The document discusses the hybrid or h-parameters model of bipolar junction transistors. It provides notations and equations for the key h-parameters, including input impedance (h11), forward current gain (h21), reverse voltage transfer ratio (h12), and output admittance (h22). It also describes how to calculate the h-parameters from transistor static characteristics and the advantages of the h-parameter model for circuit analysis and design.

1. Bipolar Junction
Transistor:
Hybrid Parameter
Arpan Deyasi
Dept of ECE, RCCIIT, Kolkata, India
12/27/2020 Arpan Deyasi, RCCIIT 1

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Hybrid Parameter
1 11 1 12 2V h I h V= + 2 21 1 22 2I h I h V= +

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Hybrid Parameter
2
1
11
1 0V
V
h
I =
=
1
1
12
2 0I
V
h
V =
=
2
2
21
1 0V
I
h
I =
=
1
2
22
2 0I
I
h
V =
=

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Hybrid Parameter: Notations used in transistor circuits
11 ih h=
short-circuit
input impedance
21 fh h=
short-circuit
forward current gain
12 rh h=
open-circuit
reverse voltage transfer ratio
22 oh h=
open-circuit
output admittance

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Transistor Hybrid Model
1 1 1 2( , )v f i v=
2 2 1 2( , )i f i v=
1 1 2i rv hi h v= +
2 1 2f oi h i h v= +

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Complete Hybrid Parameter Circuit

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CurrentGain
2 1 2f oI h I h V= +
2 1f o L LI h I h I Z= +
2 1 2f o LI h I h I Z= −
2 2 1o L fI h I Z h I+ =

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CurrentGain
2
1 1 (1 )
fL
I
o L
hI I
A
I I h Z
= =− =−
+
2 1(1 )o L fI h Z h I+ =
2
1 (1 )
f
o L
hI
I h Z
=
+
(1 )
f
I
o L
h
A
h Z
= −
+

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InputImpedance
1 1 2i rV h I h V= +
1 1i r L LV h I h I Z= +
1 1 1i r I LV h I h A I Z= +
1 1 2i r LV h I h I Z= −

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InputImpedance
1
1
I i r I L
V
Z h h A Z
I
= = +
(1 )
f
I i r L
o L
h
Z h h Z
h Z
= −
+
f r
I i
L o
h h
Z h
Y h
= −
+

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VoltageGain
2 2 LV I Z= −
2 1I LV A I Z=
2 1
1 1
I L
V
V A I Z
A
V V
= =
2
1
I L
V
I
V A Z
A
V Z
= =

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VoltageGain
.
(1 )
f L
V
o L I
h Z
A
h Z Z
= −
+
.
(1 )
(1 )
f L
V
fo L
i r L
o L
h Z
A
hh Z
h h Z
h Z
= −
+  
− 
+ 

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OutputAdmittance
2 1 2f oI h I h V= +
2 1
2 2
f o
I I
h h
V V
= +
With VS = 0 1 1 2 0S i rR I h I h V+ + =
1
2
r
S i
I h
V R h
= −
+

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2
2
r
f o
S i
I h
h h
V R h
=− +
+
OutputAdmittance
0
r f
o
S i
h h
Y h
R h
= −
+

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CurrentGainwithSourceResistance
1 1I S S SI Z I R I R+ =
1( )I S S SI Z R I R+ =
1
( )
S
S I S
RI
I Z R
=
+

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CurrentGainwithSourceResistance 2 2 1
1
IS
S S
I I I
A
I I I
=− =−
S
IS I
R
A A
→∝
→
( )
S
IS I
I S
R
A A
Z R
=
+
.
(1 ) ( )
f S
IS
o L I S
h R
A
h Z Z R
= −
+ +
1
IS I
S
I
A A
I
=

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VoltageGainwithSourceResistance
1 1I S S IV Z V R V Z+ =
1( )I S S IV Z R V Z+ =
1
( )
S I
I S
V Z
V
Z R
=
+

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VoltageGainwithSourceResistance
2 2 1
1
VS
S S
V V V
A
V V V
= =
1
VS V
S
V
A A
V
=
( )
S I
VS V
I S
V Z
A A
Z R
=
+

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VoltageGainwithSourceResistance
.
( ) (1 )
.
(1 )
fS I
VS
I S o L
L
f
i r L
o L
hV Z
A
Z R h Z
Z
h
h h Z
h Z
= −
+ +
×
 
− 
+ 
0S
VS V
R
A A
→
→

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PowerGain
2
1
P
P
A
P
=
2 2
1 1
P
V I
A
V I
= −
P V IA A A=

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PowerGain
2
(1 )
(1 )
f
P
o L
L
f
i r L
o L
h
A
h Z
Z
h
h h Z
h Z
 
= × 
+ 
 
− 
+ 

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Calculation of Hybrid Parameters [NPN]
IB
VBE
VCE1
11
C
BE
i
B V const
V
h h
I =
∆
= =
∆
Input Resistance
2 1
2 1
BE BE
i
B B
V V
h
I I
−
=
−
VBE1 VBE2
IB2
IB1

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Calculation of Hybrid Parameters [NPN]
IB
VBE
VCE2VCE1
Reverse Transfer Ratio
12
B
BE
r
CE I const
V
h h
V =
∆
= =
∆
2 1
2 1
BE BE
r
CE CE
V V
h
V V
−
=
−
VBE1 VBE2

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VCE
IC
IB1
IB2
Calculation of Hybrid Parameters [NPN]
Forward Current Transfer Ratio
21
C
C
f
B V const
I
h h
I =
∆
= =
∆
2 1
2 1 C
C C
f
B B V const
I I
h
I I =
−
=
−
IC2
IC1

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VCE
IC
IB2
Calculation of Hybrid Parameters [NPN]
Output Transconductance
22
B
C
o
C I const
I
h h
V =
∆
= =
∆
2 1
2 1 C
C C
o
CE CE V const
I I
h
V V =
−
=
−
IC2
IC1
VCE1 VCE2

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h-parameters are Real Numbers up to radio frequency
They are easy to measure
They can be determined from transistor static characteristic
They are convenient to use in circuit analysis and design
Easily convertible from one configuration to other
Readily supplied by manufacturers
What are the salient features of hybrid parameters?

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Dataset for Different Configurations

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Conversation of h-parameters