### Common Source

Common Source Stage with Resistive Load

As discussed in earlier sections, the transconductance gm of the MOSFET converts the Gate - Source voltage VGS to a small signal change in the Drain current ID. The Drain current ID if passed through a resistor produces a voltage drop across it which is the output voltage.

This configuration is shown in Figure 2.

Figure 2: nMOSFET Common Source Stage with Drain Resistor

Analysis:

1. If the input voltage Vin is 0V, output Voltage Vout = VDD

2. As the input voltage Vin increases from 0V and nears the threshold voltage VTH, the transistor turns ON. As the transistor turns ON, current flows in the transistor from the resistor RD and this reduces the output voltage VOUT.

3. Neglecting channel length modulation, we have
$V_{OUT}=V_{DD}-R_D\frac12\mu_nC_{OX}\frac WL\left(V_{in}-V_{th}\right)^2$

4. The MOS is operating in saturation region now

5. As the input voltage Vin increases further, Vout drops more and the MOS transistor still operates in the saturation region.

6. This continues till the value of the input voltage Vin exceeds the output voltage Vout by the threshold voltage Vth. Let this input voltage be indicated by Vin1.
$V_{in1}-V_{th}=V_{DD}-R_D\frac12\mu_nC_{OX}\frac WL\left(V_{in1}-V_{th}\right)^2$

7. As Vin becomes greater than Vin, the MOS enters into the triode region.

8. Any further increase in the input voltage Vin, the MOS is driven into the deep triode region

9. To prevent the drop of transconductance in the triode region we ensure the operation of the device such that the output voltage Vout is greater than the difference between the input voltage and threshold voltage.
Vout > Vin- Vth

10. The Voltage Gain Av is given by
Av  =  -gmRD

11. If the signal is large i.e. large signal swing, the  gain of the circuit changes substantially and now operates in the large signal mode.

The small signal  model for the saturation region is shown in Figure 3, below.

Figure 3:  Small Signal Model

Note:

1. The dependence of gain on signal level leads to non linearity.

2. To reduce nonlinearity, the gain has to be made less dependent on the signal dependent parameters such as gm.