Lpw Circuit Theory 2013

8/14/2019 Lpw Circuit Theory 2013

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INSTITUTE OF TECHNOLOGY, NIRMA UNIVERSITY

B.Tech. Semester IV (IC)

2EE225:CIRCUIT THEORY

INDEX

SR.

NO.TITLE

PAGEDATE SIGN

REMAR

KSFROM TO

1. To verify Superposition Theorem.

2. To verify Thevenin Theorem.

3. To verify Reciprocity Theorem.

4. To verify Norton Theorem.

5. To verify Maximum Power Transfer Theorem.

6.

(i) To determine the zparameters of atwo port resistive network.

(ii)To determine the zparameters ofSeries connection of two 2-port resistive

networks and verify the result by direct

calculation.

7.

(i) To determine the y parameters of a twoport resistive network.

(ii) To determine the y parameters of the

parallel connection of two 2-port resistive


calculation.

8.

(i) To determine the ABCD parameters of atwo port resistive network.

(ii) To determine the ABCD parameters of the

cascade connection of two 2-port resistive


calculation.

9.

(i) To determine the hparameters of a twoport resistive network.

(ii) To determine the h parameters of the

series parallel connection of two 2-port

resistive networks and verify the result by

direct calculation.

10.

(i) To determine the gparameters of a twoport resistive network.

(ii)To determine the g parameters of theparallel-series connection of two 2-port

resistive networks and verify the result by

direct calculation.

11.Simulation of series RC,RL and RLC circuits

with Virtual Laboratory.

12.Simulation of Parallel RC,RL and RLC

circuits with Virtual Laboratory.


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EXPERIMENT NO: 1 DATE

AIM : To verify Superposition Theorem.

APPARATUS:

(1) Regulated power supply (D.C) 0 - 30V 2

(2) Board containing the network 1

(3) Ammeters 0 - 250 mA 3

(4) Voltmeter 0 - 30 V 1

SUPERPOSITION THEOREM

THEORY:

The superposition theorem states that the response in any element of a linear bilateral

network containing two or more sources is the algebraic sum of the responses obtained by

each source acting separately at a time and with all the other sources set equal to zero,

leaving behind their internal resistance in the network.

According to this theorem, if there are a number of e.m.fs acting simultaneously in any

linear bilateral network, each e.m.f acts independently of the others i.e as if the other

e.m.fs doesn't exist. The value of current in any element of the netwrok is the algebraic

sum of the currents due to each e.m.f. Similarly voltage across any element/branch is the

algebraic sum of the voltages which each e.m.f would have produced while

acting separately at a time. In other words, current through or voltage across

any conductor of the network is obtained by superimposing the currents and voltages

due to each e.m.f. in the network .It is important to note that this theorem is applicable

only to linear networks.

The superposition theorem is applied to determine currents and voltages which are

linearly related to the sources acting on the network. Power can not be determined by

superposition principle since the relationship between power and current or voltage is

quadratic.

In Fig(a) I1, I2and I3represent values of currents due to simultaneous action of the two

sources of e.m.fs in the network. In fig(b) I1', I2' and I' represent values of currents due to

source of e.m.f E1 alone. In fig (c) I1", I2" and I" represent values of currents due to

source of e.m.f E2alone. By superimposing the current values of fig (b) and fig (c)

the actual values of currents due to both the sources can be obtained as under:


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Obviously : I1= I1' + I1" (algebraic)

I2= I2" + I2' (algebraic)

I = I' + I" (algebraic)

PROCEDURE :

1. Connect the circuit diagram as shown in the fig .2. Connect the network with two e.m.f sources and adjust the source voltages such that

current values are not exceeded beyond the ranges and ratings of the resistance and

note down the meter readings.

3. Set the e.m.f E2 to zero and note down the readings. due to E1 alone. If any meterindicates negative, interchange the connection of that meter and consider that reading

as negative.

4. Adjust E2 as before (as per step. 2) and set E1 to zero and note down the meterreadings If any meter indicates negative, interchange the connection of that meter

and note down the reading of that meter with opposite sign w.r.t. the step 3.

5. Verify the superposition theorem and tabulate the results.

OBSERVATION TABLE:

SR.

NO

E1

Volts

E2

Volts

I1

mA

I2

mA

I3

mA

V1

Volts

V2

Volts

V3

Volts

1

2 0

3 0

CALCULATION:

I1 = I1' + I1" (Algebraic) V1 = V1' + V1" (Algebraic)



RESULT TABLE:

SR.

NO

I1

mA

I2

mA

I3

mA

V1

Volts

V2

Volts

V3

Volts

Practical

Theoretical

CONCLUSION:


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AIM : To verify Reciprocity Theorem.

APPARATUS:

(1) Regulated power supply (D.C) 0 - 30V 2

(2) Board containing the network 1

(3) Ammeters 0 - 250 mA 3

(4) Voltmeter 0 - 30 V 1

RECIPROCITY THEOREM:

THEORY:

The reciprocity theorem states that in a linear, bilateral, single source network the ratio of

excitation to response is constant when the positions of excitation and response are

interchanged.

On the basis of mesh current analysis with a single voltage source acting in the network, the

theorem may be demonstrated by considering the following equation for mesh current Ir.

Ir = V1(1r/z) + V2(2r/z) +.. + Vr(rr/ z) + Vs(sr/ z)

Let the only source in the network be Vsthen

Ir = Vs (sr/ z)

The ratio of excitation to response is

Vs/ Ir= z/ sr= Ztransfer sr ------------------------------(1)

Now when the position excitation and response are interchanged the source becomes Vrand

the current Is.

Is= Vr(rs/ z)

The ratio of excitation to response is

Vr / Is= z/ rs= Ztransfer rs --------------------------(2)

The two transfer impedances in (1) and (2) are equal in any linear, bilateral network since in

such networks the impedance matrix [z] is symmetrical with respect to the principal diagonal,


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and the cofactors rs and sr are equal. Thus the current in mesh r which results from a

voltage source in mesh s is the same as the current in mesh s when the voltage source is

moves to mesh. It must be noted that currents in other parts of the network will not remain

same.

The reciprocity theorem also applies to networks containing a single current source. Here the

theorem states that the voltage which results at a pair of terminal m n due to a current source

acting at terminals a b is the same as the voltage at terminals a b when the current source is

moved at terminals m n. It should be noted that voltages at other points in the network would

not remain the same.

PROCEDURE:

1. For the circuit shown in figure1 calculate the values of current (I) for different values ofsource voltage and record them in the observation table.

2. Connect the circuit as shown in figure1 , measure then values of current (I) (for sourcevoltage of same values in step 1) and record them in the observation table.

3. For the circuit shown in figure (2), calculate the values of current (I) (for source voltage ofsame values as in step 1) and record them in the observation table.

4. Connect the circuit as shown in figure (2), measure the values of current (I)(for sourcevoltage of same values as in step 1) and record them in the observation table.

OBSERVATION TABLE:

Sr No. Voltage

(V)

Current (I) A/mA Voltage

(V)

Current (I) (A/mA)

Exp. The. Exp. The.

1.

2.

3.

4.

CONCLUSION:


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QUIZ :

1. Superposition theorem can be applied only to circuits having ________.

2. Superposition theorem requires as many circuits to be solved as there are

(a) sources , nodes and meshes

(b) sources and nodes

(c) sources

(d) nodes.

3. Total resistance of a parallel circuit is _______ the smallest branch resistance.

4. Is superposition theorem applicable to POWER as it is applicable to voltage and current?


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AIM : To verify Thevenin Theorem.

APPARATUS:

(1) Board containing network 1

(2) Milli ammeter (MC) 0 - 50 mA. 1

(3) Voltmeter (MC) 0 - 10V 1

(4) Regulated power supply 0-30V 1

THEVENIN THEOREM:

THEORY:

Thevenins theorem state that any two terminal network whether simple or complex can

be replaced by a single source of voltage Vth in series with a single resistance Rth (in

case of d.c) or impedance Zth(in case of a.c) Hence Thevenin's equivalent circuit consists

of Vthin series with Rth(or Zth) as shown in fig(B). Once a Thevenin's circuit is obtained

it is connected across the resistance RL in which current is to be determined. Once the

current value in RLis known, potential difference across it can be calculated if required.

For obtaining Thevenin's circuit, proceed as follows:

1. Remove the resistance RL and measure (or calculate) voltage Ethbetween theterminals from where RL has been removed.

2. Replace all the e.m.f sources by their internal resistance (or impedances) andmeasure (or calculate) Rth (or Zth) between the terminals from where RL has been

disconnected.

3. Draw the Thevenin's equivalent network.4. For calculating current in RL, connect RL which was removed earlier across this

Thevenin's circuit.

5. Current through RLis given byVth

IL = -----------

Rth+ RL


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PROCEDURE:

1. Connect the circuit as shown in the fig(1).2. Switch on the supply and adjust the supply voltage such that meter readings are not

exceeded their ranges and ratings of the resistances. Note down the current through the

load resistance RL.

3. Disconnect the resistance RL from the circuit and measure the voltage across theterminals from where the resistance RL is disconnected. This voltage is known as Eth.

Refer fig(2).

4. Replace source of e.m.f. by its internal resistance and measure the total resistance (orimpedance) of the network between the terminals from where the resistance RL is

disconnected. This resistance (or impedance) is known as Rth(or Zth). Refer fig(3).

5. Calculate the current through RLusing the formula.Vth

IL = -----------

Rth + RL

6. Compare it with the value obtained in step (2)

OBSERVATION TABLE:

SR.

NO

VOLTAGE

ACROSS

RL

VLvolts

CURRENT

THROUGH

RL

ILmA

RL=

VL/IL

Eth

Volts

REMARKS

1

2- - Disconnect the

resistance RL

(Measurement of Rth)

SR

NO

SUPPLY

VOLTAGE

V volts

CURRENT

I mA

Rth=

V / I

REMARKS

1 Set source e.m.f to zero

2 Set source e.m.f to zero


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CALCULATION :

(1) RL= VL/IL = =

(2) Rth= V/I = =

Vth

(3) IL = ----------- = =

Rth + RL

RESULT TABLE :

THEORETICAL PRACTICAL

Vth

Rth

IL

CONCLUSION:


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AIM : To verify Norton Theorem.

APPARATUS:

(1) Board containing network 1

(2) Milli ammeter (MC) 0 - 50 mA. 1

(3) Voltmeter (MC) 0 - 10V 1


NORTON THEOREM:

THEORY :

This theorem is an alternative to the Thevenin's theorem. In fact, it is the dual of

Thevenin's theorem. Where as Thevenin's theorem reduces a two - terminal active

network to an equivalent constant voltage source and series resistance Norton's theorem

replaces the network by an equivalent constant current source and a parallel resistance.

It states that any two - terminal active network containing voltage/current sources and

resistances/impedances when viewed from its output terminals is equivalent to a

constant current source and a parallel resistance (or impedance). The constant current is

equal to the current which would flow in a short - circuit placed across the terminals

and parallel resistance (or impedance) is the resistance (or impedance) of the network

when viewed from these open circuited terminals after all sources of e.m.fs have been

supressed and replaced by their internal resistances (or impedances).

PROCEDURE for analysis of network:

1. Remove the resistance RL, short the terminals through an ammeter from where RLhas been removed and observe ( or calculate) the reading of the ammeter. This gives

the value of the current of the Nortons current source, Isc.

2. Replace the source by its internal resistance (or impedance) and measure (orcalculate) the resistance RN(or impedance ZN) between the terminals from where RL

has been removed.

3. Connect the RN(or ZN) in parallel with the current source and connect RL whichwas disconnected earlier across Norton's equivalent circuit.

4. Current through the resistance RL is given byRth

IL = Isc ----------Rth+ RL


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PROCEDURE:

1. Connect the circuit as shown in fig 1.2. Switch on the power supply and adjust the supply voltage such that meter readings

are not exceeded their ranges and ratings of the resistances. Note down the current

through the resistance RL.

3. Disconnect the resistance RL and short the terminals through the ammeter fromwhere RLhas been removed and measure(or calculate) the current. This gives the

value of the current (Isc) of the current source. Refer fig(2).

4. Replace source of e.m.f by its internal resistance (or impedance) and measure the totalresistance (or impedance) of the network between the terminals from where the

resistance(RL) has been removed. This is known as RN(or ZN).

5. Calculate the current through RL according toRN

IL = Isc -----------

RN+ RL

and compare its value obtained in step (2)

OBSERVATION TABLE:

SR.

NO

VOLTAGE

ACROSSRL

VLvolts

CURRENT

THROUGHRL

ILmA

RL=

VL/IL

ISC

mA

REMARKS

1 -

2 Disconnect RL and

short the terminals

through ammeter


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(Measurement of RN)

SR.

NO

SUPPLY

VOLTAGE

V volts

CURRENT

I mA

RN= V / I REMARKS

1 Set source e.m.f. to zero

2 Set source e.m.f. to zero

CALCULATION :

(1) RL= VL/IL = =

(2) RN= V/I = =

RN

(3) IL = Isc ----------- = =

RN+ RL

RESULT TABLE:

THEORETICAL PRACTICAL

ISC

RN

IL

CONCLUSION: -

QUIZ: -

1. For which type of network the Norton's theorem is applicable?2. The circuit whose parameters change with voltage or current is called a _______ circuit.

3. _________ theorem is quite useful when the current in one branch of a network is to be

determined or when the current in an added branch is to be calculated.


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4.. The circuit whose parameters are constant is called a linear circuit. (yes/no)

5. In Thevenin's theorem to find Zth,all independent ________ are set to zero and allindependent_______ are open circuited.

6. Thevenin equivalent circuit is preferred when the circuit is analyzed in terms of _________and __________ .

7. Norton equivalent circuit is preferred when the circuit is analyzed in terms of _________ and__________ .

8. When connected to a 4 resistor, a battery has a terminal voltage of 10.8 V but produces 12V on an open circuit. Determine the Thevenin equivalent circuit for the battery.

9. Given the Thevenin`s equivalent of an electric circuit, how will you determine the Norton`sequivalent?

.


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AIM: To verify Maximum Power Transfer Theorem and Tellegan`s Theorem.

APPARATUS:

(1) Board

(2) Ammeter 0 - 10 ma 01

(3) Voltmeter 0 - 10V 01


MAXIMUM POWER TRANSFER THEOREM

THEORY :

Maximum power transfer theorem deals with transfer of maximum power from a

source to load. This theorem in d.c circuit states the relationship between the load

resistance and the internal resistance of the source for maximum power transfer from

source to load. This condition is also referred as resistance matching and it is

very important in electronics and communication circuits for obtaining maximum

output. Let us consider a circuit supplying a power to a load of resistance RL ohms.

The circuit of fig (1) can be simplified to the circuit of fig (2) by using Thevenin's

theorem, From fig (2) the current through RL is given by

E

I = -------Ri + RL

Power transferred to the load

PL= I2RL

E 2

= -------- RL

Ri + RL

E2

RL= ----------- -----------(1)

(Ri + RL)2

In the above expression the resistance Rs and voltage E are constant. Hence PL varies

wth respect to only variable RL Power delivered to the load is a maximum if,

d PL

------ = 0

d RL


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Differentiating the expression (1) w.r.to RL and equating to zero, we obtain the

condition for maximum power i.e RL = Ri

Hence for maximum power transfer the load resistance should be equal to the internal

resistance of the source,

E2RL

Pmax = ------------

(RL+ Ri)

2

E2

= ------- watts (because RL= Ri)

4RL

PROCEDURE:

(1)Connect the circuit as shown in the fig.(3)(2)Switch on the supply and adjust suitable voltage of the supply.(3)Vary the load resistance from zero onward in suitable steps. For each step take meter

readings.

(4)Calculate the power taken by the load for each value of the load resistance.(5)Draw the graph of PLv/s RL.

OBSERVATION TABLE :

SR.

NO

SUPPLY

VOLTAGE

Vs (Volts)

LOAD

CURRENT

IL( mA)

VOLTAGE

ACROSS

LOADVL(Volts)

LOAD

RESISTANCE

RL= VL/IL

POWER

DELIVERED TO

THERESISTANCE,

RL

PL= IL2XRL

1.2.3.4.5.

CALCUATION :

VL

(1) RL= -----

IL

(2) PL= IL2. RL


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CONCLUSION: -

QUIZ: -

1. When a source is delivering maximum power to a load, the efficiency of the circuit is___________ .

2. Assuming that we can determine the Thevenin equivalent resistance of our wall socket,why don`t heater, microwave oven and TV manufacturer match each appliances

Thevenin equivalent resistance of this value? Would not is permited max power transfer

from the utility company to our household appliances?

3. A black box with a circuit in it is connected to a variable resistor. An ideal ammeter andan ideal voltmeter are used to measure current and voltage respectively. The results are:

R V I

2 3 1.5 Determine the maximum power from the box.

8 8 1.0

14 10.5 0.75

4. Maximum power transfer theorem is particularly useful for analyzing _________networks.

5. For high efficiency of transfer of power, internal resistance of the source should be__________.


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AIM : (i) To determine z parameters of a given TwoPort Resistive

Network.

(ii) To determine the z parameters of series connection of two 2-port

resistive networks and verify the result by direct calculation.

APPARATUS :

(1) Ammeter 0-50mA 2

(2) Voltmeter 0-10V 1

(3) Regulated power supply 0 - 30V. 1

(4) Board containing two port network 1

THEORY:

In electrical network theory a port may be regarded as a pair of terminals in which

current in to one terminal equals the current out of the other. A network may have one,

two or n ports in general. A one port network is completely identified when voltage

current relationship at the terminals of the port is given.

A general two port network shown in fig (1) has two pairs of voltage - current

relationships. The V1 and I1 are the variables at port 1 and V2 and I2 are the variables

at port 2. Only two of the four variables are independent and specifications of any two

of them determine the remaining two. The dependence of two of the four variables on

the other two is described in a number of ways, depending on which of the variables

are chosen to be independent variables. As such there are six possible sets of equations

describing a two port network, six different types of parameters are defined as z

parameters, y parameters, transmission parameters, inverse transmission parameters,

hybrid parameters and inverse hybrid parameters.

Z - parameters:

In case of z parameters, V1and V2are expressed in terms of I1 and I2.

i.e. V1= z11I1 + z12I2 - (1)

V2= z21I1+ z22I2 - (2)

These parameters may be defined in terms of a single voltage and current by letting either

I1= 0 or I2= 0.

Thus,


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V1

z11 = ___

I1 I2= 0

V1

z12 = ___

I2 I1= 0

V2

z21 = ___

I1 I2= 0

V2

z22 = ____

I2 I1= 0

It may be observed that (i) all the z parameters have the dimensions

of impedance and (ii) they are specified only when the current in one of ports is

zero i.e open circuit at port 1 or port 2. Hence z parameters are designated as

open circuit impedance parameters.

ZPARAMETERS OF SERIES CONNECTION OF TWO 2-PORT

RESISTIVE NETWORK:

Two port network analysis is useful for finding different parameters. The z

Parameters are useful in characterizing series connected two port networks. They

are found under open circuit conditions and hence they are referred as open circuit

impedance functions. They are defined and found as under:

The z parameters are useful in characterizing series connected two port

networks. The overall z parameters from the individual z parameters can be

found as under when the networks are connected in series.

For network Na

V1a

=

z11a z12a I1a

V2a z21a z22a I2a ---------(1)


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For network Nb

V1b

=

z11b z12b I1b

V2b z21b z22b I2b ---------(2)

For overall network N

V1

=

z11 z12 I1

V2 z21 z22 I2 ---------(3)

Note that

I1= I1a= I1band V1= V1a+ V1b

I2= I2a= I2band V2= V2a+ V2b------(4)

Combining equation (1), (2) and (4), we get

V1

=

Z11a+z11b z12a +z12b I1

V2 Z21a+z21b z22a +z22b I2 ---------(5)

Comparing equation (5) with equation (3), we get

z11= z11a + z11b

z12= z12a + z12b

z21= z21a + z21b

z22= z22a + z22b----------------(6)

This result may be generalized for any number of networks

connected in series. The individual parameters are added to determine the

overall Z parameters.

PROCEDURE :

(1) Connect the circuit for Network Naas shown in fig (1).

(2) Apply voltage at port 1 keeping port 2 open circuited as shown in

fig (2). Measure voltages and current at the port terminals. Keep levels of voltages

and current such that meter readings are not exceeded their ranges and ratings of

the resistances.

(3) Apply voltage at port 2 keeping port 1 open circuited as shown in

fig (3). Measure voltages and current at the port terminals.


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(1)Calculate z parameters using measured values of voltages and currentsand verify the results theoretically.

(2)Connect the circuit as shown in fig (4) for network Nb only. Repeat steps 2 to4 for Network Nb

(6) Connect the networks Na and Nb in series as shown in fig(5) to form

the overall network N.

(7) Repeat steps 2 to 4 to find the z - parameters of network N and Verify the

results theoretically.

(8) Keep levels of voltages and currents such that the meter readings are

not exceeded their ranges and ratings of resistances.

OBSERVATION TABLE :

(1) Network : Na

SR.

NO.

V1a

Volts

I1a

mA

V2a

Volts

I2a

mA

REMARK

1 0 Port - 2 open circuited


(2) Network : Nb

SR.

NO.

V1b

Volts

I1b

mA

V2b

Volts

I2b

mA

REMARK



(3) Network N :

SR.

NO.

V1

Volts

I1

mA

V2

Volts

I2

mA

REMARK




21/49

CALCULATION :

For Network Na :

V1a

z11a = ___ = _________________________________

I1a I2a= 0

V1a

z12a = ___ = _________________________________

I2a I1a = 0

V2a

z21a = ___ = ________________________________

I1a I2a= 0

V2a

z22a = ___ = ________________________________

I2a I1a= 0

For Network Nb :

V1b

z11b = ___ = _________________________________

I1b I2b= 0

V1b

z12b = ___ = _________________________________

I2b I1b= 0

V2b

z21b = ___ = ________________________________

I1b I2b= 0

V2b

z22b = ___ = ________________________________

I2b I1b= 0


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For Network N :

V1

z11 = ___ = _________________________________

I1 I2= 0

V1

z12 = ___ = _________________________________

I2 I1= 0

V2

z21 = ___ = ________________________________

I1 I2= 0

V2

z22 = ___ = ________________________________

I2 I1= 0

Check :

(1) z11= z11a+ z11b = ____________ = ____________

(2) z12= z12a+ z12b = ____________ = ____________

(3) z21= z21a+ z21b=____________ = ____________

(4) z22= z22a+ z22b = ____________ = ____________

RESULT TABLE :

NETWORK Practical Theoratical

Network Na

z11a=______ z21a= ______

z11a=______ z21a= ______

z11a=______ z21a= ______

z11a=______ z21a= ______

z11b =______ z21b = ______ z11b=______ z21b= ______


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Network Nb

z11b=______ z21b= ______ z11b=______ z21b= ______

Network N

z11=______ z21= ______

z11=______ z21= ______

z11=______ z21= ______

z11=______ z21= ______

CONCLUSION: -

QUIZ: -

1. What do you mean by two port network?2. z parameters are known as _________ circuit parameters.3. If for any two port passive network z12is 4 ohm, what will be the value of z21?4. What are the applications of two port parameters?5. Why two networks are connected in series to get overall z parameters?6. For two networks connected in series if z21 a= 4 ohm and z21b= 6 ohm , what will

be the value of z21 ?


24/49


AIM : (i) To determine y parameters of a given TwoPort Resistive

Network.

(ii) To determine the y parameters of the parallel connection of two

2-port resistive networks and verify the result by direct

calculation.

APPARATUS :

(1) Ammeter 0-50mA 2

(2) Voltmeter 0-10V 1

(3) Regulated power supply 0 - 30V. 1

(4) Board containing two port network 1

THEORY:

y parameters :

In case of y parameters , I1 and I2 are expressed in terms of V1 and V2

i.e I1 = y11V1 + y12V2

I2 = y21V1 + y22V2

The individual y parameters are defined by

I1

y11 = ___

V1 V2= 0

I1

y12 = ___

V2 V1= 0

I2

y21 = ____

V1 V2 = 0

I2

y22 = ___

V2 V1= 0

It may be observed that

(i) All the y-parameters have the dimensions of admittance.

(ii) They are specified only when voltage at one of the ports is zero i.e short

circuit at port 1 or port 2. Hence y parameters are known as short circuit

admittance parameters.


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YPARAMETERS OF PARALLEL CONNECTION OF TWO 2- PORT

RESISTIVE NETWORK.

The y - parameters ( short - circuit admittance parameters ) are useful in

characterizing parallel connected two - port networks.

They are found under short circuit conditions and hence they are referred

as short circuit admittance parameters.

The y-parameters are useful in characterizing parallel connected two port

networks. The overall y parameters from the individually parameters can be

found as under when the networks are connected in parallel.

For network Na

I1a y11a y12a V1a

I2a

=

y21a y22a V2a

---------(1)

For network Nb

I1b y11b y12b V1b

I2b

=

y21b y22b V2b

---------(2)


I1 y11 y12 V1

I2

=

y21 y22 V2

---------(3)

Note that

V1= V1a= V1band I1= I1a+ I1b

V2= V2a= V2band I2= I2a+ I2b------(4)


I1 y11a+y11b y12a +y12b V1

I2

=

y21a+y21b y22a +y22b V2

---------(5)


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y11= y11a + y11b

y12= y12a + y12b

y21= y21a + y21b

y22= y22a + y22b----------------(6)

This result may be generalised for any number of networks connected

in parallel. The individual short circuit admittance parameters are added to

determine the overall Y parameters.

PROCEDURE :

(1)Connect the circuit diagram of Network Na as shown in fig(1).(2)Apply voltage at port 1 short circuiting the port 2 through

an ammeter as shone in fig (2). Measure voltage and currents at both

the port terminals.

(3)Apply voltage at port 2 short circuiting the port 1 throughan ammeter as shown in fig (3). Measure voltage and currents at both

the ports.

(4)Calculate y parameters using measured values of voltageand currents and verify the results theoretically.

(5)Connect the circuit as shown in fig (4) for network Nb only. Repeatsteps 2 to 4 for Network Nb.

(6)Connect the networks Na and Nb in parallel as shown in fig(5)to form network N and repeat steps 2 to 4 for Network N. find its

y - parameters. Verify the results theoretically.

(7)Keep levels of voltages and currents such that the meterreadings are not exceeded their ranges and ratings of resistances

OBSERVATION TABLE :

(1) Network : Na

SR.

NO.

V1a

VOLTS

I1a

mA

V2a

VOLTS

I2a

mA

REMARK

1 0 Port - 2 short circuited



27/49

(2) Network : Nb

SR.

NO.

V1b

VOLTS

I1b

mA

V2b

VOLTS

I2b

mA

REMARK



(3) Network N :

SR.

NO.

V1

VOLTS

I1

mA

V2

VOLTS

I2

mA

REMARK



CALCULATION :

For Network Na :

I1a

y11a = ___ = ________________________________

V1a V2a= 0

I1a

y12a = ___ = ________________________________

V2a V1a= 0

I2a

y21a = ___ = _________________________________

V1a V2a= 0

I2a

y22a = ___ = ________________________________

V2a V1a= 0

For Network Nb :

I1b

y11b = __ = _________________________________

V1b V2b= 0


28/49

I1b

y12b = ___ = _________________________________

V2b V1b= 0

I2b

y21b = ___ = _________________________________

V1b V2b= 0

I2b

y22b = ___ = ________________________________

V2b V1b= 0

For Network N :

I1

y11 = ___ = ________________________________

V1 V2= 0

I1

y12 = ___ = ________________________________

V2 V1= 0

I2

y21 = ___ = _________________________________

V1 V2= 0

I2

y22 = ___ = ________________________________

V2 V1= 0

Check :

(1) y11= y11a+ y11b = ____________ = ____________

(2) y12= y12a+ y12b = ____________ = ____________

(3) y21= y21a+ y21b =____________ = ____________

(4) y22= y22a+ y22b = ____________ = ____________


29/49

RESULT TABLE :

NETWORK Practical Theoretical

Network Nay11a=______ y21a= ______

y11a=______ y21a= ______

y11a=______ y21a= ______

y11a=______ y21a= ______

Network Nb

y11b =______ y21b = ______

y11b=______ y21b= ______

y11b=______ y21b= ______

y11b=______ y21b= ______

Network N

y11=______ y21= ______

y11=______ y21= ______

y11=______ y21= ______

y11=______ y21= ______

CONCLUSION: -

QUIZ: -

1. y parameters are also known as _______ circuit parameters.2. If for any two port passive network y12is 0.4 mho, y21= ______.3. If two networks Naand Nbare connected in parallel y11a= 3 mho and y11b= 4 mho

what will be the value of y11= ______.


30/49


AIM : (i) To determine ABCD parameters of a given twoport resistive

network.

(ii) To determine the ABCD parameters of the cascade connection of

two 2-port resistive networks and verify the result by direct

calculation.

APPARATUS :

(1) Network board

(2) Ammeters 0 - 50mA 2


(4) Regulated power supply 0-30 V 1

THEORY :

The transmission parameters serve to relate the voltage and current at one port to

voltage and current at the other port. In equation form,

V1 = AV2 - BI2

I1 = CV2 - DI2

where A, B, C and D are the transmission parameters. They are also known

as chain parameters, the ABCD parameters and general circuit parameters.

Their first use is in the analysis of power transmission lines. From the

circuit conditions, they can be found as follows,

V1

A = _____

V2 I1=0

V1

-B = _____

I2 V2=0I1

C = _____

V2 I2=0

I1

-D = _____

I2 V2=0


31/49

ABCD PARAMETERS OF CASCADE CONNECTION OF TWO 2-PORT

RESISTIVE NETWORK.

The transmission parameters are useful in describing two port networks which

are connected in cascade or in a chain arrangement. The overall parameters

from the individual parameters can be found as under when the networks are

connected in cascade.

For network Na

V1a Aa Ba V2a

I1a= Ca Da -I2a

---------(1)

For network Nb

V1b Ab Bb V2b

I1b

=

Cb Db -I2b

---------(2)


V1 A B V2

I1

=

C D -I2

---------(3)

Note that

V1a= V1 V2a = V1b I2b= I2

I1a = I1 I1b = - I2a V2b = V2 ------(4)

Substituting these in equation (1) and equation (2), we get

V1 Aa Ba Ab Bb V2

I1

=

Ca Da Cb Db -I2

---------(5)


A B Aa Ba Ab Bb AaAb+BaCb AaBb+ BaDb

C D=

Ca Da Cb Db=

CaAb+ DaCb CaBb+ DaDb------(6)


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PROCEDURE :

(1)Connect circuit diagram of Network Naas shown in fig (1).(2)Apply voltage at port 1 of network Na short circuiting the port

2 through an ammeter as shown in fig (4). Measure voltages and

currents at both the ports.

(3)Apply voltage at port 1 of network Na keeping port 2 open circuited asshown in fig (5). Measure voltages and currents at both the ports.

(4)Calculate ABCD parameters using measured values of voltagesand currents.

(5)Connect the circuit as shown in fig (2) for network Nb only. Repeatsteps 2 to 4 for network Nb.

(6)Connect both the networks in cascade as shown in fig (3). This formsnetwork N.

(7)To measure parameters of network N follow the steps 2 to 4.(8)Verify the parameters theoretically and tabulate the results.(9)For each network verify that AD - BC = 1.

OBSERVATION TABLE :

(1) Network : Na

SR.

NO.

V1a

Volts

I1a

mA

V2a

Volts

I2a

mA

REMARK



(2) Network : Nb

SR.

NO.

V1b

Volts

I1b

mA

V2b

Volts

I2b

mA

REMARK




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(3) Network N :

SR.

NO.

V1

Volts

I1

mA

V2

Volts

I2

mA

REMARK

1 0 Port - 2 short circuited2 0 Port - 2 open circuited

CALCULATION :

For Network Na :

V1a

Aa = ___ = _________________________________

V2a I2a= 0

V1a

Ba = ___ = _________________________________

-I2a V2a= 0

I1a

Ca = ___ = _______________________________

V2a I2a= 0

I1a

Da = ___ = _______________________________

-I2a V2a= 0

For Network Nb :

V1b

Ab = ___ = _________________________________

V2b I2b= 0

V1b

Bb = ___ = _________________________________

-I2b V2b= 0


34/49

I1b

Cb = ___ = _______________________________

V2b I2b= 0

I1b

Db = ___ = ________________________________

-I2b V2b= 0

For Network N :

V1

A = ___ = _________________________________

V2 I2= 0

V1

B = ___ = _________________________________

-I2 V2= 0

I1

C = ___ = ________________________________

V2 I2= 0

I1

D = ___ = ________________________________

-I2 V2= 0

Check :

A = AaAb+BaCb =_________________

B = AaBb+ BaDb =_________________

C = CaAb+ DaCb =_________________

D = CaBb+ DaDb =_________________


35/49

RESULT TABLE :

NETWORK - Na NETWORK - Nb NETWORK - N

Pract. Theo. Pract. Theo. Pract. Theo.

Aa Ab ABa Bb B

Ca Cb C

Da Db D

CONCLUSION :

QUIZ :

1. ABCD parameters are also known as ___________ or _________ parameters.2. Why two networks are connected in cascade connection to get overall ABCD

parameter?

3. If A= 7 , B= 8 ohm and C = 2.5 mho , what will be the value of D?

4. Ratio of driving voltage in one mesh to resulting current in other mesh is knownas ________ impedance.

5. State the conditions for a network to be loss less in terms of ABCD parameters?6. State the condition for a network to be reciprocal and symmetrical.7. For _________ connection of two 2-port networks, ABCD parameters have to be

multiplied.

8. Are the ABCD parameters A(s), B(s),C(s) and D(s) the network functions?9. The relation ADBC = 1 is valid for ________ and _________ networks.10.Why negative sign is introduced in the equations?


36/49


AIM : (i) To determine h - parameter of a given TwoPort Resistive

Network.

(ii) To determine the hparameters of the series parallel

connection of two 2-port resistive networks and verify the result

by direct calculation.

APPARATUS :

(1) Network board




THEORY :

h parameters representation is widely used in modeling of electronic

components and circuits, particularly transistors. As both short circuit

and open circuit terminal conditions are utilized hence, this parameter

representation is known as hybrid parameter representation. In this form

of representation, the voltage of the input poet and the current of the

output port are expressed in terms of the current of the input poet and the

voltage of the output port.

We know that

V1= h11I1 + h12V2

I2= h21I1+ h22V2

In matrix form

V1 h11 h12 I1

I2=

h21 h22 V2---------(1)

Where

V1

h11 = ___ = Input impedance when output is short circuited

I1 V2= 0

V1

h12

= ___ = Reverse voltage ratio when input open circuited

V2 I1= 0


37/49

I2

h21 = ___ = Forward current ratio when output short circuited

I1 V2= 0

I2

h22 = ___ = Output admittance when input is open circuited

V2 I1= 0

h PARAMETERS FOR SERIES PARALLEL CONNECTION OF

TWO 2-PORT NETWORK.

Two port networks are said to be connected in series-parallel if the input

ports are connected in series while the output ports are connected inparallel.

For network Na

V1a h11a h12a I1a

I2a

=

h21a h22a V2a

---------(2)

For network Nb

V1b h11b h12b I1b

I2b

=

h21b h22b V2b

---------(3)

For overall network Nc

V1 h11 h12 I1

I2

=

h21 h22 V2

---------(4)

Note that

I1= I1a= I1band V1= V1a+ V1b

I2= I2a+ I2band V2= V2a= V2b------(4)


V1 h11a+h11b h12a +h12b I1

I2

=

h21a+h21b h22a +h22b V2

---------(5)


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h11= h11a+h11b

h12= h12a +h12b

h21= h21a+h21b

h22= h22a +h22b----------------(6)

This result may be generalized for any number of networks

connected in series-parallel. The overall h-parameter matrix for series-

parallel connected two port networks is simply the sum of h-parameter

matrices of each individual two-port network connected in series-parallel.

PROCEDURE :

(1)Connect the circuit diagram of network Naas shown in fig (1).(2)Apply voltage at port 1 keeping port 2 short-circuited. Measure

voltages and current at the port terminals as shown in fig (4). Keep

levels of voltages and current such that meter readings are not

exceeded their ranges and ratings of the resistances.

(3)Apply voltage at port 2 keeping port 1 open circuited as shown in fig(5). Measure voltages and current at the port terminals.

(4)Calculate h parameters using measured values of voltagesand currents and verify the results theoretically

(5)Connect the circuit as shown in fig (2) for network Nb only. Repeatsteps 1 to 4 for network Nb.

(6)Connect the networks Naand Nbin series parellel as shown in fig (3) toform the network N.

(7)Repeat steps 2 to 4 to find h parameter for network N and verify resultstheoretically.

(8)Keep levels of voltages and currents such that the meterreadings are not exceeded their ranges and ratings of resistances


39/49

OBSERVATION TABLE :

(1) Network : Na

SR.

NO.

V1a

Volts

I1a

mA

V2a

Volts

I2a

mA

REMARK



(2) Network : Nb

SR.

NO.

V1b

Volts

I1b

mA

V2b

Volts

I2b

mA

REMARK



(3) Network N :

SR.

NO.

V1

Volts

I1

mA

V2

Volts

I2

mA

REMARK



CALCULATION :

For Network Na :

V1a

h11a = ___ =

I1a V2a= 0

V1a

h12a = ___ =

V2a I1= 0


40/49

I2a

h21a = ___ =

I1a V2a= 0

I2a

h22a = ___ =

V2a I1a= 0

For Network Nb :

V1b

h11b = ___ =

I1b V2b= 0

V1b

h12b = ___ =

V2b I1= 0

I2b

h21b = ___ =

I1b V2b= 0

I2b

h22b = ___ =

V2b I1b= 0


41/49

For Network N :

V1

h11 = ___ =

I1 V2= 0

V1

h12 = ___ =

V2 I1= 0

I2

h21 = ___ =

I1 V2= 0

I2

h22 = ___ =

V2 I1= 0

Check :

(1) h11= h11a+h11b = ____________= ____________

(2) h12= h12a +h12b = ____________= ____________

(3) h21= h21a+h21b =____________ = ____________

(4) h21= h21a+h21b= ____________ = ____________

CONCLUSION: -


42/49


AIM : (i) To determine g - parameter of a given TwoPort Resistive

Network.

(ii) To determine the g parameters of the parallel-series

connection of two 2-port resistive networks and verify the result

by direct calculation.

APPARATUS :

(1) Network board




THEORY :

Hybrid parameters (h parameters) and Inverse hybrid parameters (g parameters) are

dual of each other. For g parameters both short circuit and open circuit terminal

conditions are utilized. In this form of representation, the current of the input port and

the voltage of the output port are expressed in terms of the voltage of the input port

and the current of the output port.

In case of g parameters, I1and V2are expressed in terms of V1 and I2.

i.e. I1= g11V1 + g12I2 - (1)

V2= g21V1+ g22I2 - (2)

I1 g11 g12 V1

V2=

g21 g22 I2---------(1)

Where

I1

g11 = ___ = Input admittance when output is open circuited

V1 I2= 0

g12 = I1 = Reverse current ratio when input short circuited

I2 V1= 0


43/49

V2

g21 = ___ = Forward voltage ratio when output open circuited

V1 I2= 0

V2

g22 = ___ = Output impedance when input is short circuited

I2 V1= 0

PARAMETERS FOR PARALLEL - SERIES CONNECTION OF TWO 2-PORT

RESISTIVE NETWORK

Two port networks are said to be connected in parallel series if the input ports are

connected in parallel while the output ports are connected in series.

For network Na

I1a g11a g12a V1a

V2a

=

g21a g22a I2a

---------(2)

For network Nb

I1b g11b g12b V1b

V2b

=

g21b g22b I2b

---------(3)

For overall network Nc

I1 g11 g12 V1

V2

=

g21 g22 I2

---------(4)


44/49

Note that

I1= I1a+ I1band V1= V1a= V1b

I2= I2a= I2band V2= V2a+ V2b------(5)


I1 g11a+g11b g12a +g12b V1

V2

=

g21a+g21b g22a +g22b I2

---------(6)


g11= g11a+g11b

g12= g12a +g12b

g21= g21a+g21b

g22= g22a +g22b----------------(6)

This result may be generalized for any number of networks connected in parallel-series.

The overall g-parameter matrix for parallel-series connected two port networks is simply

the sum of g-parameter matrices of each individual two-port network connected in

parallel-series.

PROCEDURE :

(1)Connect the circuit diagram of network Naas shown in fig (1).(2)Open the output port and excite the input port with a known voltage

source Vs as shown in fig (2) so that V1= Vs and I2= 0.

(3)Determine I1and V2to obtain g11and g21.(4)Then the input port is short circuited and output port is excited with the

same voltage source Vs as shown in fig (3) so that V2= Vs and V1= 0.(5)Determine I1and I2to obtain g12and g22.(6)Connect the circuit as shown in fig (4) for network Nb only. Repeat

steps 2 to 4 for network Nb.

(7)Connect the networks Na and Nb in parallel-series as shown in fig (5) toform the network N.

(8)Repeat steps 2 to 4 for Network N and verify results theoretically.(9)Keep levels of voltages and currents such that the meter

readings are not exceeded their ranges and ratings of resistances


45/49

OBSERVATION TABLE :

(1) Network : Na

SR.

NO.

V1a

Volts

I1a

mA

V2a

Volts

I2a

mA

REMARK



(2) Network : Nb

SR.

NO.

V1b

Volts

I1b

mA

V2b

Volts

I2b

mA

REMARK



(3) Network N :

SR.

NO.

V1

Volts

I1

mA

V2

Volts

I2

mA

REMARK



CALCULATION :

For Network Na :

I1a

g11a = ___ =

V1a I2a= 0

I1a

g12a = ___ =

I2a V1a= 0


46/49

V2a

g21a = ___ =

V1a I2a= 0

V2a

g22a = ___ =

I2a V1= 0

For Network Nb :

I1b

g11b = ___ =

V1b I2b= 0

I1b

g12b = ___ =

I2b V1b= 0

V2b

g21b = ___ =

V1b I2b= 0

V2b

g22b = ___ =

I2b V1b= 0

For Network N

I1

g11 = ___ =

V1 I2= 0

I1

g12 = ___ =

I2 V1= 0


47/49

V2

g21 = ___ =

V1 I2= 0

V2

g22 = ___ =

I2 V1= 0

Check :

(1) g11= g11a+g11b = ____________

(2) g12= g12a +g12b = ____________

(3) g21= g21a+g21b =____________

(4) g21= g21a+g21b= ____________

CONCLUSION: -

QUIZ: -

1. Will the g parameter matrix of a passive network always be symmetric?2. g-parameters matrix will not exist for which type of two port networks?3. If for any two port passive network g12is 0.6, g21= ______.4. If two networks Naand Nbare connected in parallel, g11a= 1.2 and g11b= 0.8

what will be the value of g11?


48/49

EXPERIMENT NO: 11 DATE :

AIM: Simulation of series RC,RL and RLC circuits with Virtual Laboratory.

PROCEDURE:

1. Open the link www.vlab.co.in

2. Click on Amrita University

3. Click on Virtual Electric Circuits.

4. Click on series RC circuits. Login through Google/Yahoo ID.

5. Click on procedure tab . Now click on simulator tab. According to procedure

prepare circuit and plot the graph.

6. Repeat step 4 and 5 for Series LC circuit and Series RLC circuit.

7. Save all the results in Network drive .
http://www.vlab.co/http://www.vlab.co/http://www.vlab.co/


49/49

EXPERIMENT NO: 12 DATE :

AIM: Simulation of Parallel RC, RL and RLC circuits with Virtual Laboratory.

PROCEDURE:

1. Open the link www.vlab.co.in

2. Click on Amrita University

3. Click on Virtual Electric Circuits.

4. Click on Parallel RC circuits. Login through Google/Yahoo ID.

5. Click on procedure tab . Now click on simulator tab. According to procedure

prepare circuit and plot the graph.

6. Repeat step 4 and 5 for Parallel LC circuit and Parallel RLC circuit.

7. Save all the results in Network drive .
http://www.vlab.co/http://www.vlab.co/http://www.vlab.co/

Lpw Circuit Theory 2013

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Transcript of Lpw Circuit Theory 2013