Large Signal Behavior

Large Signal Behavior

1. Assume the input voltage Vin is reduced from a large positive value.

2. Assume that the channel length modulation effect is 0

If the input voltage Vin ≥ Vb - Vth, the MOS transistor is in OFF condition.

∴ Vout  =  VDD

$I_D=\frac12\mu_nC_{OX}\frac WL\left(V_b-V_{in}-V_{th}\right)^2$

For smaller values of Vin, and if the MOS transistor is operating in the Saturation region.

The output voltage Vout when the MOS transistor is operating in the saturation region is given by:

$V_{out}=V_{DD}-\frac12\mu_nC_{OX}\frac WL\left(V_B-V_{in}-V_{th}\right)^2R_D$

As Vin decreases, Vout also decreases, thus driving the MOS Transistor into triode region if

$V_{DD}-\frac12\mu_nC_{OX}\frac WL\left(V_b-V_{in}-V_{th}\right)^2R_D=V_b-V_{th}$

Let  us calculate the small signal gain and is given by

$\frac{\partial V_{out}}{\partial V_{in}}=-\mu_nC_{ox}\frac WL\left(V_b-V_{in}V_{th}\right)\left(-1-\frac{\partial V_{th}}{\partial V_{in}}\right)R_D$

Also we know,

$\partial V_{th}/\partial V_{in}=\partial V_{sb}=\eta$

The small signal gain can be re written in terms of transconductance and body effect as:

$\frac{\partial V_{out}}{\partial V_{in}}=\mu_nC_{ox}\frac WLR_D\left(V_b-V_{in}-V_{th}\right)\left(1+\eta\right)\\=g_m\left(1+\eta\right)R_D$

Note:

• The Voltage Gain is Positive
• The body effect increases the transconductance of the stage

• To increase the gain of a common Gate amplifier, do the following:

• Widen the MOS transistor so that gm increases

• Increase RD