BJT TRANSISTOR MODELING:

• The key to transistor small-signal analysis is the use of the equivalent circuits (models).
• A Model is a combination of ircuit elements like voltage or current sources,resistors,capacitors etc that best approximates the behavior of a device under specific operating conditions.
• Once the model (ac equivalent circuit) is determined, the schematic symbol for the device can be replaced by the equivalent circuit and the basic methods of circuit analysis applied to determine the desired quantities of the network. Hybrid equivalent network – employed initially.
• The only drawbak is that It is defined for a set of operating conditions that might not match the actual operating conditions.

HYBRID MODEL DERIVATION FOR INPUT AND OUTPUT RESISTANCE VOLTAGE AND CURRENT GAIN:

• Applying KVL to the input side:

     $V_{i} = I_{b}\beta_{re} + I_{e}R_{E}$ ..

    $20V_{pp} = I_{b} \beta_{ re} +( \beta+1) I_{b}R_{E}$

• Input impedance looking into the network to the right of RB is

   $Z_{b} = V_{i} \dfrac I \beta_{ re}+ ( \beta +1)R_{E}$

Since b>>1, $( \beta +1) = \beta$...

• Thus

   $Z_{b} = V_{i} I_{b} (\beta_{re}+R_{E})= 20V_{PP} I_{b} (\beta_{re}+R_{E})$

• Since RE is often much greater than re,

     $Z_{b} = \beta R_{E}, Z_{i} = R_{B}||Z_{b}$

• Zo is determined by setting Vi to zero, Ib = 0 and b Ib can be replaced by open circuit equivalent.

• The result is,

     $Z_{o} = R_{C}$

• AV : We know that,

      $V_{o} = - I_{o}R_{C} = - \beta I_{b}R_{C} = - \beta\dfrac{(V_{i})}{(Z_{b})}R_{C}$

      $A_{V} = \dfrac{V_{o}} V_{i} = \dfrac{V_{o}} {20V_{pp}}= - \beta\dfrac{(R_{C})}{(Z_{b})}$

• Substituting,

    $Z_{b} = \beta(re + R_{E}) A_{V} =\dfrac{ V_{o}} {V_{i}} = - \beta \dfrac{R_{C}} {(re + R_{E}) }$

RE >>re,

  $A_{V} =\dfrac{ V_{o}} { V_{i}} =\dfrac{V_o}{20V_{pp}}= \beta \dfrac{R_{C}} {R_{E}}$

• Phase relation: The negative sign in the gain equation reveals a 180 degree phase shift between input and output.