# Homework Help: MOS Cascode Amp: Find the early voltage and channel length

1. Sep 3, 2012

### tquiva

Problem: In a MOS cascade amplifier, the cascade transistor is required to raise the output resistance by a factor of 40. If the transistor is operated at VOV = 0.2 V, what must its VA be? If the process technology specifies V'A = 5 V/μm, what channel length must the transistor have?

Given:
VOV = 0.2 V, VA = ?
V'A = 5 V/μm, L = ?

Known:
ro = VA/IDS = (V'A*L)/(IDS)
==> L = (ro*IDS)/(V'A)
==> V'A = IDS*ro

gm = (2*IDS)/(VOV) where IDS = (1/2)*μn*Cox*(W/L)*VOV2

My Approach:
From the known equations, I have derived the equations needed to obtain VA and L. The unknown variables needed are:
IDS, then gm, then ro, which all then give me the values for VA and L with the derived equations.

However, I just realized that in order to obtain IDS with the equation above, I would need μn*Cox*(W/L), which in this case seems unobtainable. Could someone please help me? I'm doing something wrong but I just can't seem to figure it out.

Any help is GREATLY appreciated!

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