Link between gm gain and gain circle

[yefj]

Hello , In general amplifier Common source circuit we can increase the gain (gm) by increasing the Width of a transistor.
How will it affect the gain circle on the smith chart? what is the link between the two?
Thanks.

 

[vivekroy]

Gain circles on a Smith chart are loci of impedances that give the same gain.
There are two types of gain circles: power gain circle and available gain circle. Which one are you talking about?
Also, note that gain, in the context of Smith chart, refers to power gain. If you make the transistor twice as wide, gm goes up twice. ro goes down by half. Intrinsic gain remains constant.
If you make your transistor twice as large, then (approximately) ro --> ro/2 and C --> 2C.. You can clearly see the movement of the optimum output impedance.

 

[yefj]

Hello vivekroy, What is the theoretical link between trsnasistor size and circle center and circle radius and circle value?
Thanks.