Basic Electronics (3110016)

Winter-2019

Question-3c

BE | Semester-1 Winter-2019 | 06-01-2020

Q3) (c)

Briefly explain the h-parameters and draw h-parameter based equivalent circuit for CE transistor and derive an equation for input impedance, output impedance, and voltage gain.

h-parameters can be understood with the help of two-port networks. Fig. - 1.
Where, input current at port 1 is $I_{1} = I_{i}$ , output current at port 2 is $I_{2} = I_{0}$ , input voltage at port 1 is $V_{1} = V_{i}$ , output voltage at port 2 is $V_{2} = V_{o}$
There are four variables. Any variable can be represented in terms of other two known variable, then one of the possible set/pair of equation are,

$V_{i} = h_{11} I_{i} + h_{12} V_{o}$ .........(1)
$I_{o} = h_{21} I_{i} + h_{22} V_{o}$ .........(2)
Where, coefficients $h_{11}, h_{12}, h_{21}, h_{22}$ are called hybrid parameters (h parameters).
In equation (1) when $V_{o}$ is set to zero, by short circuiting output terminal, then $h_{11}$ is derived as $h_{11} = \frac{V_{i}}{I_{i}}$ , $h_{11}$ is called the Input Impedance.
In equation (1) when $I_{i}$ is set to zero, by open circuiting input terminal, then $h_{12}$ is derived as $h_{12} = \frac{V_{i}}{I_{o}}$ , $h_{12}$ is called the Reverse voltage gain.
In equation (2) when $V_{o}$ is set to zero, by short circuiting output terminal, then $h_{21}$ is derived as $h_{21} = \frac{I_{o}}{I_{1}}$ , $h_{21}$ is called the Forward current gain.
In equation (2) when $I_{i}$ is set to zero, by open circuiting input terminal, then $h_{22}$ is derived as $h_{22} = \frac{I_{o}}{V_{2}}$ , $h_{22}$ is called the Transconductance or Output Admittance.
Since, unit of these parameters are completely different from each other, this set of parameters are called hybrid parameters.
Based on equations, the equivalent circuit for input as well as output can be derived as per Fig, - 2 & 3.
For CE configuration of transistor, input current is $I_{i} = I_{b}$ , output current is $I_{o} = I_{c}$ , input voltage is $V_{i} = V_{be}$ , output voltage is $V_{o} = V_{ce}$ .
Hence set/pair of equation are

$V_{be} = h_{11} I_{b} + h_{12} V_{ce}$ .........(3)
$I_{c} = h_{21} I_{b} + h_{22} V_{ce}$ .........(4)

Input Impedance:

h_{11} = \frac{V_{be}}{I_{b}}

Voltage Gain:

h_{12} = \frac{V_{be}}{V_{ce}}

Output Impedance:

\frac{1}{h_{22}} = \frac{V_{ce}}{I_{c}}

Basic Electronics (3110016)

Q3) (c)

Briefly explain the h-parameters and draw h-parameter based equivalent circuit for CE transistor and derive an equation for input impedance, output impedance, and voltage gain.

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