Gm - boosted Cross Coupled Pair (XCP) and Negative Impedance

In this post we will take the concepts introduced in the previous posts further. In the last post we discussed the resistance look into drain when a voltage amplifier is inserted between the drain and the gate of NMOS transistor (figure 1a). Refer to figure 1a right part, to calculate output resistance we applied a positive voltage vx to the output node. If the gain A > 0, a positive current Ix will flow out from the voltage source confirming that Req is positive. Now we apply a negative voltage -vx to the drain and for A > 0 as shown in figure 1b left. The current Ix flow out of the transistor drain.

Differential circuit

We combine these two circuits and make a differential pair. The voltage sources are connected in opposite with respective to the ground. And moreover the same current is flowing through each voltage source and resulting no current to ground (Refer figure 2a). The differential impedance looking into two drains is given by Zeq, which is twice the value we obtained in previous circuit. Since the positive Vx still results in positive Ix, Zeq is positive impedance. 

Now let us play with the circuit. Instead of applying input to the voltage amplifier from the same voltage source, let apply from other voltage source, i.e., the cross coupling. Now the current Ix flows in opposite direction. For each NMOS, when the voltage at drain node increases (or decreases) the voltage at its gate decreases (or increases) resulting the trans-impedance current flow out of drain (or into the drain). Since positive Vx result in negative Ix, the differential impedance is negative. 

The last circuit is well known "Gm - boosted Cross Coupled Pair (XCP)"  circuit which has many applications in RF electronics, memory sense amplifiers etc.