Gain of amplifier with current source load

Hi all,

I had a slight confusion about how a current source load influences the intrinsic gain of a MOS after seeing the images below.
In the first image, the gain is intuitive. The current source load exhibits an infinite output impedance so that the effective Zout is equal to r0. Here, using KCL I assume that the current flowing through r0 is I0-gmVgs, but the total current through Rs is I0, which means there is no small signal increment.
In the second image, for a common gate amplifier, he says that the total current through the device M1 is from the ideal source I1, so that the source potential cannot change the current through the device. This would mean that there is no small signal current increment. Would this mean the gain is zero?

samster19 said:

In the second image, for a common gate amplifier, he says that the total current through the device M1 is from the ideal source I1, so that the source potential cannot change the current through the device. This would mean that there is no small signal current increment. Would this mean the gain is zero?

Click to expand...

Hi,
In the common-gate structure, the source voltage is determined by a voltage source, Vx. So, the transistor's gm will produce a current equal to gm * (0 - Vx). This current varies with Vx. However, the total current passing through the drain is constant because of the current source in the drain. So, when you change Vx, the current through the ro must change. In other words, gm * (0 - Vx) circulates into the ro and Vout(drain) = ( gm*Vx ) * ro + Vx.