Understanding the necessity of Tail Current Source in Differential Amplifier/Simulation (SPICE)
A differential amplifier amplifies the difference between two inputs. The purpose of the 'tail' current is to split that difference between the two sides of the amp. To do this the input voltage must be referenced to ground, so that any increase in current on side causes a corresponding decrease on the other, and vice versa. 

 

If V1 increases then M1 conducts more and passes more current. Since I1 is fixed that means less current must flow through M2. But how does current through M2 reduce? Voltage at the Source terminals of both M1 and M2 increases, reducing M2's Gate- Source voltage and making it conduct less. The result is equal but opposite output signals on each side.

I have set V1 and V2 to produce sine waves with opposite polarity (180&deg; out of phase). Try it with V2 amplitude = 0V and you will see that output appears on both sides even though the input signal is only on one side.