# Common Source JFET Amplifier Gain

I would be thankful if someone could explain me what is the general formula used to calculate the gain of a common source jfet amplifier.

I have the fallowing circuit:

Since this circuit was taken out from a book, the author says that:"The voltage gain is equal to gm times the signal resistance in the drain leg. There are two paths to signal ground from the drain terminal.One is through Rd and the other is through RL."

If we make the small signal model we will realise that Rd is in paralel with RL so rd = Rd||RL hence the Gain = gm * rd

Okay, all nice and good but I don't understand that, since we use source degeneration resistor, why we bother ourself calculating the transconductance (gm) in order to calculate the gain, when we could calculate the voltage gain by dividing Rd with Rs ( Gain = -Rd/Rs ) just like in bjt.. Or this formula isn't available anymore at JFET?

Ps: The author of the book assumed a gm of 3mS which after calculating the gain it results a 4.5 voltage gain. If we divide Rd with Rs we will get a voltage gain of 6.6.

• The source resistor is bypassed by the capacitor which in a simple analysis would be assumed to have zero impedance at the frequency of interest. If the source resistor was not bypassed the gm would be reduced as you say. – Kevin White Jun 13 '18 at 15:43
• The mentioned formula gain=-Rd/Rs is a rough approximation only and can be used for Rs>>1/gm only. This restriction applies also to the BJT case. In your circuit the resistor Rs is bypassed by a capacitor and does not appear in the gain formula (if Cs is sufficiently large). – LvW Jun 13 '18 at 15:48

The mentioned formula

gain=-rd/Rs

is a rough approximation only and can be used for Rs>>1/gm only (without any bypass capacitor). This restriction applies also to the BJT case. In your circuit the resistor Rs is bypassed by a capacitor and does not appear in the gain formula (if Cs is sufficiently large).

Here is the correct formula:

gain=-gm * rd/(1+gm * rs)

with rs=Rs||(1/jwCs).

As you can see, for rs<<1/gm the formula reduces to gain=-gm * rd.

In contrary, for Cs=0 and Rs>>1/gm the mentioned gain formula reduces to gain=-rd/Rs (as mentioned at the beginning).