two port network two Two-port Networks.pptx

K R K Rao - July 2014 1
Two-port Networks
K. Radhakrishna Rao

Two Port Networks
 Two port network can be three terminal with one
terminal common to input and output ports. The
common terminal can be ground.
 Or four terminals with only ground as common
terminal
 We can have four variables two of which can be
independent and the other two become dependent.
 If we further restrict our choice to one independent
variable at input port and one at output, we have four
types of representations possible. They are z, y and
h, g parameters.

y-parameters
 Y-parameters:
 Voltages are independent variables and currents are
dependent
 These are called Short Circuit parameters based on
the method of measuring. These are the most popular
parameters as shorting at high frequencies can easily
be done.
0
0
0
0
V
y
V
y
I
V
y
V
y
I
i
f
r
i
i
i





Passive network two-port parameters
r
f
r
f
r
f
r
f
g
g
h
h
z
z
y
y






,
,

Linear Two Port Passive Networks
 Resistive Attenuator
(Probe)
R2 R1
+
Vi
-
+
Vo
-
1
1 2
o
i
V R
V R R



g-parameters of Resistive
Attenuator
1
1 2 1 2
1 1 2
1 2 1 2
1 R
R R R R
R R R
R R R R

 
 
 
 
 
 
 
 

 Capacitive Attenuator
C1
C2
+
Vi
-
+
Vo
-
2
1 2
o
i
V C
V C C



 Inductive Attenuator
1
1 2
o
i
V L
V L L


L1
L2
+
Vi
-
+
Vo
-

 Ideal Transformer
2
1
o
i
V N
V N

N1 N2

g-parameters of Transformer
2
1
2
1
0
0
N
N
N
N

 
 
 
 
 
 

g-Parameter
 For Attenuator: Most appropriate parameter where
voltage transfer from input port to output port is
important i.e., ‘g’ parameter
i r
i i
f o
o o
g g
I V
g g
V I
 
   
 
   
   
 

Current Attenuators
 Appropriate parameters ‘h’ parameter
i r
i i
f o
o o
h h
V I
h h
I V
 
   
 
   
   
 
R1
R2
+
Vi
-
Io
Ii
1
1 2
o
i
I R
I R R



Transformer
1
2
o
i
I N
I N

N1 N2
+
Vi
-
Ii
Io

Other Examples of Passive two-ports
 Transconductors
 y-parameters or sc
(short-circuit
parameters)
R
+
Vi
-
+
Vo
-
Ii Io
1 1
1 1
R R
R R

 
 
 
 

 
 

Other Examples of Passive two-ports
 Transresistors
 z-parameters or oc
(open-circuit
parameters)
R R
R R
 
 
 
R
+
Vi
-
+
Vo
-
Ii
Io

Interconnect Models
1
1
o
i
V
V sCR


R
C
+
Vo
-
+
Vi
-

Transfer function of Ideal Delay
 Transfer function of
Ideal Delay is given by
 Elmore’s Delay






s
e 


Interconnect Models
2
1
1
o
i
V
V sCR s LC

  2
2
1
1
o o
s s
Q
 

 
 
  
   
   
1 1
;
o
o
Q
CR
LC


 
R
C
L +
Vo
-
+
Vi
-

Interconnect Models
?
o
i
V
V

R1
C1
R2
C2
R3
C3
+
Vo
-
+
Vi
-

Interconnect Models
?
o
i
V
V

R1
C1
L1
R2
C2
L2
+
Vo
-
+
Vi
-

Crystal Equivalent
Cs
L
Rs
Cp

Band Pass Filter
 Antenna, IF/RF
Transformers
2
2
2
1
1
o
i
o
o o
sL
V R
sL
V
s LC
R
s
Q
s s
Q

 
 
 
 

 
 
 
 
 
 
 

 
 
  
   
   
R
C L
1
;
o
o
R
Q
L
LC


 

Band Pass Filter
 Magnitude Plot
 Phase Plot

2


2

0
0
2


o
i
V
V
o
i
V
V
1
max
2
o
Q

 




Q indicates the number of
dominant peaks!

Output of the resonant circuit for a
square wave input

Example of a resistive ladder
 Passivity:
Forward transmission = Reverse Transmission
Output Expression = v(5)
Input Source Name = V1
Transfer function = 0.019861
Input Impedance = 14163.2
Output Impedance = 2824.23

Interchange input and output ports as
also driving source and mode of output
 Passivity:
Forward transmission = Reverse Transmission
Output Expression = I(R1)
Input Source Name = I1
Transfer function = 0.019861
Input Impedance = 2824.23

h & g are hybrid parameters
 h-parameter has independent variable at
 Input as current and at output as voltage
 Here forward transfer parameter is short circuit
current gain and reverse transfer parameter is the
open circuit voltage gain
0
0
0
0 ,
V
h
I
h
I
V
h
I
h
V
i
f
r
i
i
i





two port network two Two-port Networks.pptx

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