## Write short note on small signal model.

Ans. Circuit do the work for which they were designed over a limited excitation range. This range is particularly specified in terms of maximum input signal movement through an angle about some nominal point. These input variations generally cause excursions around some nonzero dc operating point internal to the circuit. In comparison to the supply voltages providing power to the circuit, these inputs are sinusoids of small amplitude. The process of small sinusoids propagation through the circuit is known as small signal analysis. Quiescent points or bias points are the points about which the circuit operates. BJTs and MOSFETs act as linear devices even though the devices are really nonlinear, for small signal application circuits it is obtained by restricting signal excursions to a region enough small to get approximately linear device behavior. MOS and bipolar transistors models are also very useful for design purpose. For difference between quiescent, small signal and large signal values, the following convention will be taken. The instantaneous total variable value will be represented by an upper case variable, or if require an upper case variable with an upper case subscript or numeral. A small signal value denoted by lower case variable and quiescent value denoted by an upper case variable with a lower case subscript. The following relationship shows the relation between these variables –

V_{c} = v + V_{c}

Where for small signal analysis V_{c} is considered to be periodic with period T and the quiescent value is explained by-

V_{c} = V_{c}(t)dt

Hence, the small signal variable is the time varying components of V_{c} . fig. 2.2 shows the relation between V_{C}, V_{C} and v.

In terms of h parameters, y parameters or g parameters, the electrical behaviour of linear multiple terminal networks can be modeled. Four terminal network for the linear small signal are shows in fig. 2.3(a) in which terminal 4 is selected as a reference. With this reference and the consideration of linearity, it follows by definition that the y parameters relate the terminal currents and voltages by the expressions as give below –

I_{1} = y_{11}v_{1} + y_{12}v_{2} + y_{13}v_{3} …..(i)

I_{2} = y_{21}v_{1} + y_{22}v_{2} + y_{23}v_{3} …..(ii)

I_{3} = y_{31}v_{1} + y_{32}v_{2} + y_{33}v_{3} …..(iii)

Here y_{kj} = `

The small signal voltage is the time varying art of the total terminal voltage and similarly the current variables are the time varying part of the parent network relative to the Q-pont as shown in fig. 2.3 (b). hence, it follows that y parameters can be determined from the large signal variables and hence from the dc model by the following expression –

For circuit design and analysis a small signal equivalent circuit of the multiport network is found useful. Fig. 2.3© shows the equivalent circuit for small signal networks.