Hybrid Parameter in BJT

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

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

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 =
=

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

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= +

Complete Hybrid Parameter Circuit

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+ =

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
= −
+

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= −

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
= −
+

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
= =

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
= −
+  
− 
+ 

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
= −
+

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
= −
+

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
=
+

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
=

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
=
+

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
=
+

.
( ) (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
→
→

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

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
 
= × 
+ 
 
− 
+ 

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

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

12/27/2020 25Arpan Deyasi, RCCIIT
VCE
IC
IB1
IB2
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

12/27/2020 26Arpan Deyasi, RCCIIT
VCE
IC
IB2
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

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?

Dataset for Different Configurations

Conversation of h-parameters

Hybrid Parameter in BJT

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