# Question in small signal model for NMOS

1. May 2, 2013

### a.hambouth

1. The problem statement, all variables and given/known data
Design the following circuit, common source with source resistance, in fig. (1). It uses the MOSFET (irfp244) where Vt= 4.15V, KN = Kn(W/L)= 2.87 A/V2. Assume vin = +/- 100 mV, DC offset = 5 V, and the frequency = 1 K Hz.
a) Design R1 and R2 so that the small signal output gain, Av, is ~ 5. Assume 1/gm << R2.
b) What is the value of ID?
c) Plot Vout & Vin when vin = +/- 400 mV, +/- 700 mV, and +/- 1V separately.
d) Explain why the small signal gain collapses as the input is increased.

2. Relevant equations
Id = (1/2) KN (VGS - Vt)2
Id = Vsource / R2 , Id = (10-Vout) / R1 , Av = Vo/Vin = R1 /((1/gm)+R2)

3. The attempt at a solution
Now what I did I assumed that from Av = R1/R2 =5 that R1=250ohm and R2=50ohm I found from Id = (1/2) KN (VGS - Vt)2 & Id = Vsource / R2 that Vs = 0.96599V or Vs = 0.74794V the first Vs is not accepted because the N-MOSFET will be off (Vgs > Vt) and the second will be on ( VG-Vg swing - Vs > Vt) . and the value for Id will be 14.9588 mA . but the problem is changing the Vin ! because the mosfet will be cut off from (Vg - Vg swing - Vs < Vt) but the multisim still give me value for Vout and Vin for different Av , Can any one tell me what i did wrong ?

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2. May 2, 2013

### rude man

EDIT: Oops, you're OK for zero input volts (in addition to the 5V bias of course)!

Your equations are all good. The given input offset voltage is only 5V which isn't much above Vt for this device.

But, OK. If you go with R2 = 50 ohms then your Vs and i are correct. But, when Vin = 4.9V I got i = 0.013A with Vs = 0.013*50 = 0.65V. The device is not cut off at 4.9V input. I suggest you made a math boo-boo when putting Vin = +4.90V.

Of course, as you drop Vin below 4.9V it eventually will cut off.

P.S. You could have gone to smaller R2, then R1 still = 5R2 of course and the current levels could have been much higher, as intended by this power transistor.

Last edited: May 2, 2013
3. May 5, 2013

### mrxxdragonxx

is there a way to find R1 and R2 other than assumption ?

4. May 5, 2013

### rude man

You choose R1 and R2 to give you the power level and voltage gain you want. Two requirements, two resistors to select.

Usually though one of them is given (like a heater load or whatever).