I had
a quick question on deriving
voltage gain of a common-source amp with source degeneration.
Please
see attached PDF
file. I
derived the voltage gain using the regular method (method 1) and by
inspection
(method2). I get different
answers from the 2 methods, although upon plugging in the
numbers
the answers are numerically
about the same (same up to the second decimal). I am unable
to
algebraically reduce the symbolic
results to show they are equal.
Method
1 in your PDF is exact
but it doesn't lend itself to intuitive understanding. Method
2 is easy
to
understand intuitively but it isn't
exact. Yes, as you noted the results are about the same.
Why
the difference? When you look at
the resistance looking into the source of the MOSFET it isn't
exactly
1/gm as
specified in Method 2 but rather
(1 + Ro/ro)/(gm +2/ro + Ro/ro2)
If ro
>> Ro
then the
resistance looking into the source is 1/gm
and the two methods give the same results.
In
later printings of the book I
changed the more advanced discussion of the resistance looking into the
source
with a very large load Ro,
see pages 688-690 here,
to keep things more
general. Specifically see Eq.
(21.81)
and Fig. 21.37.
For
the question at the bottom of the PDF,
superposition allows you to look at sources separately so it is
fine
to short-out the input source when
determining the resistance looking into the drain. For exact
analysis
make sure you use the same
circuit for all analyses. Don't lump the resistance looking into the
drain
into a single resistor connected
to the output, like we do for the fast/intuitive analysis, and then try
to
calculate the exact gain.