Electronics

1. Assistant Professor
Electronics and Communications Engineering
Narula Institute of Technology
Arnima Das
M. Tech (WBUT), B. Tech (WBUT)
Transistor Biasing and
Stability 4

2. Topics
Covered in
this lecture
• h-parameters in CE configuration
• Hybrid model
• Expression of
• voltage gain
• current gain
• input & output impedance
• Transconductance
in Emitter follower circuit

3. h-parameters
𝒉𝟏𝟏 =
𝑽𝟏
𝑰𝟏 𝑽𝟐=𝟎
= 𝒉𝒊
This is known as the Input
impedance with output short
circuit
𝒉𝟏𝟐 =
𝑽𝟏
𝑽𝟐 𝑰𝟏=𝟎
= 𝒉𝒓
This is the fraction of output
voltage at input with input open
circuited or Reverse voltage gain
with input open circuited
Arnima Das - Dept. of Electronics and Communications Engineering - Narula Institute of Technology 3

4. h-parameters
𝒉𝟐𝟏 =
𝑰𝟐
𝑰𝟏 𝑽𝟐=𝟎
= 𝒉𝒇
This is known as the negative of
current gain with output short
circuited
𝒉𝟐𝟐 =
𝑰𝟐
𝑽𝟐 𝑰𝟏=𝟎
= 𝒉𝒐
This is the output admittance
with input open circuited
Arnima Das - Dept. of Electronics and Communications Engineering - Narula Institute of Technology 4

5. h-parameters in common emitter bias
• For a transistor in Common Emitter mode, the two
port network input and output will change as –
• Ib will be the input current and Vb the input voltage
• Ic will be the output current and Vc the output
voltage
Arnima Das - Dept. of Electronics and Communications Engineering - Narula Institute of Technology 5
• The type of configuration in which the
transistor is operated can also be reflected
in the subscripts of the h-parameters with
c, b, or e –
• E.g. in the typical amplifier configuration,
i.e. common emitter bias the parameters
can be written as –
𝒉𝒊𝒆, 𝒉𝒓𝒆, 𝒉𝒇𝒆, 𝒉𝒐𝒆

6. h-parameters in common emitter bias
• 𝒉𝟏𝟏 =
𝜹𝑽𝒃
𝜹𝑰𝒃 𝑽𝒄=𝑪
= 𝒉𝒊𝒆
• 𝒉𝟏𝟐 =
𝜹𝑽𝒃
𝜹𝑽𝒄 𝑰𝒃=𝑪
= 𝒉𝒓𝒆
• 𝒉𝟐𝟏 =
𝜹𝑰𝒄
𝜹𝑰𝒃 𝑽𝒄=𝑪
= 𝒉𝒇𝒆
• 𝒉𝟐𝟐 =
𝜹𝑰𝒄
𝜹𝑽𝒄 𝑰𝒃=𝑪
= 𝒉𝒐𝒆
Arnima Das - Dept. of Electronics and Communications Engineering - Narula Institute of Technology 6
The quantities 𝛿𝑉𝑏, 𝛿𝐼𝑏, 𝛿𝑉
𝑐, 𝛿𝐼𝑐 represent the incremental base and collector voltage and current

7. Conversion of h-parameters
Arnima Das - Dept. of Electronics and Communications Engineering - Narula Institute of Technology 7

8. Advantages of h-parameters
• At audio frequency the h-parameters are real numbers, so, reactive elements are absent in two-
port devices
• h-parameters can be readily measured
• They offer simple mathematical expressions for various performance quantities, such as voltage
gain, current gain, input & output impedance, Transconductance, etc.
• They are convenient to use in circuit analysis and design
• A set of h-parameters of the transistor is usually specified by the transistor manufacturers
Arnima Das - Dept. of Electronics and Communications Engineering - Narula Institute of Technology 8

9. Hybrid model of transistor
• The four h-parameters can be used to
construct a mathematical model known
as the hybrid model or h-parameter
equivalent circuit
• Here, the input impedance, output
admittance, reverse voltage gain and
forward current gain all are represented
by equivalent linear components
Arnima Das - Dept. of Electronics and Communications Engineering - Narula Institute of Technology 9

10. Hybrid model of transistor
• The hybrid model can be shown in various
bias configuration for a transistor
• The figure here shows the Common
Emitter configuration for the transistor
where –
• Input terminals are Base (B) and Emitter (E)
• Output terminals are Collector (C) and
Emitter (E)
Arnima Das - Dept. of Electronics and Communications Engineering - Narula Institute of Technology 10

11. Emitter follower circuit
• In the emitter follower or Common collector amplifier
using n-p-n transistor, when the base voltage
increases, the emitter current also increases.
• So, the voltage drop across the load resistance
increases, making emitter more positive
• Here, the emitter voltage follows the base voltage
• So, it is called Emitter Follower circuit
Arnima Das - Dept. of Electronics and Communications Engineering - Narula Institute of Technology 11

12. Expression of Gain
• Current gain in the emitter follower
amplifier can be given as –
𝐴𝐼 = −
𝐼𝑒
𝐼𝑏
= −
ℎ𝑓𝑐
1+ℎ𝑜𝑐𝑅𝑒
As, ℎ𝑓𝑐 = − 1 + ℎ𝑓𝑒 & ℎ𝑜𝑐 = ℎ𝑜𝑒
So, 𝐴𝐼 =
1+ℎ𝑓𝑒
1+ℎ𝑜𝑒𝑅𝑒
• Voltage gain in the emitter follower
amplifier can be given as –
𝐴𝑉 =
𝑉𝑒
𝑉𝑏
=
𝐴𝐼𝑅𝑒
𝑅𝑏
Assuming, ℎ𝑓𝑒 ≫ 1 & ℎ𝑜𝑒 ≈ 0
So, 𝐴𝑉 =
ℎ𝑓𝑒𝑅𝑒
ℎ𝑖𝑒+ℎ𝑓𝑒𝑅𝑒
Arnima Das - Dept. of Electronics and Communications Engineering - Narula Institute of Technology 12

13. Expression of impedance
• Input impedance in the emitter
follower amplifier can be given as –
𝑅𝑖 =
𝑉𝑏
𝐼𝑏
= ℎ𝑖𝑐 + 𝐴𝐼ℎ𝑟𝑐𝑅𝑒
As, ℎ𝑖𝑐 = ℎ𝑖𝑒 & ℎ𝑟𝑐 = 1
So, 𝑅𝑖 = ℎ𝑖𝑒 + 𝐴𝐼𝑅𝑒
• Output impedance in the emitter
follower amplifier can be given as –
𝑅𝑜 =
𝑅𝑏 + ℎ𝑖𝑐
𝑅𝑏ℎ𝑜𝑐 + ℎ𝑖𝑐ℎ𝑜𝑐 − ℎ𝑓𝑐ℎ𝑟𝑐
=
𝑅𝑏 + ℎ𝑖𝑒
1 + 𝑅𝑏ℎ𝑜𝑒 + ℎ𝑖𝑒ℎ𝑜𝑒 + ℎ𝑓𝑒
Arnima Das - Dept. of Electronics and Communications Engineering - Narula Institute of Technology 13

14. Transconductance
• The rate of change of output current with
respect to input voltage when output
voltage is constant is known as
transconductance of a two-port network
• For the emitter follower circuit this can be
defined as -
𝑔𝑚 =
𝛿𝐼𝑒
𝛿𝑉𝑏 𝑉𝑒=𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡
• Therefore,
𝑔𝑚 =
ℎ𝑓𝑐
ℎ𝑖𝑐𝛿𝐼𝑏 𝑉𝑒=𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡
=
ℎ𝑓𝑒
ℎ𝑖𝑒 𝑉𝑒=𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡
Arnima Das - Dept. of Electronics and Communications Engineering - Narula Institute of Technology 14

15. Transconductance
• The circuit here shows simplification of
the h-parameter model using
transconductance.
• Here the voltage and current source is
replaced by a single source of value
𝑔𝑚𝑉𝐵𝐸
• This is known as the simplified low-
frequency hybrid-pi model for BJT
Arnima Das - Dept. of Electronics and Communications Engineering - Narula Institute of Technology 15

16. Further study
• https://www.youtube.com/watch?v=RnClfkGvk_c
• https://www.youtube.com/watch?v=wT8fZJIl3Nk
• https://www.youtube.com/watch?v=4rcopzJWayQ
Arnima Das - Dept. of Electronics and Communications Engineering - Narula Institute of Technology 16