TwoPort Networks

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Two-Port Networks

• BEE2113 Signals Systems
• R. M. Taufika R. Ismail
• FKEE, UMP

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Introduction
Two-port n/w
One-port n/w
Eg
Eg
R
L
C
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Reciprocal symmetrical n/w

• Reciprocal n/w A two-port n/w which is linear
  has no dependent sources
• Symmetrical n/w A two-port n/w which has
  mirrorlike symmetry about some central line
  i.e. a line can be found that divides the n/w
  into two similar halves

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Impedance (z) Parameters
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Or
Equivalent circuit
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The values of the parameters are
I2 0 means o/c port 2
I1 0 means o/c port 1
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Finding z11 and z21 o/c port 2 and apply source
to port 1
Finding z12 and z22 o/c port 1 and apply source
to port 2
For reciprocal case z12 z21
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Example 1 (Pb.19.1, pg.890)
Obtain the z parameters for the following n/w.
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Solution
Finding z11 and z21 o/c port 2 and apply source
to port 1
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Finding z12 and z22 o/c port 1 and apply source
to port 2
(or simply since reciprocal case)
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Example 2 (P.P.19.2, pg.854)
Calculate I1 and I2 in the following two-port
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Solution
Method 1 Use equivalent circuit
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From (2)
Subst. into (1)
Hence
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Method 2 Use matrix operations
Hence,
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Therefore
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Admittance (y) Parameters
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Or
Equivalent circuit
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The values of the parameters are
V2 0 means s/c port 2
V1 0 means s/c port 1
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Finding y11 and y21 s/c port 2 and apply source
to port 1
Finding y12 and y22 s/c port 1 and apply source
to port 2
For reciprocal case y12 y21
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Example 3 (P.P.19.3, pg.857)
Obtain the y parameters for the following n/w.
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Solution
Finding y11 and y21 s/c port 2 and apply source
to port 1
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(No Transcript)
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Finding y12 and y22 s/c port 1 and apply I2 to
port 2
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(or simply since reciprocal case)
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Relation between z and y parameters
Therefore,
or
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Hybrid (h) Parameters
Dependent variables
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Or
Equivalent circuit
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The values of the parameters are
V2 0 means s/c port 2
I1 0 means o/c port 1
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Finding h11 and h21 s/c port 2 and apply source
to port 1
Finding h12 and h22 o/c port 1 and apply source
to port 2
For reciprocal case h12 -h21
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Inverse Hybrid (g) Parameters
If I1 and V2 are chosen as the dependent
variables, then
That is
or
g parameters
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Example 4 (Pb.19.34, pg.894)
Obtain the h and g parameters of the following
two-port n/w.
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Solution
Finding h11 and h21 s/c port 2 and apply source
to port 1
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(No Transcript)
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Finding h12 and h22 o/c port 1 and apply source
to port 2
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(No Transcript)
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Hence,
Finding g,
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Transmission (T or ABCD) Parameters
Dependent variables
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Input V1 , I1
Output V2 , -I2
Linear Two-port
-I2 is used rather than I2 because the
current at port 2 is considered to be leaving
the network!
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The values of the parameters are
I2 0 means o/c port 2
V2 0 means s/c port 2
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Finding A and C o/c port 2 and apply source to
port 1
Finding B and D s/c port 2 and apply source to
port 1
For reciprocal case AD - BC 1
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Inverse Transmission (t) Parameters
V1 and I1 are chosen as the dependent variables
If V2 and I2 are chosen as the dependent
variables, then
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Notice that
because
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Hence,
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where
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Example 5 (Pb.19.49, pg.896)

• Using impedances in the s-domain, obtain the
  transmission parameters for the following circuit.

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Solution
Finding A and C o/c port 2 and apply source to
port 1
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(No Transcript)
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Finding B and D s/c port 2 and apply source to
port 1
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Hence,
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Summary
In summary,
For reciprocal case
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(No Transcript)
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Interconnections of N/w 1.Series
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We have
and
Notice that
and
Hence
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Interconnections of N/w 2.Parallel
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We have
and
Notice that
and
Hence
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Interconnections of N/w 3.Cascade
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We have
and
Notice that
and
Hence
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In summary,
series
cascade
parallel
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Example 6 (P.P.19.13, pg.876)
Obtain the y parameters for the n/w
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Solution
Na
Nb
Then find the y parameters for each of Na and Nb
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Finding y parameters for Na
Finding y11 and y21
Finding y12 and y22
I1
I2
I1
I2
V1 -
V2 -
(reciprocal case)
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Finding y parameters for Nb
Finding y11 and y21
Finding y12 and y22
I1
I2
I1
I2
V1 -
V2 -
(reciprocal case)
(symmetry)
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We find that
Therefore, since Na and Nb are connected in
parallel,