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**THE HYBRID MODEL FOR TWO PORT NETWORK:**

Based on the definition of hybrid parameters the mathematical model for two port networks known as h-parameter model can be developed. The hybrid equations can be written as:

(The following convenient alternative subscript notation is recommended by the **IEEE Standards), given as:**

*i***=11= input o = 22 = output**

*f ***=21 = forward transfer r = 12 = reverse transfer**

We may now use the four h parameters to construct a mathematical model of the device of Fig.(1). The hybrid circuit for any device indicated in Fig.(2). We can verify that the model **of Fig.(2) satisfies above equations by writing Kirchhoff's voltage and current laws for input and output ports.**

If these parameters are specified for a particular configuration, then suffixes e,b or c are also included, e.g. h_{fe} ,h_{ib} are h parameters of common emitter and common collector amplifiers.

**Using two equations, the generalized model of the amplifier can be drawn as shown in fig. 2 **

fig. 2

**TRANSISTOR HYBRID MODEL:**

The hybrid model for a transistor amplifier can be derived as follows:

Let us consider CE configuration as shown in** **fig. 3. The variables, i_{B}, i_{C} ,v_{C}, and v_{B} represent total instantaneous currents and voltages, i_{B} and v_{C} can be taken as independent variables and v_{B}, I_{C} as dependent variables.

fig. 3

V_{B} = f_{1}(i_{B} ,v_{C} )

I_{C} = f_{2}(i_{B} ,v_{C}).

Using Taylor 's series expression, and neglecting higher order terms we get,

The partial derivatives are taken keeping the collector voltage or base current constant. The Î”v_{B}, Î”v_{C}, Î”i_{B}, Î”i_{C} represent the small signal (incremental) base and collector current and voltage and can be represented as v_{B},_{ }i_{C, }i_{B} ,v_{C}.

_{where}

The model for CE configuration is shown in fig. 4.

To determine the four h-parameters of transistor amplifier, input and output characteristic are used. Input characteristic depicts the relationship between input voltage and input current with output voltage as parameter. The output characteristic depicts the relationship between output voltage and output current with input current as parameter. **Fig. 5**, shows the output characteristics of CE amplifier

The current increments are taken around the quiescent point Q which corresponds to i_{B} = I_{B} and to the collector voltage V_{CE} = V_{C}

The value of h_{oe} at the quiescent operating point is given by the slope of the output characteristic at the operating point (i.e. slope of tangent AB).

h_{ie} is the slope of the appropriate input on **fig. 6**, at the operating point (slope of tangent EF at Q).

A vertical line on the input characteristic represents constant base current. The parameter h_{re} can be obtained from the ratio (V_{B2}â€“ V _{B1} ) and (V_{C2}â€“ V _{C1} ) for at Q.

Typical CE h-parameters of transistor 2N1573 are given below:

h_{ie} = 1000 ohm.

h_{re} = 2.5 * 10^{â€“4}

h_{fe} = 50

h_{oe}=25 A/V

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