# HYBRID EQUIVALENT FOR CE TRANSISTOR

The figure shows the transistor connected in common emitter configuration and the figure also shows the hybrid equivalent circuit of such a transistor.

_{be}) and the output current (i

_{c}) are given by the following equations:

V_{be} = h_{ie}.i_{b} + h_{re}.V_{c}

i_{e} = h_{fe}.i_{b} + h_{oe}.V_{c}

## Hybrid expression

Expression can be obtained from the general hybrid formulas derived in this article HYBRID EQUIVALENT OF TRANSISTOR by adding a second subscript letter ‘e’ (which stands for common emitter) with the h-parameters and are as discussed below.

## Current Gain

It is given by the relation,

A_{i} = -(h_{fe}/(1 + h_{oe}.r_{L}))

Where r_{L} is the A.C load resistance. Its value is equal to the parallel combination of resistance R_{c} and R_{L}. Since h_{fe} of a transistor is a positive number, therefore A_{i} of a common emitter amplifier is negative.

## Input Resistance

The resistance looking into the amplifier input terminals (i.e. base of a transistor) is given by the relation,

R_{i} = h_{ie} + h_{re}.A_{i}.r_{L} = h_{ie} – ((h_{re}.h_{fe})/(h_{oe} + (1/r_{L})))

The input resistance of the amplifier stage (called stage input resistance R_{is}) depends upon the biasing arrangement. For a fixed bias circuit, the stage input resistance is,

R_{is} = R_{i}//R_{B}

If the circuit has no biasing resistances, then R_{is} = R_{i}.

## Voltage Gain

It is given by the relation,

A_{v} = A_{i}.r_{1}/R_{i}

Since the current gain (A_{i}) of a common emitter amplifier is negative, therefore the voltage gain (A_{v}) is also negative. It means that there is a phase difference of 180^{o} between the input and output. In other words, the input signal is inverted at the output of a common emitter amplifier. The voltage gain, in terms of h-parameters, is given by the relation.

A_{v} = h_{fe}.r_{1}/(h_{ie} + ∆h.r_{L})

Where

∆h = h_{ie}.h_{oe} – h_{re}.h_{fe}

## Output Resistance

The resistance looking into the amplifier output terminals is given by the relation,

R_{o} = (R_{s} + h_{ie})/(R_{s}.h_{oe} + ∆h)

Where

R_{s} = Resistance of the source, and

∆h = h_{ie}.h_{oe} – h_{re}.h_{fe}

The output resistance of the stage,

R_{oe} = R_{o} // r_{L}

Overall Voltage Gain

It is given by the relation,

A_{v} = (A_{v}.R_{is})/(R_{s} + R_{is})

Overall Current Gain

It is given by relation,

A_{ie} = A_{i}.R_{s}/(R_{s} + R_{is})