# Two-Port Networks

Document Sample

```					Two-Port Networks

Lecture 12
Introduction
I1              I2

V1                        V2

Port 1              Port 2
(Input)             (Output)

• An access point is named as a port
• Regardless of what is inside the circuit if you know the
relationship between V1, I1, I2 and V2 you can find out
what happens to a parameter when one or more other
parameters are changed
• Two-Port parameters
–   Impedance
–   Hybrid
–   Transmission                                          2
I1          I2
I1 = y11V1 + y12V2   V1                    V2
I2 = y21V1 + y22V2
Port 1          Port 2
(Input)         (Output)

When V2 = 0          When V1 = 0
I1                 I1
y 11              y 12 
V1                 V2
I2                     I2
y 21               y 22      
V1                     V2
3
•   y11 -   short-circuit input admittance
•   y12 -   short-circuit transfer admittance
•   y21 -   short-circuit transfer admittance
•   y22 -   short-circuit output admittance

4
Example 01
I1         2Ω          I2
Find y parameters
V1                               V2
1Ω        3Ω                I1 = y11V1 + y12V2
I2 = y21V1 + y22V2

3                        1
y11  S                y21   S
2                        2
5
1
y12   S                  y22  S
2                        6

5
Example 02
• Substitute port 1 with a 2A current source
and port 2 with a 4Ω resistor. Find I2.
I1 = y11V1 + y12V2
I2 = y21V1 + y22V2
I1  2A   V2  I 2  4
3    1                      2
2  V1  V2               I2   A
2    2                     11
1    5
I 2   V1  V2
2    6
6
Impedance (z) Parameters
V1 = z11I1 + z12I2
V2 = z21I1 + z22I2

When I2 = 0          When I1 = 0
V1                V1
z 11             z 12 
I1                I2
V2                  V2
z 21             z 22   
I1                  I2
7
Impedance (z) Parameters
•   z11 - open-circuit input impedance
•   z12 - open-circuit transfer impedance
•   z21 - open-circuit transfer impedance
•   z22 - open-circuit output impedance

8
Example 03
I1   2Ω            j2Ω    I2

Find z parameters
V1                                    V2
-j4Ω

V1                           V1
z 11      2  j4           z 12       j4
I1                           I2

V2                              V2
z 21       j4              z 22         j2
I1                              I2
9
Example 04
• Substitute Port 1 with a 120V voltage
source with an internal resistance of 1Ω
and port 2 with a 4Ω resistor. Find V2.
V1 = z11I1 + z12I2   120  I1  ( 2  j4)I1  j4I 2
V2 = z21I1 + z22I2   V2   j4I1  j2I 2
I 2  1.61137A
V2 = -I2*4

10
Hybrid (h) Parameters
V1 = h11I1 + h12V2
I2 = h21I1 + h22V2

When V2 = 0            When I1 = 0
V1                  V1
h 11               h 12 
I1                  V2
I2                  I2
h 21               h 22 
I1                  V2
11
Hybrid (h) Parameters
•   h11 - short-circuit input impedance
•   h12 - open-circuit reverse voltage gain
•   h21 - short-circuit forward current gain
•   h22 - open-circuit output admittance

12
Example
I1                    I2

12Ω        3Ω
V1                               V2
6Ω

V1 = h11I1 + h12V2
I2 = h21I1 + h22V2
h11  14 Ω                        2
h 21  
3
2                        1
h12 
3
h 22      S
9
13
Transmission Parameters
V1 = AV2 - BI2
I1 = CV2 - DI2

When I2 = 0      When V2 = 0
V1
A              B
V1
V2
I2
I1
C                   I1
V2            D
I2       14
Transmission Parameters
•   A - open-circuit voltage ratio
•   B - negative short- circuit transfer impedance
•   C - open-circuit transfer admittance
•   D - negative short-circuit current ratio

15
I1
Example
I2

1Ω            1Ω
V1             1F                      V2

V1 = AV2 - BI2
A = 1+jω               C = jω          I1 = CV2 - DI2

B = 2+jω               D = 1+jω
16
Series Connection
V1
I1
z1

I2
z2
V2
V1                  V2
I1             I2
z1                  z2
V              I1 = I 2
V = V1 + V2   17
Series Connection

I1         IA1               IA2         I2
Linear,
VA1          Passive          VA2
Network A

V1                                             V2

IB1               IB2
Linear,
VB1          Passive          VB2
Network B

18
I1         IA1                  IA2          I2
Linear,
VA1          Passive             VA2
Network A

V1                                                 V2

IB1                  IB2
Linear,
VB1          Passive             VB2
Network B

Network A
[ ] [
VA1
VA2
=
ZA11
ZA21
ZA12
ZA22   ][ ]  IA1
IA2

Network B           [ ] [
VB1
VB2
=
ZB11
ZB21
ZB12
ZB22   ][ ]  IB1
IB2
19
Network A + Network B

[ ] [
VA1+VB1
VA2+VB2
=
ZA11+ZB11
ZA21+ZB21           ][ ]
ZA12+ZB12
ZA22+ZB22
I1
I2

I1= IA1= IB1
I2= IA2= IB2

20
Parallel Connection

V1                          V1
I1                            I1
z1                          z1
I        V2
I2
z2
I2   z2
V2                          V
I = I1+ I2
V = V1 = V2
21
Parallel Connection

IA1                     IA2
Linear,
Passive Network
VA1                      VA2
A

I1                                     I2

V1                                          V2

IB1                     IB2
Linear,
Passive Network
VB1                      VB2
B

22
IA1                              IA2
Linear,
Passive Network
VA1                               VA2
A

I1                                                     I2

V1                                                          V2

IB1                              IB2
Linear,
Passive Network
VB1                               VB2
B

Network A
[ ] [  IA1
IA2
=
YA11
YA21
YA12
YA22   ][ ]  VA1
VA2

Network B   [ ] [  IB1
IB2
=
YB11
YB21
YB12
YB22   ][ ]  VB1
VB2

23
Network A + Network B

[ ] [
IA1+IB1
IA2+IB2
=
YA11+YB11
YA21+YB21
YA12+YB12
YA22+YB22   ][ ]
V1
V2

V1= VA1= VB1
V2= VA2= VB2

24
IP1                   IP2                   IQ1                 IQ2

Linear,                                  Linear,
Passive                                  Passive
VP1        Network P           VP2   VQ1            Network Q          VQ2

NETWORK P                                      NETWORK Q

[ ] [ ][ ] [ ] [ ][ ]
VP1
IP1
=
AP BP
CP DP
VP2
-IP2
VQ1
IQ1
=
AQ
CQ
BQ
DQ
VQ2
-IQ2

VP2 = VQ1
-IP2 = IQ1
25
Substituting Network Q

[ ] [ ] [ ][ ]
V1
I1
=
AP BP
CP DP
AQ
CQ
BQ
DQ
V2
-I2

[ ][
V1
I1
=
APAQ+BPCQ
CPAQ+DPCQ
APBQ+BPDQ
CPBQ+DPDQ   ][ ]
V2
-I2

26

```
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
 views: 16 posted: 4/13/2012 language: pages: 26