### MOSFET Large and Small signal Model

MOSFET Large Signal Model

The discussions so far on the Drain current (quadratic characteristics) and the capacitance model in the previous section constitute the Large Signal Model. The model is used to analyze the circuits where the signal is high and thus disturbs the bias points. The model also discusses the non linear effects also.

MOSFET Small Signal Model

1. The change in Gate - Source Voltage VGS results in change in Drain current IDS by gmVGS.

2. This is modeled as a Voltage Dependent current source connected between the Source and Drain terminals

3. The Gate current is too small to be considered

This is an ideal MOSFET small signal model and is shown in Figure 21.

Figure 21: MOSFET Small Signal Model

Let us recollect that because of channel length modulation, the drain current also varies with the Drain Source Voltage. This can be modeled here as a voltage dependent current source.

This is shown in figure 22 below:

Figure 22: Small Signal Model showing the effect of channel length modulation - dependent current source

As the current is linearly dependent on the voltage, this can be represented by a linear resistor r0 connected between the Drain and Source.

The value of this resistor is given by:

$r_0=\frac{\partial V_{DS}}{\partial I_D}$

Using the equations developed earlier, we can rewrite the above equation as:

$r_0=\frac1{{}^{\partial ID}/\partial V_{GS}}=\frac1{{\displaystyle\frac12}\mu_nc_{OX}{\displaystyle\frac WL}\left(V_{GS}-V_{TH}\right)^2.\lambda}$

The small signal model showing the channel length modulation r0 effect is shown in Figure 23 below.

Figure 23: MOSFET Small Signal Model showing the Channel Length Modulation effect r0 effect

Now let us consider the effect of the body on the MOSFET functioning. It has been observed that when all other terminal voltages are held constant and the body or bulk voltage is varied, then the drain current is found to be a function of the body voltage.

In other words under such circumstances it can be assumed that the Body can be considered as a second Gate.

This effect can be modeled by a current source which is connected between Drain  and  Source. The dependency term used is gmb and the dependency is gmbVbs.

The term gmb is given by the equation:

$g_{mb}=\frac{\partial I_D}{\partial V_{BS}}=\mu_nC_{OX}\frac WL\left(V_{GS}-V_{TH}\right)\left(-\frac{\partial V_{TH}}{\partial V_{BS}}\right)$

Such a Small signal  model reflecting the body effect is shown in Figure 24

Figure 24: Small Signal Model

Note:

It can be seen from the above figure that the polarity of the gmVgs and gmbVBS is same.

That means the effect of raising the gate voltage is the same as raising the Body or Bulk voltage.