage 2. Note down the values of V1 ,V2 ,I1 and calculate the A,C parameters 3. Connect the circuit as per the case 2 and apply desired voltage 4. Note down the values of V1 ,I1,I2 and calculate the B,D parameters 5. Compare the practical values with theoretical values.
Dept of EEE
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Hybrid Parameters: Case 1: A + – 0-200mA
R2
R1
+ V +
0-200mA A R3
–
–
Case 2:
R2
R1 +
–
A
+ 0-200mA
V
0-30V V R3
–
+
–
Procedure for Hybrid Parameters:
1. Connect the circuit as per the case 1 and apply desired voltage 2. Note down the values of V1 ,I1, I2 and calculate the H11,H21 parameters 3. Connect the circuit as per the case 2 and apply desired voltage 4. Note down the values of V2 ,V1,I2 and calculate the H12,H22 parameters 5. Compare the practical values with theoretical values.
Dept of EEE
35
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Tabular Column for ‘ABCD’ parameters:
(When I2 = 0 , Port.2 Open) V1
V2
A = V1/ V2 : C = I1/ V2 I1
A
C
Theoretical Practical
(When V2 = 0 , Port.1 Short Circuited) V1
I1
I2
B
B = V1/ I2 : D = I1/ I2 D
Theoretical Practical
Tabular Column for ‘H’parameters:
(When Port2 is short circuited, V2= 0) H11 = V1/ I1 : H21 = I2/ I1 I2 I1 V1 H11 H21 Theoretical Practical
(When Port1 is Open circuited, I1 = 0) H12 = V1/ V2 : H22 = I2/ V2 V2
V1
I2
H12
H22
Theoretical Practical
Result:
Dept of EEE
36
AGI
9. MESH ANALYSIS IN THE RECIPROCITY CIRCUIT
Aim: To verify the Reciprocity Theorem with DC Input and finding the Current using PSPICE software. Apparatus required:
1. Personal Computer with PSPICE software installation. Circuit Diagram:
P-Spice circuit:
Dept of EEE
37
AGI
Procedure:
1. Start the personal Computer and Open the Text Editor which is on the desktop. 2. For the above given circuit decide the node points for each component and also put a dummy voltage source for measuring the current at nodes if necessary. necess ary. 3. Write the program for the above ckt as given below 4. Save the file as .cir and close the file 5. Open the PSPICE AD , open the same file which is saved by a name earlier in the Text editor. 6. You observe a dialog “Simulation completed successfully” 7. Open the file menu and Click the Examine out put. 8. You observe the following output results what ever the requirements needed. PSPICE Program: *RECIPROCITY
THEOREM
VS
1
0
DC
10V
VX
1
2
DC
0V
R1
2
3
1.1K
R2
3
4
2.2K
R3
3
0
3.3K
VY
4
0
DC
0V
.OP .END
Output:
Dept of EEE
38
AGI
10. NODAL ANALYSIS IN THE SUPER POSITION THEOREM CIRCUIT
Aim: To verify the Superposition Theorem with DC Input and finding the Current using PSPICE software. Apparatus required:
1. Personal Computer with PSPICE software installation. Circuit Diagram :
P-Spice circuit:
Dept of EEE
39
AGI
Procedure:
1. Start the personal Computer and Open the Text Editor which is on the desktop. 2. For the above given circuit decide the node points for each component and also put a dummy voltage source for the sake of measuring the current at nodes if necessary. 3. Write the program for the above ckt as given below 4. Save the file as .cir and close the file 5. Open the PSPICE AD , which is on the desk top and open the same file which is saved by a name earlier in the Text editor. 6. You observe a dialog “Simulation completed successfully” 7. Open the file menu and Click the Examine out put. 8. You can observe the output. PSPICE Program: *SUPERPOSITION
THEOREM
V1
1
0
DC
10V
VX
1
2
DC
0V
R1
2
3
1.1K
R2
3
5
2.2K
R3
3
4
3.3K
VY
4
0
DC
0V
VZ
5
6
DC
0V
V2
6
0
DC
15V
.OP .END
Output :
Dept of EEE
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AGI
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