'formulating gain by inspection' Behzad Razavi

[BartlebyScrivener]

On p63 a method is introduced for formulating the gain by inspection. It is said that

'The magnitude of the gain is the resistance seen at the drain node divided by the total resistance in the source path'

This sounds great ... but other than his simple example I cannot get it to work!!

For example, for a source degenerate circuit including ro and gmb I would say that the total resistance in the source path is

Rs + ( 1/gm // 1/gmb // ro )

Which does not give me the value of gm calculated in equation (3.55)

I get \[\frac{ro(gm+gmb)+1}{ro[Rs(gm+gmb)+1] + Rs }\]

Which is incredibly close ... but no cigar. It should be

\[\frac{ gm*ro}{ ro[Rs(gm+gmb)+1] + Rs}\]

Any clue as to what I am doing wrong? It looks so easy!!!

 

[FvM]

Rs + ( 1/gm // 1/gmb // ro )

1/gm is wrongly counted here as a resistor equivalent because it also depends on Vin. Review the derivation of 3.55 from 3.52f and see the difference.

 

[BartlebyScrivener]

Thanks for your reply. I see that the derivation is done differently, but on the next page it returns to 3.51 and then states that

'The magnitude of the gain is the resistance seen at the drain node divided by the total resistance in the source path' and that 'this method greatly simplifies the analysis of more complex circuits'

In the circuit shown (fig 3.20 source degeneration without CLM or BE) it then just disconnects the node and shows 1/gm and then goes on to give an example using it as a rule. I'm not really sure when this rule can be applied, where 1/gm came from? In that case, gm was dependent on vin?

With the attempt I put above, I was just guessing at what this method was. Is there anyone you could explain it to me? Thanks.

 

[FvM]

3.51 is describing the simplified case, ignoring ro and gmb. 3.52 to 3.55 results in the same when omitting it. As far as I understand, also "gain by inspection" is referring to the simplified case.

 

[BartlebyScrivener]

Ok, so I am just trying to apply it where it shouldn't be applied! I wish the book was a little clearer about where the rule applied. Thanks for your help.