Chapter 14 Frequency Response
Download
Report
Transcript Chapter 14 Frequency Response
Chapter 18
Two-port Networks
the four terminals have
four-terminal been paired into ports
network
KCL
two-port
network
At all times, the instantaneous current flowing
into one terminal is equal to the instantaneous
current flowing out the other.
i1
i2
i4
i3
i1+i2+i3+i4=0(KCL)
i1
i1=-i2 ; i3=-i4
i4
V1 z11I1 z12I 2
V2 z21I1 z22I 2
I1 y11V1 y12V2
I 2 y21V1 y22V2
V1 AV2 BI2
I1 CV2 DI2
V2 aV1 bI1
I 2 cV1 dI1
V1 h11I1 h12V2
I 2 h21I1 h22V2
I1 g11V1 g12I 2
V2 g21V1 g22I 2
The network is linear(without independent sources).
Impedance Parameters
Impedance or z parameters are defined by
V1 z11I1 z12I 2
V2 z21I1 z22I 2
impedance
matrix Z
V1 z11I1 z12I 2 Voc1
V2 z21I1 z22I 2 Voc2
z11 VI11
I 2 0
Open-circuit input impedance.
z12 VI 21
I1 0
Open-circuit transfer impedance from port 1 to port 2
z21 VI12
I 2 0
Open-circuit transfer impedance from port 2 to port 1
z22
V2
I 2 I 0
1
Open-circuit output impedance.
Determining of the z parameters: (a) finding z11 and z21, (b)
finding z12 and z22
Examples
(a) T equivalent circuit (for reciprocal case only), (b) general
equivalent circuit
Admittance Parameters
Admittance or y parameters are defined by
I1 y11 y12 V1
I 2 y21 y22 V2
admittance
matrix Y
I1 y11V1 y12V2
I 2 y21V1 y22V2
I1 y11V1 y12V2 I sc1
I 2 y21V1 y22V2 I sc 2
y11 VI11
V2 0
Short-circuit input admittance.
y12 VI12
V1 0
Short-circuit transfer admittance from port 1 to port 2
y21 VI21
V2 0
Short-circuit transfer admittance from port 2 to port 1
y22 VI22
V1 0
Short-circuit output admittance.
Determination of the y parameters: (a) finding y11 and y21,
(b) finding y12 and y22.
(a) -equivalent circuit (for reciprocal case only), (b) general
equivalent circuit.
Hybrid Parameters
Hybrid or h parameters are defined by
V1 h11I1 h12V2
I 2 h21I1 h22V2
hybrid matrix
Z
h11 VI11
V2 0
h12 VV12
I1 0
Open-circuit reverse voltage gain
h21 II12
V2 0
Short-circuit forward current gain
h22
I2
V2 I 0
1
Short-circuit input impedance.
Open-circuit output admittance.
The h-parameter equivalent network of a two-port network
Inverse hybrid parameters (g parameters)
I1 g11V1 g12I 2
V2 g21V1 g22I 2
The g-parameter model of a two-port network
Transmission Parameters
Transmission or T parameters are defined by
V1 A B V2
I1 C D I 2
V1 a11V2 a12I 2
I1 a21V2 a22I 2
Transmission
matrix T
A VV12
I 2 0
B VI 21
C VI12
D
V2 0
I 2 0
I1
I 2 V 0
2
Open-circuit voltage ratio
Negative short-circuit transfer impedance
Open-circuit transfer admittance
Negative short-circuit current ratio
Inverse transmission parameters
V2 aV1 bI1
I 2 cV1 dI1
Reciprocal Two-Port Circuits
------------- linear and has no dependent source
If a two-port circuit is reciprocal, the following
relationships exist among the port parameters:
z12 z21
y12 y21
h12 h21
g12 g 21
T AD BC 1
T ad bc 1
Symmetric Two-Port Circuit
A reciprocal two-port circuit is symmetric if its ports can
be interchanged without disturbing the values of the
terminal currents and voltages.
If a two-port circuit is symmetric, the following
relationships exist among the port parameters: (besides
those exist in reciprocal)
z11 z22
y11 y22
h h11h22 h12h21 1
g g11g22 g12g21 1
A D
ad
Question: How many calculations or measurements are
needed to determine a set of parameters of a two-port
circuit?
For a general two-port with sources:
For a general linear two-port:
6
4
For a reciprocal two-port:
3
For a symmetric two-port:
2
Relationships between
parameters
Example:
z parameters
V1 z11I1 z12I 2
V2 z21I1 z22I 2
z 22
z12
y11
, y12
,
z
z
z 21
z11
y21
, y22
z
z
y parameters
I1 y11V1 y12V2
I 2 y21V1 y22V2
where
z z11z22 z12z21
Interconnection of networks
Series connection of
two two-port networks
Z Za Zb
Parallel connection of two
two-port networks
Y Ya Yb
Cascade connection of
two two-port networks
T Ta Tb
Transistor amplifier with source and load resistance