Please answer the following questions for the common source

Please answer the following qu?estions for the common source amplifier below.

What is the voltage at node a? What is the width of devices 2 and 3? In terms of transconductances and output conductances and capacitances, what is the dominant pole? Approximately, what is the value of this pole? Note that the load capacitance is very large. What is the equation for low frequency gain? Evaluate numerically. How does the low frequency gain change if l_bias doubles holding V_eff and L constant for all devices?

Solution

The gain of this amplifier is determined partly the
transconductance
of the
MOSFET. This depends on
the bias point in the circuit;
here it averages about 9 mA/V. This means that a change in the gate voltage
causes a change in the drain current that is 9 mA/V times the gate voltage
change.

The drain current goes through a 4k ohm resistor. The capacitor connected
to the source is supposed to act as a short circuit at the input frequency,
so it and the source resistor can be ignored.
A change in input of 50 mV causes a change in drain voltage of 9 mA/V * 50 mV *
4000 ohms, or about 1.8 V. This means the predicted output gain is
36. Here it is less
because the transconductance changes over the input cycle (the amplifier
isn\'t quite linear), we are ignoring the output resistor, and the source
capacitor isn\'t quite a short circuit like we supposed.

The current is the same in both halves. The switch on the left changes the current flow in the left half, which is mirrored in the right half. The switch on the right causes the resistor to be bypassed, but the current mirror ensures that the flow of current does not change.

If the left MOSFET is in saturation mode, its current is determined only by the gate-source voltage. The left MOSFET has its gate and drain tied together, so the drain voltage determins the current. The right MOSFET has the same gate-source voltage, so the current must be the same, as long as it is in saturation mode.