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Two Port network
h  PARAMETERS OR HYBRID PARAMETERS
Because of the forward bias of the baseemitter junction, the device has a very low input resistance. For opencircuit impedance measurement of Z_{12} and Z_{22}, it is very difficult to make the input open circuited. Z_{11} and Z_{12} can be measured by open circuit impedance measurements, since the collectoremitter junction is reversed biased.
V_{1} = h_{11}I_{1} + h_{12}V_{2}
I_{2} = h_{21}I_{1 }+h_{22}V_{2}
where,h_{i} : input impedance with the output shortcircuited.
h_{r} : reverse voltage gain with the input opencircuited.
h_{f} : Forward current gain with the output shortcircuited.
h_{o} : Output admittance with the input opencircuited
Condition of Reciprocity
h_{12} =  h _{21 }
Condition of Symmetry
hparameter Equivalent Circuit
gPARAMETERS OR INVERSE HYBRID PARAMETERS
I_{1} = g_{11} V_{1} + g_{12}I_{2}
V_{2} = g_{21}V_{1} + g_{22}I_{2}
The gparameters can be defined as,
..... (i.e. input admittance with output open circuited)
...(i.e. forward voltage gain with output open circuited)
......(i.e. forward voltage gain with output open circuited)
....(i.e. output impedance with input short circuited)
Condition of Reciprocity
g_{12} =  g_{21}
Condition of Symmetry
gparameter Equivalent Circuit
INTER RELATIONS IN NETWORK PARAMETERS
Y  parameter in terms of Zparameters
ABCDparameters in terms of Z parameters
V_{1} = Z_{11}I_{1} + Z_{12}I_{2}
V_{2} = Z_{21}I_{1} + Z_{22}I_{2}
from equation (ii),
from equation (i) and (ii),
NOTE: ABCD parameters relate voltage and current in the primary to the voltage and current in the secondary
Zparameters in terms of hparameters
V_{1} = h_{11}I_{1} + h_{12}V_{2} ..................... (i)
I_{2} = h_{21}I_{1} + h_{22}V_{2} .....................(ii)
from equation (ii)
Similarly
Condition Under which passive Twoport Network is reciporcal and Symmeterical
Parameters condition for Reciprocity Condition for Symmetry 
INTERCONNECTION OF TWOPORT NETWORKS
1. Series Connection
I_{1a }= I_{1b} = I_{1} I_{2a} = I_{2b} = I_{2}
V_{1} = V_{1a} + V_{1b}
so, in matrix form the Zparameters of the seriesconnected combined network can be written as
2. Parallel Connection
3. Series Parallel Connection hparameters
I_{1a} = I_{1b} = I_{1}
V_{1} = V_{1a} + V_{1b }........................(i)
I_{2 }= I_{2a} + I_{2b} ........................(ii)
Where
4. Parallel Series Connection
Where
5. Cascade Connection
I_{1} = I_{1a}
V_{1} = V_{1a}
I_{2} = I_{2b}
I_{1b} = –I_{2a}
V_{1b} = V_{2a}
BARLETTS BISECTION THEOREM
Network is symmetrical as well as reciprocal Z_{OC} – Open circuited driving point impedances for half of section.
Z_{SCH} – Short circuited driving point impedances for half of section.
SYMMETRICAL LATTICE NETWORK
Z_{b} ~ Z_{OCH}
Z_{a} ~ Z_{SCH}
IMAGE IMPEDANCE
Network parameters
Z – PARAMETERS
.........the input driving point impedance with the output port opencircuited
....The reverse transfer impedance with the input port opencircuited
....the forward transfer impedance with the output port opencircuited
.....the output driving point impedance with input port opencircuited
V1 = (Z_{11 }–Z_{12})I_{1}+ Z_{12} (I_{1} + I_{2})
V_{2} = (Z_{21} – Z_{12}) I_{1} + (Z_{22} –Z_{12})I_{2}
+ Z_{12 }(I_{1} + I_{2}) ...........(ii)
Condition of Reciprocity and Symmetry Reciprocal Network
Z_{11} = Z_{22}
..............(Because in Y_{11} we have short circuit condition whereas in Z_{11} we have open cuicuit condition) input driving point admittance
.....(reverse transfer admittance)
....(forward transfer admittance)
...(output driving point admittance)
Equivalent Circuit Yparameter
For this equivalent II–network
For reciprocal network Y12 = Y21
For sysmmetrical network Y11 = Y22
TRANSMISSION PARAMETERS (ABCD)
V1 = AV2 + B (–12)
I1 = CV2 + D (–I2)
The transmission parameters are
.....(i.e. the reverse voltage ratio with the receiving end open circuited)
....(i.e. the transfer admittance with the receiving end opencircuited)
...(i.e. the transfer impedance with the receiving end shortcircuited )
....(i.e. the reverse current ratio with the receiving end short circuited.)
Condition for Reciprocity
Condition for Symmetry
A = D
INVERSE TRANSMISSION PARAMETERS
The inverse transmission parameter can be defined as
.....(forward voltage ratio with sending end open circuited)
...( transfer a dmittance with sending end open circuited)
. .. (t ra ns fe r impeda nce wi th sending end short circuited)
....(forwar d current ratio with sending end short circuited)
Condition of Reciprocity
Condition for Symmetry
A'=D'
h–PARAMETERS OR HYBRID PARAMETERS
where,
hi : input impedance with the output shortcircuited.
hr : reverse voltage ga in with the input opencircuited.
hf : Forward cur rent gain with the output shortcircuited.
ho : Output admittance with the input opencircuited.
Condition of Reciprocity
h_{12} =  h_{21}
Condition of Symmetry
hparameter Equivalent Circuit
gPARAMETERS OR INVERSE HYBRID PARAMETERS
The gparameters can be defined as,
...... (i.e. input admittance with output open circuited)
......(i.e. forward voltage gain with output open circuited)
......(i.e. forward voltage gain with output open circuited)
......(i.e. output impedance with input short circuited)
Condition of Reciprocity
g12 =  g 21
Condition of Symmetry
gparameter Equivalent Circuit
INTER RELATIONS IN NETWORK
PARAMETERS
Y  parameter in terms of Zparameters
ABCDparameters in terms of Z parameters
V_{1} = Z_{11}I_{1} + Z_{12}I_{2}
V_{2} = Z_{21}I_{1} + Z_{22}I_{2}
from equation (ii),
from equation (i) and (ii),
NOTE: ABCD parameters relate voltage and current in the primary to the voltage and current in the secondary Zparameters in terms of hparameters
V_{1} = h_{11}I_{1} + h_{12}V_{2} ..................... (i)
I_{2} = h_{21}I_{1} + h_{22}V_{2} .....................(ii)
from equation (ii),
Similarly
Condition Under which passive Twoport Network is reciporcal and Symmeterical
Parameters Condition for Reciprocity Condition for Symmetry 
INTERCONNECTION OF TWOPORT NETWORKS
1 . Serie s Connection
From diagram,
I_{1a} = I_{1b} = I_{1} I_{2}a = I_{2}b = I_{2}
V_{1} = V_{1}a + V_{1}b
Also
so, in matrix form the Zparameters of the seriesconnected combined network can be written as
2 . Parallel Connection
I_{1} = I_{1}a + 1_{1}b
I, = I_{2}a + I_{2}b
V_{1}a = V_{1}b = V_{1}
V_{2}1 = V_{2}b = V_{2}
3 . Series Parallel Connection hparameters
Where
4 . Parallel Series Connection
Where
5 . Cascade Connection
BARLETTS BISECTION THEOREM
Network is symmetrical as well as reciprocal Z_{OC} – Open circuited driving point impedances for half of section.
Z_{SCH} – Short circuited driving point impedances for half of section.
SYMMETRICAL LATTICE NETWORK
Z_{b} » Z_{OCH }
Z_{a} » Z_{SCH}
IMAGE IMPEDANCE
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