TWO-PORT
NETWORK
EKT 919/3
CrashCourse Sidang Akademik 2009/2010
(1 June 2010 – 28 June 2010)
Lecturer: Pn. Wan Nur Suryani Firuz Bt Wan Ariffin (012-4820815)
Cik Ismahayati Binti Adam(012-7744923)
PLV:Pn. Nazatul Shima Binti Saad (013-5954737)
TWO-PORT NETWORK
Terminal equations
Two-port parameters
Relationships among two-port
parameters
Analysis of terminated two-port
circuit
Interconnected two-port circuits
TERMINAL EQUATIONS
I1

V1

I2
s-domain
circuit
s-domain two-port basic building block

V2

Terminal equations relationships
1st Relationship:
V1  z11I1  z12 I 2
V2  z 21I1  z 22 I 2
2nd Relationship:
I1  y11V1  y12V2
I 2  y21V1  y22V2
3rd Relationship:
V1  a11V2  a12 I 2
I1  a21V2  a22 I 2
4th Relationship:
V2  b11V1  b12 I1
I 2  b21V1  b22 I1
5th Relationship:
V1  h11I1  h12V2
I 2  h21I1  h22V2
6th Relationship:
I1  g11V1  g12 I 2
V2  g 21V1  g 22 I 2
TWO PORT NETWORK:
Terminal equations
Two-port parameters
Relationships between parameters
Analysis of terminated two-port
circuit
Interconnected two-port circuits
IMPEDANCE PARAMETERS
z parameters
V1
z11 
I1
V2
z 21 
I1

I 2 0

I 2 0
V1  z11I1  z12 I 2
V2  z21I1  z22 I 2
V1
z12 
I2
V2
z 22 
I2

I1  0

I1  0
ADMITTANCE PARAMETERS
y parameters
I1  y11V1  y12V2
I 2  y21V1  y22V2
I1
y11 
V1
I2
y21 
V1
S
V2  0
S
V2  0
I1
y12 
V2
y22
I2

V2
S
V1  0
S
V1  0
a parameters
V1
a11 
V2
I1
a21 
V2
I 2 0
V1
a12  
I2
I 2 0
I1
a22  
I2
S

V2  0
V2  0
b parameters
V2
b11 
V1
I2
b21 
V1
I1  0
V2
b12  
I1
V1  0
I1  0
I2
b22  
I1
V2  0
S

a and b parameters are called transmission parameters
HYBRID PARAMETERS
h parameters
V1
h11 
I1 V
2 0
I2
h21 
I1
V2  0

V1
h12 
V2
I2
h22 
V2
I1  0
S
I1  0
INVERSE HYBRID PARAMETERS
g parameters
I1
g11 
V1
V2
g 21 
V1
S
I 2 0
I1
g12 
I2
g 22
I 2 0
V2

I2
V1  0

V1  0
Example 1
Find z parameter for the below
circuit:
I1
I2
5

V1


20
15
V2

Solutions:
When port 2 open-circuit, I2=0
so,
V1
z11 
I1
I 2 0
20(20)

 10
40
When I2=0, thus V2
15
V2 
V1  0.75V1
15  5
V2
z 21 
I1
I 2 0
0.75V1

 7.5
V1 / 10
Now, when I1=0,so
V2
z 22 
I2
I1  0
15(25)

 9.375
40
When port 1 open-circuit, I1=0,
so:
20
V2
V1 
V2  0.8V2 I 2 
5  20
9.375
V1
z12 
I2
I1  0
0.8V2

 7.5
V2 / 9.375
TWO-PORT NETWORK
Terminal equations
Two-port parameters
Relationships between parameters
Analysis of terminated two-port
circuit
Interconnected two-port circuits
RELATIONSHIPS BETWEEN
PARAMETERS
I1 y12
I 2 y22
y22 I1 y12 I 2
V1 


y11 y12
y
y
y21 y22
y11 I1
y21 I 2
y11I 2 y21I1
V2 


y11 y12
y
y
y21 y22
Compare these two above equations:
y22
y12
z11 
z12  
y
y
y21
y11
z 21  
z22 
y
y
Find z parameters as functions of a
parameters
1
a22
V2 
I1 
I2
a21
a21
 a11a22

a11
V1 
I1  
 a12  I 2
a21
a
 21

Therefore,
a11
z11 
a21
a
z12 
a21
1
z 21 
a21
a22

a21
z 22
RECIPROCAL TWO-PORT
CIRCUITS
If a two-port circuit is reciprocal, the following
relationships exist among port parameters:
z12  z 21
y12  y21
a11a22  a12 a21  a  1
b11b22  b12b21  b  1
h12  h21
g12   g 21
Symmetric of a reciprocal two-port
circuits
Following relationships exist among port
parameters:
z11  z22
y11  y22
a11  a22 b11  b22
h11h22  h12h21  h  1
g11g 22  g12 g 21  g  1
Example of symmetric two-port circuits
Symmetric tee
I2
I1
Za
Za

V1


Zb
V2

Symmetric pi
I2
I1
Zb


V1

Za
Za
V2

Symmetric bridge tee
Zc
I2
I1
Za
Za


V1

Zb
V2

Symmetric lattice
I2
I1
Za

V1


Zb
V2
Zb

Za
TWO-PORT NETWORK
Terminal equations
Two-port parameters
Relationships between parameters
Analysis of terminated two-port
circuit
Interconnected two-port circuits
ANALYSIS OF TERMINATED TWOPORT CIRCUITS
I1
I2
Zg

Vg
V1

Two-port model
of a
network

V2

ZL
6 characteristics of terminated two-port
circuit
Input impedance (Zin=V1/I1) or admittance
(Yin=I1/V1)
Output current, I2
Thevenin voltage and impedance (ZTh, VTh)
with respect to port 2
Current gain I2/I1
Voltage gain V2/V1
Voltage gain V2/Vg
6 characteristics in term of z parameters
4 parameter equations that describe the
circuit:
V1  z11I1  z12 I 2
V2  z21I1  z22 I 2
V1  Vg  I1Z g
V2   I 2 Z L
1st characteristic (input impedance)
 z 21I1
I2 
Z L  z 22
z12 z 21
Z in  z11 
z 22  Z L
2nd characteristic (output current, I2)
I1 
I2 
Vg  z12 I 2
z11  Z g
 z 21Vg
( z11  Z g )( z 22  Z L )  z12 z 21
3rd characteristic (Thevenin voltage @
impedance)
V2
V2 I
I 2 0
2 0
V1
 z 21I1  z 21
z11
z21
 VTh  Vg
Z g  z11
Impedance Thevenin
 z12 I 2
I1 
z11  Z g
V2
I2
Vg  0
z12 z21
 ZTh  z22 
z11  Z g
4th characteristic (current gain)
I2
 z 21

I1 Z L  z 22
5th characteristic (voltage gain V2/V1)
  V2 

V2  z21I1  z22 
 ZL 
  V2 

z11I1  V1  z12 
 ZL 
V1 z12V2
I1 

z11 z11Z L
V2
z 21Z L

V1 z11Z L  z11 z 22  z12 z 21
z 21Z L

z11Z L  z
6th characteristic (voltage gain V2/Vg)
Vg
z12V2
I1 

Z L ( z11  Z g ) z11  Z g
z 21Vg
z 21 z12V2
z 22
V2 


V2
Z L ( z11  Z g ) z11  Z g Z L
V2
z21Z L

Vg ( z11  Z g )( z22  Z L )  z12 z21
TWO-PORT NETWORK
Terminal equations
Two-port parameters
Relationships between parameters
Analysis of terminated two-port
circuit
Interconnected two-port circuits
INTERCONNECTED TWO-PORT
CIRCUITS
Cascade connection
Two-port parameters
V1  a11V2  a12 I 2
I1  a21V2  a22 I 2
 V2  a12
 I 2
V1  a11
 V2  a22
 I 2
I1  a21
Interconnection (V’2=V’1 and I’2= -I’1)
 V1  a12
 I1
V1  a11
 V1  a22
 I1
I1  a21
Relationship V’1 and I’1 with V2 and I2 in
second circuit :
 V2  a12
 I 2
V1  a11
 V2  a22
 I 2
I1  a21
 a11
  a12
 a21
 )V2  (a11
 a12
  a12
 a22
 ) I 2
V1  (a11
 a11
  a22
 a21
 )V2  (a21
 a12
  a22
 a22
 ) I 2
I1  (a21
 a11
  a12
 a21

a11  a11
 a12
  a12
 a22

a12  a11
 a11
  a22
 a21

a21  a21
 a12
  a22
 a22

a22  a21
Reference book
Electric Circuits, James W. Nilsson
and Susan A. Riedel, Prentice Hall