Input common-mode voltage range for differential amplifier

[Suv213]

Greetings

I am attempting to build the MOS differential amplifier with the current source, on page 5 of the following document . I want to determine the input common-mode range of the circuit. To my understanding, the lower end of the input common-mode range is determined by the input voltage that keeps the current source in saturation. In seeing this document, there is a current mirror with 2 MOSFETs used. How would one determine the common-mode voltage needed for saturation, in this regard?

Any help would be appreciated as I am looking to get the basics right.

 

[frankrose]

Vcm.min = Vgs.1 + Vdsat.3 + VSS = Vth.1 + Vdsat.1 + Vdsat.3 + VSS = Vth.1 + sqrt(Id3)*(sqrt(0.5/beta1)+1/sqrt(beta3)) + VSS
,where Id3 = (beta3/beta4)*id4, and id4 is tuned with the potentiometer

This example circuit is available in any CMOS IC design book or tutorial.
Thus, I would recommend you to open one, for example from Behzad Razavi: Design of Analog CMOS Integrated Circuits. It is explained in details.