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NIRMA UNIVERSITY INSTITUTE OF TECHNOLOGY
B.Tech. Semester III (Electrical), July 2017
EE02: NETWORK ANALYSIS & SYNTHESIS (LPW)
INDEX
SR.
NO. TITLE
PAGE DATE SIGN REMARKS FROM TO
1. To verify the Superposition Theorem.
2. To verify the Thevenin Theorem.
3. To verify the Norton Theorem.
4. To verify the Maximum Power Transfer
Theorem.
5. To verify the Reciprocity Theorem and
the Tellegen`s Theorem
6.
(i) To determine the z – parameters of a two port resistive network.
(ii) To determine the z – parameters of Series connection of two port
resistive networks.
7.
(i) To determine the y – parameters of a two port resistive network.
(ii) To determine the y – parameters of the
parallel connection of two port
resistive networks.
8.
(i) To determine the ABCD parameters of a two port resistive network.
(ii) To determine the ABCD parameters
of the cascade connection of two port
resistive networks.
9.
(i) To determine the h – parameters of a two port resistive network.
(ii) To determine the g – parameters of a
two port resistive network
10.
To study the response in RLC series
circuit and determine various time
response specifications.
11. To study the step response of first order
RC circuit and cascaded RC sections
12.
To design and test a passive constantk
High Pass Filter and measure its cutoff
frequency
2
EXPERIMENT NO: 1 DATE:
AIM : To verify Superposition Theorem.
APPARATUS:
(1) Regulated power supply (D.C) 0  30V 2
(2) Board for containing the network 1
(3) Ammeters 0  250 mA 3
(4) Voltmeter 0  30 V 1
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 emfs acting simultaneously in any linear
bilateral network, each emf acts independently of the others i.e. as if the other emfs doesn't
exist. The value of current in any element of the network is the algebraic sum of the currents
due to each emf. Similarly voltage across any element/branch is the algebraic sum of the
voltages which each emf 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.
In Fig(a) I1, I2 and I3 represent 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 E2 alone. 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:
I1 = I1' + I1" (algebraic)
I2 = I2" + I2' (algebraic)
I = I' + I" (algebraic)
3
PROCEDURE:
1. Connect the circuit diagram as shown in the fig (1)
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 meter
indicates negative, interchange the connection of that meter and consider that reading as
negative. Refer fig(2) .
4. Adjust E2 as before (as per step. 2) and set E1 to zero and note down the meter readings
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. Refer fig(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)
I2 = I2' + I2" (Algebraic) V2 = V2' + V2" (Algebraic)
I3 = I3' + I3" (Algebraic) V3 = V3' + V3" (Algebraic)
RESULT TABLE:
SR.
NO
I1
mA
I2
mA
I3
mA
V1
Volts
V2
Volts
V3
Volts
Practical
Theoretical
4
CONCLUSION:
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? Why?
5. Calculate the voltage across 5 A source in the given circuit
6. The potential of the point A in the given network
7. The current through 30 Ω branch in the given circuit is
8. The current in 1 Ω resistor is
5
EXPERIMENT NO: 2 DATE :
AIM : To verify Thevenin’s Theorem
APPARATUS:
(1) Board containing network 1
(2) Ammeter 0  50 mA. 1
(3) Voltmeter 0  10V 1
(4) Regulated power supply 030V 1
THEORY:
Thevenin’s 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 Vth
in 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 RL is 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 Eth between the terminals
from where RL has been removed.
2. Replace all the e.m.f sources by their internal resistance (or impedances) and measure
(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 RL is given by
Vth
IL = 
Rth + RL
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.
6
3. Disconnect the resistance RL from the circuit and measure the voltage across the terminals
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 (or
impedance) 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 RL using the formula.
Vth
IL = 
Rth + RL
6. Compare it with the value obtained in step (2)
OBSERVATION TABLE:
SR.
NO
VOLTAGE
ACROSS
RL
VL volts
CURRENT
THROUGH
RL
IL mA
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
CALCULATION :
(1) RL = VL/IL = =
(2) Rth = V/I = =
Vth
(3) IL =  = =
Rth + RL
7
RESULT TABLE:
THEORETICAL PRACTICAL
Vth
Rth
IL
CONCLUSION: 
QUIZ :
1. While Thevenizing a circuit between two terminals, Vth is equal to __________. 2. Thevenin’s resistance is determined by _____________________. 3. While determining Rth in Thevenin’s and Norton’s equivalent
(a) only current source are made dead (b) only voltage sources are made dead (c) all independent sources are made dead (d) all current and voltage sources ar emade dead
4. In Thevenin’s theorem Z is determined by _____________. 5. Which theorem is applicable for both linear and nonlinear circuits? 6. The Thevenin impedance across the terminals AB of the given network is
7. To find current in a resistance connected in one branch of a network thevenin’s
theorem is used. VTH = 20V and RTH = 5 Ω. The current in the resistant is.
(a) is 4 A (b) is 4A or less
(c) is less than 4 A (d) equal to 4 A or less than 4 or more than 4 A.
(e) none of these
8 . In an ac network, the thevenin’s impedance and Norton’s impedance as seen from any
two terminals are.
(a) always the same (b) sometimes the same
(c) generally the same (d) mostly the same
8
EXPERIMENT NO: 3 DATE:
AIM : To verify Norton Theorem.
APPARATUS:
(1) Board containing network 1
(2) Ammeter 0  50 mA. 1
(3) Voltmeter 0  10V 1
(4) Regulated power supply 030V 1
THEORY :
This theorem is an alternative to the Thevenin’s theorem. In fact, it is the dual of
Thevenin's theorem. Whereas 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 RL has
been removed and observe (or calculate) the reading of the ammeter. This gives the
value of the current of the Norton’s current source, Isc.
2. Replace the source by its internal resistance (or impedance) and measure (or calculate)
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 which
was disconnected earlier across Norton's equivalent circuit.
4. Current through the resistance RL is given by
9
Rth
IL = Isc 
Rth + RL
PROCEDURE:
1.Connect the circuit as shown in fig (4).
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 from where
RL has been removed and measure(or calculate) the current. This gives the value of the
current (Isc) of the current source. Refer fig(5).
4. Replace source of e.m.f by its internal resistance (or impedance) and measure the total
resistance (or impedance) of the network between the terminals from where the resistance
(RL) has been removed. This is known as RN (or ZN). Refer fig (6).
1. Calculate the current through RL according to
RN
IL = Isc 
RN + RL
and compare its value obtained in step (2)
OBSERVATION TABLE:
SR.
NO
VOLTAGE
ACROSS
RL VL volts
CURRENT
THROUGH
RL
IL mA
RL =
VL/IL
ISC
mA
REMARKS
1

2 Disconnect RL and short
the terminals through
ammeter
(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
10
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.
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 all
independent_______ are open circuited.
6. Thevenin’s 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. Given the Thevenin`s equivalent of an electric circuit, how will you determine the Norton`s
equivalent? Justify with detailed example.
11
EXPERIMENT NO: 4 DATE:
AIM: To verify Maximum Power Transfer Theorem.
APPARATUS:
(1) Board for connecting network
(2) Ammeter 0  10 mA 01
(3) Voltmeter 0  10V 01
(4) Regulated power supply 030V 01
THEORY :
Maximum power transfer theorem deals with transfer of maximum power from a source
to load. This theorem in dc 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
E 2 RL
=  (1)
(Ri + RL)2
In the above expression the resistance Rs and voltage E are constant. Hence PL varies
with respect to only variable RL Power delivered to the load is a maximum if,
d PL  = 0
d RL
12
Differentiating the expression (1) wrt 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,
E2 RL 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 PL v/s RL.
OBSERVATION TABLE :
SR.
NO
SUPPLY
VOLTAGE
Vs (Volts)
LOAD
CURRENT
IL ( mA)
VOLTAGE
ACROSS
LOAD
VL(Volts)
LOAD
RESISTANCE
RL = VL/IL
POWER
DELIVERED TO
THE
RESISTANCE,
RL
PL = IL2 X RL
1.
2.
3.
4.
5.
CALCUATION :
VL (1) RL = 
IL
(2) PL = IL2. RL
13
CONCLUSION: 
QUIZ: 
1. Maximum power transfer theorem is applicable when the sources are connected in
_____________.
2. Assuming that we can determine the Thevenin’s equivalent resistance of our wall socket,
why don`t heater, microwave oven and TV manufacturer match each appliances Thevenin
equivalent resistance of this value? Will it not is permit max power transfer to flow 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 and
an 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. The maximum power that can be distributed in the load in circuit shown is
6. If Rg in the circuit shown is variable between 20Ω and 80Ω, then the maximum power
transferred to the load RL will be
14
7. Which one of the following impedance values of load will cause maximum power to be
transferred to the load for the network shown in the given figure?
(a) 2+j2 (b) 2j2 (c) –j2 (d)2
8. The value of the resistance R in the circuit shown in figure is varied in such a manner that the
power dissipated in the 3 Ω resistor is maximum. Under this condition, the value of r will be
(a) 3 Ω (B)9Ω (3) 12 Ω (4)6 Ω
9. Maximum power transfer theorem finds application in
(a) Power circuits (b) distribution circuits
(c) Communication circuits (d) both communication and power circuits
15
EXPERIMENT NO: 5 DATE:
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
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 Vs then
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 Vr and
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,
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.
16
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 figure (4), calculate the values of current (I) for different values of
source voltage and record them in the observation table.
2. Connect the circuit as shown in figure (4), measure then values of current (I) (for source voltage
of same values in step 1) and record them in the observation table.
3. For the circuit shown in figure (5), calculate the values of current (I’) (for source voltage of
same values as in step 1) and record them in the observation table.
4. Connect the circuit as shown in figure (5), measure the values of current (I’)(for source voltage
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.
TELLEGEN`S THEOREM
THEORY :
Tellegen`s Theorem is one of the most general theorems in network theory. It applies to
any network made up of lumped two terminal network elements, regardless of their nature,
i.e., the elements may be linear or nonlinear, passive or active, time invariant or time
varying. The circuit may contains independent of dependent sources.
If N1 and N2 are two different circuits, as shown in fig (4) and fig(5), having the same graph
with the same reference directions assigned to the branches in the two circuits. Let vk and
ik be the voltages and currents in N1 and vk` and ik` similarly be the voltages and currents
17
in N2, where all vk and vk` satisfy Kirchhoff`s Voltage Law (KVL) and all ik and ik` satisfy
Kirchhoff`s Current Law (KCL). Then Tellegen`s theorem state that
b b
vk ik = 0 and vk` ik` = 0 k=1 k=1
where b = No. of branches.
PROCEDURE :
(1) For the circuit shown in figure(4), measure the values of all the currents. ( i1, i2, i3, etc.)
(2) Measure other voltages (v1, v2, v3 etc.) for the same value of v1.
(3) Repeat steps 1 and 2 for the circuit shown in figure (5).
OBSERVATION :
i1 = v1 = i1` = v1` =
i2 = v2 = i2` = v2` =
i3 = v3 = i3` = v3` =
i4 = v4 = i4` = v4` =
CALCULATIONS:
b
vk ik = k=1
b
vk` ik` = k=1
b
vk ik` = k=1
b
vk` ik = k=1
18
CONCLUSION:
QUIZ:
1. Power delivered by the independent sources of the network must be equal the sum of power
absorbed in all other branches of the network. True/False
2. Verify Tellegen’s Thoerem considering two networks having identical graphs.
3. Which theorem is a manifestation of Law of Conservation of Energy?
4. To which networks is Reciprocity theorems applicable?
5. Tellegen’s theorem can be applied to __________ networks.
6. What is the use of Tellegen’s theorem?
7. If the current in the 7 Ω resistor branch is 0.5A as shown in the figure and now if the source is
connected in series with 7 Ω branch and the terminals AB are shorted, the current in the 5 Ω
resistor is,
(a) 1 A (b) 9.5 A (c) 9.75 A (d) none of the above
8. Reciprocity theorem is applicable to
(a) Any electric circuit (b) a linear network
(c) a linear network and constant voltage source (d) a linear, bilateral network
19
EXPERIMENT NO: 6 DATE:
AIM : (i) To determine z parameters of a given Two–Port Resistive
Network.
(ii) To determine the z – parameters of series connection of two 2port
resistive networks and verify the result by direct calculation.
APPARATUS :
(1) Ammeter 050mA 2
(2) Voltmeter 010V 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, V1 and V2 are expressed in terms of I1 and I2.
i.e. V1 = z11 I1 + z12 I2  (1)
V2 = z21 I1 + z22 I2  (2)
These parameters may be defined in terms of a single voltage and current by letting either
I1 = 0 or I2 = 0.
20
Thus,
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.
Z – PARAMETERS OF SERIES CONNECTION OF TWO 2PORT
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)
For network Nb
V1b
=
z11b z12b I1b
V2b z21b z22b I2b (2)
21
For overall network N
V1
=
z11 z12 I1
V2 z21 z22 I2 (3)
Note that
I1 = I1a = I1b and V1 = V1a + V1b
I2 = I2a = I2b and 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 i
n series. The individual parameters are added to determine the overall Z
parameters.
PROCEDURE :
1. Connect the circuit for Network Na as shown in fig (1).
2. Apply voltage at port 1 keeping port 2 open circuited as shown in
fig (4). 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 (5). Measure voltages and current at the port terminals.
4. Calculate z parameters using measured values of voltages and currents and
verify the results theoretically.
5. Connect the circuit as shown in fig (2) for network Nb only. Repeat steps 2 to 4 for
Network Nb
6. Connect the networks Na and Nb in series as shown in fig(3) to form the
overall network N.
22
(7) Repeat steps 2 to 4 to find the z  parameters of network N
and Verify the results theoretically.
OBSERVATION TABLE:
(1) Network : Na
SR.
NO.
V1a
Volts
I1a
mA
V2a
Volts
I2a
mA
REMARK
1 0 Port  2 open circuited
2 0 Port  1 open circuited
(2) Network : Nb
SR.
NO.
V1b
Volts
I1b
mA
V2b
Volts
I2b
mA
REMARK
1 0 Port  2 open circuited
2 0 Port  1 open circuited
(3) Network N :
SR.
NO.
V1
Volts
I1
mA
V2
Volts
I2
mA
REMARK
1 0 Port  2 open circuited
2 0 Port  1 open circuited
CALCULATION:
For Network Na :
V1a
z11a = ___ = _________________________________
I1a I2a = 0
V1a
z12a = ___ = _________________________________
I2 a I1a = 0
V2a
z21a = ___ = ________________________________
I1 a I2a= 0
23
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
For Network N:
V1
z11 = ___ = _________________________________
I1 I2 = 0
V1
z12 = ___ = _________________________________
I2 I1 = 0
V2
z21 = ___ = ________________________________
I1 I2 = 0
24
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 Theoretical
Network Na
z11a =______ z21a = ______
z11a =______ z21a = ______
z11a =______ z21a = ______
z11a =______ z21a = ______
Network Nb
z11b =______ z21b = ______
z11b =______ z21b = ______
z11b =______ z21b = ______
z11b =______ z21b = ______
Network N
z11 =______ z21 = ______
z11 =______ z21 = ______
z11 =______ z21 = ______
z11 =______ z21 = ______
CONCLUSION: 
25
QUIZ: 
1. What do you mean by two port network?
2. Z parameters are known as _________ circuit parameters.
3. The Z11 and Z22 parameters of the given network are,
4. Why two networks are connected in series to get overall z parameters? Discuss by
taking detailed example.
5. For two networks connected in series if z21 a = 4 Ω and z21b = 6 Ω, what will be the
value of z21 ?
6. The equivalent circuit of a twoport reciprocal network using zparameters is shown here
The zparameters are (z11,z12,z21,z22)
(a) 10,5,5,15 (b) 15,5,5,20 (c) 5,5,5,10 (d) 10,10,5,15
7. When a number of 2ports networks are connected in cascade, the individual
(a) Zoc matrices are added (b) Ysc matrices are added
(c) Chain matrices are multiplied (d) hmatrices are multiplied
26
EXPERIMENT NO: 7 DATE:
AIM : (i) To determine y parameters of a given Two–Port Resistive
Network.
(ii) To determine the y – parameters of the parallel connection of two
2port resistive networks and verify the result by direct
calculation.
APPARATUS :
(1) Ammeter 050mA 2
(2) Voltmeter 010V 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 = y11 V1 + y12 V2
I2 = y21 V1 + y22 V2
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 yparameters 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.
27
Y – PARAMETERS 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 yparameters 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)
For overall network N
I1
y11 y12 V1
I2
=
y21 y22
V2
(3)
Note that
V1 = V1a = V1b and I1 = I1a + I1b
V2 = V2a = V2b and I2 = I2a + I2b (4)
Combining equation (1), (2) and (4), we get
I1
y11a+y11b y12a +y12b V1
I2
=
y21a+y21b y22a +y22b
V2
(5)
28
Comparing equation (5) with equation (3), we get
y11 = y11a + y11b
y12 = y12a + y12b
y21 = y21a + y21b
y22 = y22a + y22b (6)
This result may be generalized 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 (4). Measure voltage and currents at both the port terminals.
(3) Apply voltage at port 2 short circuiting the port 1 through an ammeter as
shown in fig (5). Measure voltage and currents at both the ports.
(4) Calculate y parameters using measured values of voltage and currents and
verify the results theoretically.
(5) Connect the circuit as shown in fig (2) for network Nb only. Repeat steps 2 to
4 for Network Nb.
(6) Connect the networks Na and Nb in parallel as shown in fig(3) to for
m network N and repeat steps 2 to 4 for Network N.
find its y  parameters. Verify the results theoretically.
OBSERVATION TABLE:
(1) Network: Na
SR.
NO.
V1a
VOLTS
I1a
mA
V2a
VOLTS
I2a
mA
REMARK
1 0 Port  2 short circuited
2 0 Port  1 short circuited
(2) Network: Nb
SR.
NO.
V1b
VOLTS
I1b
mA
V2b
VOLTS
I2b
mA
REMARK
1 0 Port  2 short circuited
2 0 Port  1 short circuited
29
(3) Network N:
SR.
NO.
V1
VOLTS
I1
mA
V2
VOLTS
I2
mA
REMARK
1 0 Port  2 short circuited
2 0 Port  1 short circuited
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
I1b
y12b = ___ = _________________________________
V2b V1b = 0
I2b
y21b = ___ = _________________________________
V1b V2b = 0
30
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 = ____________ = ____________
RESULT TABLE:
NETWORK Practical Theoretical
Network Na
y11a =______ y21a = ______
y11a =______ y21a = ______
y11a =______ y21a = ______
y11a =______ y21a = ______
31
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 y12 is 0.4 mho, y21 = ______.
3. If two networks Na and Nb are connected in parallel y11a = 3 mho and y11b = 4 mho
what will be the value of y11 = ______.
4. For the port network shown, select the correct statement
(a)It does not have zparameters (b)It has zparameters
(c)It does not have yparameters (d)It does not have ABCD parameters
32
EXPERIMENT NO: 8 DATE:
AIM : (i) To determine ABCD parameters of a given two–port 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
(3) Voltmeter 0  10V 1
(4) Regulated power supply 030 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=0
I1
C = _____
V2 I2=0
I1
D = _____
I2 V2=0
33
ABCD PARAMETERS OF CASCADE CONNECTION OF TWO 2PORT 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)
For overall network N
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)
Comparing equation (5) with equation (3), we get
A B
Aa Ba
Ab Bb
AaAb+BaCb AaBb + BaDb
C D
=
Ca Da
Cb Db
=
CaAb + DaCb CaBb+ DaDb
(6)
34
PROCEDURE:
(1) Connect circuit diagram of Network Na as 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 as shown
in fig (5). Measure voltages and currents at both the ports.
(4) Calculate ABCD parameters using measured values of voltages and currents.
(5) Connect the circuit as shown in fig (2) for network Nb only. Repeat steps 2 to 4
for network Nb.
(6) Connect both the networks in cascade as shown in fig (3). This forms network
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
1 0 Port  2 short circuited
2 0 Port  2 open circuited
(2) Network : Nb
SR.
NO.
V1b
Volts
I1b
mA
V2b
Volts
I2b
mA
REMARK
1 0 Port  2 short circuited
2 0 Port  2 open circuited
(3) Network N :
SR.
NO.
V1
Volts
I1
mA
V2
Volts
I2
mA
REMARK
1 0 Port  2 short circuited
2 0 Port  2 open circuited
35
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
I1b
Cb = ___ = _______________________________
V2b I2b = 0
I1b
Db = ___ = ________________________________
I2b V2b = 0
36
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 =_________________
37
RESULT TABLE:
NETWORK  Na NETWORK  Nb NETWORK  N
Pract. Theo. Pract. Theo. Pract. Theo.
Aa Ab A
Ba 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. State the conditions for a network to be loss less in terms of ABCD parameters?
5. State the condition for a network to be reciprocal and symmetrical.
6. For _________ connection of two 2port networks, ABCD parameters have to be
multiplied.
7. Are the ABCD parameters A(s), B(s),C(s) and D(s) the network functions?
8. The relation AD – BC = 1 is valid for ________ and _________ networks.
9. Why negative sign is introduced in the equations?
38
EXPERIMENT NO: 9 DATE:
AIM : (i) To determine h  parameter of a given Two–Port Resistive
Network.
(ii) To determine g  parameter of a given Two–Port Resistive
Network.
APPARATUS:
(1) Network board
(2) Ammeters 0  50mA 2
(3) Voltmeter 0  10V 1
(4) Regulated power supply 030 V 1
THEORY :
Hybrid Parameters (h parameters)
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
I2
39
h21 = ___ = Forward current ratio when output short circuited
I1 V2 = 0
I2
h22 = ___ = Output admittance when input is open circuited
V2 I1 = 0
Inverse Hybrid Parameters (g parameters)
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, I1 and V2 are expressed in terms of V1 and I2.
i.e. I1 = g11 V1 + g12 I2  (1)
V2 = g21 V1 + g22 I2  (2)
I1
g11 g12 V1
V2
=
g21 g22
I2
(1)
Where
I1
g11 = ___ = Input admittance when output is open circuited
V1 I2 = 0
I1
g12 = ___ = Reverse current ratio when input short circuited
I2 V1 = 0
V2
g21 = ___ = Forward voltage ratio when output open circuited
V1 I2 = 0
V2
40
g22 = ___ = Output impedance when input is short circuited
I2 V1 = 0
PROCEDURE :
Hybrid Parameters
(1) Connect the circuit diagram of network Na as shown in fig (1).
(2) Apply voltage at port 1 keeping port 2 shortcircuited. 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 voltages
and currents and verify the results theoretically
Inverse Hybrid Parameters
(1) Connect the circuit diagram of network Na as shown in fig (1).
(2) Open the output port and excite the input port with a known voltage source Vs
as shown in fig (4) so that V1 = Vs and I2 = 0.
(3) Determine I1 and V2 to obtain g11 and g21.
(4) Then the input port is short circuited and output port is excited with the same
voltage source Vs as shown in fig (5) so that V2 = Vs and V1 = 0.
(5) Determine I1 and I2 to obtain g12 and g22.
OBSERVATION TABLE:
Hybrid parameters
SR.
NO.
V1a
Volts
I1a
mA
V2a
Volts
I2a
mA
REMARK
1 0 Port  2 short circuited
2 0 Port  1 open circuited
Inverse Hybrid Parameters
SR.
NO.
V1a
Volts
I1a
mA
V2a
Volts
I2a
mA
REMARK
1 0 Port  2 open circuited
2 0 Port  1 short circuited
41
CALCULATION:
Hybrid Parameters :
V1a
h11a = ___ =
I1a V2a = 0
V1a
h12a = ___ =
V2a I1 = 0
I2a
h21a = ___ =
I1a V2a = 0
I2a
h22a = ___ =
V2a I1a= 0
Inverse Hybrid Parameters:
I1a
g11a = ___ =
V1a I2a = 0
I1a
g12a = ___ =
I2a V1a = 0
V2a
g21a = ___ =
V1a I2a = 0
42
V2a
g22a = ___ =
I2a V1 = 0
CONCLUSION: 
QUIZ: 
1. For _________ connection of 2 networks hparameters have to be added.
2. Will the h parameter matrix of a passive network be a symmetrical?
3. If two networks Na and Nb are connected in series parallel, h11a =3 and h11b = 4 what will
be the value of h11?
4. For network shown, the parameters h11 and h21 are
5. In a twoport network. the condition for reciprocal in terms of ‘h’ parameters is,
(a) h12=h21 (b) h11= h22 (c) h11= h22(d) h12=h21
6. The ideal transformer cannot be described by
(a) h parameter (b) ABCD parameter
(c) g parameter (d) z parameter
7. For a symmetrical network
(a)h11 = h22 (b)h12 = h21
(c)h11 h22 h12 h21 = 0 (d)h11 h22 h12 h21 = 1
8. For a single element two port network of the given figure , h21 is
9. If a two port is reciprocal, which of the following is not true?
(a) z21 =z12 (b) y21 = y12
(c) h21 =h12 (d) AD = BC +1
43
EXPERIMENT NO: 10 DATE:
AIM : To study the response in RLC series circuit and determine various time
response specifications.
APPARATUS:
( i ) Decade resistance
(ii ) Decade capacitance
(iii ) Decade inductance
(iv) C.R.O.
( v ) Square wave generator.
THEORY : The behaviour of a circuit or system which contains two independent energy
storing elements is completely determined by a second order differential
equation.
For the circuit in fig (1) writing equation by applying KVL we get,
L di/dt + Ri + 1/c I dt = V
On differentiation,
L d2i / dt2 + R di/dt + 1/c i = 0
d2i / dt2 + R/L di / dt + 1/LC i = 0
Roots of characteristics equation are given by
s1 , s2 =  R/2L + (R/2L)2 (1/LC)
On this basis, we can predict the nature of response for three conditions.
(i ) (R/2L)2 > 1/LC , the response is over damped. Roots are real negative and
distinct.
(ii ) (R/2L)2 = 1/LC , roots are equal and negative repeated roots.
The response is critically damped, the values of resistance to achieve this is
called critical resistance, Rcr.
Hence
(Rcr/ 2L )2 = 1/LC
which give Rcr = 2 L / C
(iii) (R/2L)2 < 1/LC , we get under damped response. Roots are complex
conjugate. Resistance R is less than RCR We define damping ratio = R /
RCR = actual damping / critical damping
44
(iv) Natural frequency of oscillation is given by wn = 1 / LC
It yields information about settling time ( ts ) i.e. the time to reach steady state
value. The larger the wn the smaller the value will be the settling time.
For underdamped system damping frequency of oscillation is given
wd = wn (1 2 ) rad / sec
Percentage overshoot is determined the ratio of maximum overshoot above final
steady level of square wave to find steady wave to final steady state level.
PROCEDURE:
(1) Connect the given circuit as shown in fig(1) and supply a square voltage of
any magnitudes.
(2) Starting from zero, increase the value of R to adjust the response to a
critical damped case. At critical resistance, C.R.O will show a good square
wave. Note down the value of RCR and compare it with theoretical values
(given RCR =2 L/C )
(3) Adjust the resistance R < RCR and get underdamped response on C.R.O.
= R / RCR = is known as damping ratio.
(4) Find the damped frequency of oscillation Wd = 2 / Td is obtained from
C.R.O. shown in fig. where Td is on obtained from C.R.O as shown in
fig(2) compare with the theoretical
(5) Find percentage peak overshoot from C.R.O as shown in fig (2)
Peak overshoot : a/b X 100
Compare it with theoretical value given by
peak overshoot = e / (1  2) x 100
(6) Repeat above steps for another value of R in order to get underdamped
response.
L = _________
C = _________
45
CALCULATIONS :
RCR = 2 L/C
wd = 2 / Td
where Td is obtaind from C.R.O. as shown in fig (2).
peak overshoot = a/b x 100 %
where a and b is obtaind from C.R.O. as shown in fig (2).
RESULT TABLE:
QUANTITY THEORITICAL PRACTICAL
RCR
wd
peak
overshoot
CONCLUSION: 
QUIZ: 
1. A load is modeled as a 250 mH inductor in parallel with a 12 resistor. A capacitor is
needed to be connected to the load so that the network is critically damped at 60 Hz.
Calculate the size of capacitor.
2. Due to which factor, transient current is produced?
3. A twoterminal black box contains one of the R,L,C elements. The black box is connected to a 220V a.c. supply. The current through the source is I. When a capacitance
of 0.1 F is inserted in series between the source and box, the current through the source is
2I. the element is
(a) a resistance (b) an inductance
(c) a capacitance of 0.5F (d) not readily identifiable from the given data
46
4. The opencircuit voltage ratio V2(s)/V1(s) of the network shown in the given figure is
(a) 1+ 2s2 (b) 1/1+ 2s2 (c) 1+ 2s (d)1/1+ 2s
5. Refer to the RLC circuit in the figure below, what kind of response will it produce?
6. Consider parallel RLC circuit in the figure below, what type of response will it produce?
7. In a series RLC circuit, setting R = 0 will produce
(a) an overdamped response (b) a critically damped response
(c) an underdamped response (d) an undamped response
8. Why does capacitor act open circuit with DC?
9. A RL circuit has R= 2 Ω and L = 4 H. The time needed for the inductor current to reach 40
% of its steady state value is ___________.
47
EXPERIMENT NO: 11 DATE:
AIM : To study the step response of first order RC circuit and cascaded RC
sections
APPARATUS :
( i ) Function generator
(ii ) C.R.O.
(iii ) 680 Ω resistor
THEORY : The simplest RC circuit is a capacitor and a resistor in series. When a circuit
consists of only a charged capacitor and a resistor, the capacitor will discharge its
stored energy through the resistor. The voltage across the capacitor, which is time
dependent, can be found by using Kirchhoff's current law, where the current
through the capacitor must equal the current through the resistor. This results in the
linear differential equation.
CdV/dt + V/R = 0
Solving this equation for V yields the formula for exponential decay:
V (t) = Vo e t/RC
Where Vo is the capacitor voltage at time t = 0.
The time required for the voltage to fall to is called the RC time constant and is
given by
τ = RC
The time required for the voltage to fall to is called the RC time constant and is
given by RC circuits are frequently used to model the timing characteristics of
computer systems. When one logic gate drives another gate, the input circuit of the
second gate can be modeled as an RC load. The propagation delay through the first
gate can then be calculated assuming ideal square wave input and the RC load. The
longer the delay time, the slower the circuit can be switched and the slower the
computer is. Conversely, the shorter the delay time, the faster the computer is. This
delay time is called “gate delay” since it relates to driving characteristics of a logic
gate. Another use of RC circuits is to model wiring characteristics of bus lines on
48
integrated circuits (IC) or on printercircuit boards (PCB). A wire can be modeled
as many cascaded sections of simple RC circuits as shown in Figure 3 using 2
sections. When a square wave is applied to one end of the bus, it takes time for the
signal to propagate to the other end. This delay time due to the wire can be
calculated based on the values of R and C in each section and the number of sections
used to model the wire. The longer the wire, the more sections are needed for
accurate model. A wire is also referred to as “interconnect” and the delay due to a
wire is also called “interconnect delay.” In highfrequency systems, the
interconnect delay tends to dominate the gate delay and is a fundamental constraint
on how fast a computer can operate.
PROCEDURE :
(1) Build the circuit in Figure 2 using R = 10 Kand C = 0.01 F. Set the function
generator to provide a square wave input as follows:
a) Period T 3 ms (to ensure that T >> RC). This value of T guarantees that the
output signal has sufficient time to reach a final value before the next input
transition. Record the value of T. b) Set amplitude from 0 V to 5 V. Note that you
need to set the offset to achieve this waveform. Use the oscilloscope to display this
waveform on Channel 1 to make sure the amplitude is correct. We use this
amplitude since it is common in computer systems.
(2) Use Channel 2 of the oscilloscope to display the output signal waveform.
Adjust the timebase to display 2 complete cycles of the signals. Record the
maximum and the minimum values of the output signal.
(3) Use the measurement capability of the scope to measure the period T of the
input signal, the time value of the 10%point of Vout, the time value of the 90%
point of Vout, and the time value of the 50%point of Vout.
(4) Clear all the measurements. Use the paired measurement capability of the
scope to measure the voltage and time values at 10 points on the Vout waveform
during one interval when Vout rises or falls with time (pick one interval only). Note
that the time values should be referred to time t = 0 at the point where the input
signal rises from 0 V to 5 V or falls from 5 V to 0 V. Record these 10 measurements.
49
For RC cascaded sections:
(1) Build the circuit in Figure 3, using 2 identical resistors R = 10 Kand two
identical capacitors C = 0.01 F. Use the same square input as above and display it
on Channel 1.
(2) Display Vout on Channel 2 and adjust the timebase to display 2 complete cycles
of the signals.
(3) Use the scope measurement capability to measure the two delay times tPHL and
tPLH between the input and output signals.
CALCULATIONS:
From the equation for Vout and using the amplitude of Vs as 500 mV, compute the
amplitude of Vout for both cases R1 = 50 and R1 = 27 K.
RESULT TABLE:
QUANTITY THEORITICAL PRACTICAL
t(rise)
t(fall)
Vout for R = 50 Ω
Vout for R = 27 kΩ
50
CONCLUSION: 
QUIZ: 
1. If you use a different input signal (e.g. a ramp waveform from the function generator) as
source input to a RC circuit, draw the response waveform look like on the scope.
2. List out the applications of RC cascaded networks.
3. RC model for a wire is good below which frequency?
4. What difference is observed in the response a single RC circuit and cascaded RC
sections?
5. What would be the step response of RL series circuit?
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EXPERIMENT NO: 12 DATE:
AIM : To design and test a passive constantk High Pass Filter and measure its cutoff
frequency
APPARATUS :
( i ) Function generator
(ii ) C.R.O.
(iii) R = 680 Ω
THEORY : The simple firstorder electronic highpass filter is implemented by placing an
input voltage across the series combination of a capacitor and a resistor and using
the voltage across the resistor as an output. The product of the resistance and
capacitance (R×C) is the time constant (τ); it is inversely proportional to the cutoff
frequency fc, at which the output power is half the input power. That is,
fc = 1/2πRC
PROCEDURE :
(1) Connect the circuit of high pass filter using R and C components.
(2) Set the input voltage, Vi = 5V using signal generator and vary the frequency
from (01 MHz) in regular steps.
(3) Note down the corresponding output voltage.
(4) Plot the graph of output voltage v/s frequency.
CALCULATIONS :
Calculate cutoff frequency of this HPF.
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OBSERVATION TABLE:
Frequency (Hz) Output voltage (volts)
RESULT TABLE :
Cutoff frequency
(Hz)
THEORITICAL
PRACTICAL
CONCLUSION: 
QUIZ: 
1. What would be the response of low pass filter?
2. How band pass filters differ from low pass and high pass filters?
3. State the difference between active and passive filters.
4. What are the demerits of constant kfilters?
5. Define a time constant of a circuit.