# Determine the drain current (PMOS-transistor)

I have the following problem:

Consider the circuit below

These component values are given: $$\R_{G2}=1.5\text{M}\Omega\$$, $$\R_{G1}=1.2\text{M}\Omega\$$, $$\K=2.3\frac{\text{mA}}{\text{V}^2}\$$,$$\V_{to}=-1.8\text{V}\$$, $$\V_{cc}=5\text{V}\$$.

What is the drain current, $$\i_D\$$?

Okay, so my thought of solving this would be the following.

First find the voltage-drop across $$\R_{G2}\$$ through voltage division.

$$\V_{G1}=V_{cc}\times \frac{R_{G2}}{R_{G1}+R_{G2}}=5\text{V}\times\frac{1.5\text{M}\Omega}{2.7\text{M}\Omega} =2.78\text{V}\$$

I interpret this as also being the voltage at the gate of the pmos. That results in $$\V_{GS}=2.78-5=-2.22\text{V}\$$

And I'm stuck here. My next step would be to find $$\V_{DS}\$$, but I am unsure of how to do so. Can anyone help me?

• Well, you know Vgs voltage so you can find Id current without any problem. Yes?
– G36
Commented Jan 5, 2020 at 18:03
• (BTW, the decimal separator is a dot in English, not a comma like in German or Dutch) Commented Jan 5, 2020 at 18:09
• Since Rd was not given, you need to assume that the MOSFET is in the saturation region. What else you can do here?
– G36
Commented Jan 5, 2020 at 18:13
• Hmm, I think I messed up on my prefixes. I meant to write $i_D=0,406mA = 0,41mA$.
– Carl
Commented Jan 5, 2020 at 18:29
• Much better this time.
– G36
Commented Jan 5, 2020 at 18:34

## 1 Answer

$$\ I_{D} = \frac{\textrm{Kp}}{2}(V_{GS}-V_T)^2$$ $$\ I_D =\frac{\textrm{2.3}}{2}((-2.22V)-(1.8V))^2 = 0.203 \textrm{m} A = 203 \mu A$$

• But we can "define" K "differently" and we can get rid of this 2 in the equation and use Id = K(Vgs - Vt)^2 instead. Also, as the author points outs, his teacher is using this equation Id = K(Vgs - Vt)^2 for saturation.
– G36
Commented Jan 5, 2020 at 19:39
• OK. convention. Commented Jan 5, 2020 at 19:41
• You right. I hope it's fine. You welcome Commented Jan 5, 2020 at 20:01