Two Port network
h - PARAMETERS OR HYBRID PARAMETERS
Because of the forward bias of the base-emitter junction, the device has a very low input resistance. For open-circuit 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 collector-emitter 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 short-circuited.
h_{r} : reverse voltage gain with the input open-circuited.
h_{f} : Forward current gain with the output short-circuited.
h_{o} : Output admittance with the input open-circuited
Condition of Reciprocity
h_{12} = - h _{21 }
Condition of Symmetry
h-parameter Equivalent Circuit
g-PARAMETERS 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 g-parameters 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
g-parameter Equivalent Circuit
INTER RELATIONS IN NETWORK PARAMETERS
Y - parameter in terms of Z-parameters
ABCD-parameters 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
Z-parameters in terms of h-parameters
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 Two-port Network is reciporcal and Symmeterical
Parameters condition for Reciprocity Condition for Symmetry |
INTERCONNECTION OF TWO-PORT 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 Z-parameters of the seriesconnected combined network can be written as
2. Parallel Connection
3. Series Parallel Connection h-parameters
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 open-circuited
....The reverse transfer impedance with the input port open-circuited
....the forward transfer impedance with the output port open-circuited
.....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 Y-parameter
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 open-circuited)
...(i.e. the transfer impedance with the receiving end short-circuited )
....(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 short-circuited.
hr : reverse voltage ga in with the input open-circuited.
hf : Forward cur rent gain with the output short-circuited.
ho : Output admittance with the input open-circuited.
Condition of Reciprocity
h_{12} = - h_{21}
Condition of Symmetry
h-parameter Equivalent Circuit
g-PARAMETERS OR INVERSE HYBRID PARAMETERS
The g-parameters 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
g-parameter Equivalent Circuit
INTER RELATIONS IN NETWORK
PARAMETERS
Y - parameter in terms of Z-parameters
ABCD-parameters 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 Z-parameters in terms of h-parameters
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 Two-port Network is reciporcal and Symmeterical
Parameters Condition for Reciprocity Condition for Symmetry |
INTERCONNECTION OF TWO-PORT 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 Z-parameters 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 h-parameters
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