Partial derivatives - Transistor hybrid model:
The partial derivatives are taken by keeping the collector voltage or base current constant as pointed out by the subscript attached to the derivative.
Δv_{B} , Δv_{C} , Δ i_{C} , Δ i_{B} present the small signal(increment) base and collector voltages and currents, they are presented by symbols _{ }v_{b} , v_{c} , i_{b} and i_{c} correspondingly.
Eqs (3) and (4) may be written like as follow:
V_{b} = h_{ie }i_{b} + h_{re} V_{c }
i_{c} = h_{fe} i_{b} + h_{oe} V_{c }
in which h_{ie} =(∂f_{1}/∂i_{B})V_{c} = (∂v_{B}/∂i_{B})V_{c} = (Δv_{B} /Δi_{B})V_{c} = (v_{b} / i_{b})V_{c}
h_{re} =(∂f_{1}/∂v_{c})I_{B} = (∂v_{B}/∂v_{c}) I_{B} = (Δv_{B} /Δv_{c}) I_{B} = (v_{b} /v_{c}) I_{B}
h_{fe }=(∂f_{2}/∂i_{B})V_{c} = (∂i_{c} /∂i_{B})V_{c} = (Δ i_{c} /Δi_{B})V_{c} = (i_{c} / i_{b})V_{c}
h_{oe}= (∂f_{2}/∂v_{c})I_{B} = (∂i_{c} /∂v_{c}) I_{B} = (Δ i_{c} /Δv_{c}) I_{B} = (i_{c} /v_{c}) I_{B}
The above equations described the h-parameters of the transistor in CE configuration. Similar theory can be extended to transistors in additional configurations.
Hybrid Model and Equations for the transistor in three dissimilar configurations are displayed below.