chapter 18 two-port networks. four-terminal network the four terminals have been paired into ports...
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Chapter 18
Two-port Networks
four-terminal network
the four terminals have been paired into ports two-port
network
At all times, the instantaneous current flowing into one terminal is equal to the instantaneous current flowing out the other.
KCL
i1
i2 i3
i4 i1 i4
i1+i2+i3+i4=0(KCL)i1=-i2 ; i3=-i4
2221212
2121111
2221212
2121111
VyVyI
VyVyI
IzIzV
IzIzV
2221212
2121111
2221212
2121111
IgVgV
IgVgI
VhIhI
VhIhV
112
112
221
221
dIcVI
bIaVV
DICVI
BIAVV
The network is linear(without independent sources).
Impedance ParametersImpedance or z parameters are defined by
impedance matrix Z
2221212
2121111
IzIzV
IzIzV
022
021
012
011
12
2
21
2
12
1
21
1
IIV
IIV
IIV
IIV
z
z
z
zOpen-circuit input impedance.
Open-circuit transfer impedance from port 1 to port 2
Open-circuit transfer impedance from port 2 to port 1
Open-circuit output impedance.
22221212
12121111
oc
oc
VIzIzV
VIzIzV
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 ParametersAdmittance or y parameters are defined by
2
1
2221
1211
2
1
V
V
yy
yy
I
I
2221212
2121111
VyVyI
VyVyI
admittance matrix Y
022
021
012
011
12
2
21
2
12
1
21
1
VVI
VVI
VVI
VVI
y
y
y
yShort-circuit input admittance.
Short-circuit transfer admittance from port 1 to port 2
Short-circuit transfer admittance from port 2 to port 1
Short-circuit output admittance.
22221212
12121111
sc
sc
IVyVyI
IVyVyI
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 ParametersHybrid or h parameters are defined by
2221212
2121111
VhIhI
VhIhV
hybrid matrix Z
022
021
012
011
12
2
21
2
12
1
21
1
IVI
VII
IVV
VIV
h
h
h
hShort-circuit input impedance.
Open-circuit reverse voltage gain
Short-circuit forward current gain
Open-circuit output admittance.
The h-parameter equivalent network of a two-port network
Inverse hybrid parameters (g parameters)
2221212
2121111
IgVgV
IgVgI
The g-parameter model of a two-port network
Transmission ParametersTransmission or T parameters are defined by
2
2
1
1
I
V
DC
BA
I
V
2222211
2122111
IaVaI
IaVaV
Transmission matrix T
0
0
0
0
22
1
22
1
22
1
22
1
VII
IVI
VIV
IVV
D
C
B
A Open-circuit voltage ratio
Negative short-circuit transfer impedance
Open-circuit transfer admittance
Negative short-circuit current ratio
Inverse transmission parameters
112
112
dIcVI
bIaVV
------------- linear and has no dependent source
If a two-port circuit is reciprocal, the following relationships exist among the port parameters:
1
1
21122112
2112
2112
bcadT
BCADT
gg
hh
yy
zz
Reciprocal Two-Port Circuits
Symmetric Two-Port CircuitA 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)
da
DA
ggggg
hhhhh
yy
zz
1
1
21122211
21122211
2211
2211
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: 6
For a general linear two-port: 4
For a reciprocal two-port: 3
For a symmetric two-port: 2
Relationships between parameters
Example: z parameters y parameters
2221212
2121111
IzIzV
IzIzV
2221212
2121111
VyVyI
VyVyI
z
zy
z
zy
z
zy
z
zy
1122,
2121
,12
12,22
11
21122211 zzzzz
where
Interconnection of networksSeries connection of two two-port networks
ba ZZZ
Parallel connection of two two-port networks ba YYY
Cascade connection of two two-port networks ba TTT
Transistor amplifier with source and load resistance