Consider following circuit. http://i812.photobucket.com/albums/zz41/uofmx12/quiz

Question

Consider following circuit.
http://i812.photobucket.com/albums/zz41/uofmx12/quiz3.jpg

A)Design all resistors. Assume half of supply voltage is dropped across drain resistor, quarter of supply across both drain source voltage and source resistor. Circuit must be biased for drain current of 2ma and the gate resistors may not draw more than 1uA. Find Vgs.

Check my answers please:
Rd=5/2ma = 2500

Rs=2.5/2ma=1250

Id=1/2 k'nW/L (Vgs-Vt)2 , Id=2mA

2mA=.5(Vgs-Vt)2

0=Vgs2 - 2.4Vgs-2.56 , Vgs=3.2 and -.8. Use 3.2 So, Vg = 5.7V

Rg1=(10-Vg) / 1uA = 4.3M

Rg2=Vg/1uA = 5.7M

B) Draw the small signal model and find gain vo/vsig

I can draw the small signal model but it uses ro, Rd, and RL. I don't know how to find ro when or VA was not provided.

Explanation / Answer

Given VDD = 10V VRD = VDD / 2 = 10/2 = 5V VDS = VDD / 4 = 10/4 = 2.5V VS = VDD / 4 = 10/4 = 2.5V ID = 2mA IG ˜ 0 RD = VRD / ID = 5/0.002 = 2.5k RS = VS / IS = VS/ID = 2.5/0.002 = 1.25k Applying KVL at the input VDD = I (RG1 + RG2 ) RG1 + RG2 = 10/(1*10-6) = 10M Let RG1 = RG2 = RG RG1 = 5M RG2 = 5M Applying KVL at the input loop VG = VGS + VS VG = VDDRG1 / (RG1 + RG2 ) = 5V VGS = 5 - 2.5 VGS = 2.5V Small signal voltage gain AV ˜ - gm rL gm = 2ID / (VGS - Vt) If the FET choosen has Vt = 1.5V gm = 2(0.002)/(2.5-1.5) = 4mS rL = RD || RL = 2.5k || 10k = 2k Av = - (0.004)(2000) Av = - 8 Or First you select the FET and from the data sheet you can note down the typical value of VA or and Vt and calculate ro , gm and then Av     Or First you select the FET and from the data sheet you can note down the typical value of VA or and Vt and calculate ro , gm and then Av    

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