Find the MOSFET bias point

[Daniel San]

1. The problem
   
   Given the following circuit find the bias point (VDS,IDS).
   
   
   
   
   
   
2. The attempt at a solution:
   
   The first thing I did was find the value of VG, the voltage from the gate of the mosfet to the -VDD source.
   
   VG =2 VDD * R2/(R1+R2)
   
   To find the current IDS I needed the voltage from the gate to the source, VGS, which is:
   
   VGS = VG - RsID
   
   Since we're operating in the saturation region I can replace ID by:
   VGS = VG - Rsk(VGS-VT)^2 (1+λVDS)
   
   where VDS is the voltage between the drain and the source.
   I also know that:
   VDS = 2VDD - (Rd+Rs)ID
   
   This is as far as I can get. I'm a little confused regarding what I should do next.
   
   If anyone could help I'd appreciate.
   
   Thanks.
   Daniel.
   
   
   

 

[(*steve*)]

Express both equations in the form Vds = ...

Then solve them for Id

Once you know Id, everything else will fall out.

 

[Laplace]

I tried solving for Id algebraically by plugging your source equations into MathCad and ended up with an out-of-memory error on a 64-bit virtual machine that had been allocated 8 GB of RAM. Then tried solving numerically and got a real solution for Id near 0.5 mA, plus two imaginary number solutions. So I would recommend setting this up in a spreadsheet form then try to get the solution to converge somewhere near 0.5 mA.