Question

How can you calculate the small-signal transconductance of a common-source MOSFET amplifier?

Answer 1

To calculate the small-signal transconductance (


g
m
    ​

) of a common-source MOSFET amplifier, you'll need to follow these steps:

Identify the MOSFET parameters:




V
gs
    ​

: The small-signal voltage applied between the gate and source of the MOSFET.



V
ds
    ​

: The small-signal voltage applied between the drain and source of the MOSFET.

Determine the MOSFET operating point (DC bias point):

Ensure the MOSFET is in the active region (saturation or triode) for proper amplification.

Find the small-signal drain current (


i
d
    ​

):

Use the transconductance parameter (


g
m
    ​

) and the small-signal gate-source voltage (



v
gs
    ​

) to find the small-signal drain current.

Calculate the small-signal transconductance (


g
m
    ​

):

The small-signal transconductance is the derivative of the small-signal drain current (


i
d
    ​

) with respect to the small-signal gate-source voltage (



v
gs
    ​

).

The small-signal transconductance (


g
m
    ​

) can be calculated using the following formula:



=
∂


∂



g
m
    ​

=
∂v
gs
    ​

∂i
d
    ​

    ​


The MOSFET transconductance parameter (


g
m
    ​

) can be given as:



=
2





g
m
    ​

=
2k
n
    ​

I
DQ
    ​

    ​


where:



k
n
    ​

 is the transconductance parameter for the MOSFET (a constant related to the device's characteristics).




I
DQ
    ​

 is the DC drain current at the operating point.

Keep in mind that these calculations assume small-signal analysis, which means that you are analyzing the circuit for small variations around the DC operating point. For more accurate results, it's essential to consider the device model's actual parameters and ensure that the MOSFET is in the active region for the given input signal levels.