 ### Network # Low frequency FET response, determining f[sub]L[/sub] of Cs capacitor

#### nvjnj

Sep 13, 2014
11
I'm trying to get the low frequency cutoff value of the capacitor Cs of the following ac equivalent circuit using the equation:
f(L)=1/(2*pi*Req*Cs) To do this, I'm supposed to reduce the circuit "seen" by capacitor Cs to an equivalent RC circuit where Req would be the equivalent resistance seen by Cs.

Employing Thevenin's Theorem, open-circuiting all current sources and short circuiting all voltage sources gives me the equivalent resistance as:

Req=RS||((RL||RD)+rd) which simpifies into the equation:
Req=RS/(1+(RS/(RDRL+rd)))

But the real equation stated in the internet and text books is:
Req=RS/(1+(RS(1+gmrd)/(RDRL+rd)))

So, I am missing the factor (1+gmrd) in my equation. Please help me figure out what I am doing wrong.

#### (*steve*)

##### ¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥd
Moderator
Jan 21, 2010
25,507
there is a current source there which is a dependent current source. You can't just open circuit that.

#### nvjnj

Sep 13, 2014
11
there is a current source there which is a dependent current source. You can't just open circuit that.
I see....I missed that.
Thanks....I'll try to redo it

#### nvjnj

Sep 13, 2014
11
I see....I missed that.
Thanks....I'll try to redo it
Okay, so I tried doing it by not removing the dependent current source. But I'm still not getting the answer. These are the steps I followed:

Req=V(open-circuit)/I(short-circuit)

V(open-circuit):
Open circuiting Cs, Voltage across this open circuit is equal to voltage across Rs. Voltage across Rs = Is*Rs, where Is is the current flowing through Rs.
Is=(rd/(rd+(Rs+RD||RL)))*gmVgs

Therefore V(short-circuit)=(rd*Rs/(rd+(Rs+RD||RL)))*gmVgs

I(short-circuit):
Short circuiting Cs would make Rs redundant and is removed. Hence current accross this path is:
Is=(rd/(rd+(RD||RL)))*gmVgs

Hence Req=(rd*Rs/(rd+(Rs+RD||RL)))*gmVgs / (rd/(rd+(RD||RL)))*gmVgs

This eliminates my gm terms, which is required in the final equation as stated in the original post. Please tell me what I am doing wrong?

#### (*steve*)

##### ¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥd
Moderator
Jan 21, 2010
25,507
Why did you calculate V(short circuit)?

#### nvjnj

Sep 13, 2014
11
Why did you calculate V(short circuit)?
Sorry, that was a typo, its actually V(open-circuit)=(rd*Rs/(rd+(Rs+RD||RL)))*gmVgs

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