What are the Vgd and Vgs of the Load NMOS in This NMOS Loaded NMOS Inverter?

[InuyashaITB]

Homework Statement

Given
Vdd = 5v, Vgg = 10v, Kn' = 20uA/V^2 (For both transistors), (W/L)o = 10um/5um, (W/L)L = 5um/20um, Vt = 1.1V (for both)

My question is what would be the Vgd, and Vgs of the load NMOS?

Homework Equations

The Attempt at a Solution

So far, what i have is:
The NMOS Load is always in linear mode. Id = Kn[(Vgsl – Vt)Vdsl – 0.5*Vdsl^2]

Vi = Vgso

Vo = Vdso

 

[rude man]

(W/L)o = 10um/5um, (W/L)L = 5um/20um
What are these?

Kn' = 20uA/V^2
Why Kn'? why the prime?

 

[InuyashaITB]

The W/L is the width over the length of the channel of the transistors. Basically Kn = Kn'*W/L

 

[rude man]

(W/L)o = 10um/5um, (W/L)L = 5um/20um

which is which? does "o" stand for the upper and "L" for the lower transistor?
also need to know Vi.

 

[InuyashaITB]

The O is the lower transistor, the L is the upper transistor (L for Load)

 

[rude man]

The O is the lower transistor, the L is the upper transistor (L for Load)

Vi?

 

[InuyashaITB]

Vi would be variable, from 0 to Vdd

 

[InuyashaITB]

The original question to this problem is to re-create its VTC curve and find all of the critical points of the VTC (Vm, Voh, Vol, Vih, Vil, NMh, NML, and power dissipation

 

[rude man]

Vi would be variable, from 0 to Vdd

It can vary all the way from 0V to 5V? That would make the problem a tall order. Do you have pspice?

Or maybe Vi is either 0V or 5V? That we could live with ...

 

[InuyashaITB]

It can vary all the way from 0V to 5V? That would make the problem a tall order. Do you have pspice?

Or maybe Vi is either 0V or 5V? That we could live with ...

Yes, if we look at the extremes it would help

 

[rude man]

Yes, if we look at the extremes it would help

OK. Because if you allow the entire range from 0 to 5V one or both devices will transition from one mode to another, making for a headache unless you do it with some kind of software. You could use spice or write your own high-level-language program.
Also, your statement that the load FET is always in the linear mode is incorrect sice there is effectively nothing connected to its source if Vi = 0.
Stay tuned.

 

[InuyashaITB]

I simulated the circuit exactly as described
https://goo.gl/photos/bHLqKvAJKTMKLym86

It seems Voh=5v
Vol=1v
Vm = 2.5v

This is all according to simulation, would this be close to what the theoretical should be

 

[rude man]

I will try to do a computation for Vi = 5V and 1V, maybe 2.5V also. Later.
EDIT: instead I will give you suggestions on how to proceed:
1. You have the L fet always in the linear mode, as you say.
2. assume the o fet is also in the linear mode. Equate the two fets' equations since the current is the same. Solve for all voltages. If the voltages meet the requirements for the linear mode for the o fet, you're done.
3. if not, then assume the o fet is in the saturated mode and repeat solving for all the voltages the same way.
For Vi = +2.5V and +5V the o fet has to be in either the linear or saturated mode.
For Vi = +1V it should be obvious what the mode of the o fet is.
Your simulation looks about right.
Remember you have Vd1 = Vs2 etc. The only unknown is Vd1 = Vs2.
P.S. an excel spreadsheet might be a good way to do this.

 

[InuyashaITB]

I will try to do a computation for Vi = 5V and 1V, maybe 2.5V also. Later.
EDIT: instead I will give you suggestions on how to proceed:
1. You have the L fet always in the linear mode, as you say.
2. assume the o fet is also in the linear mode. Equate the two fets' equations since the current is the same. Solve for all voltages. If the voltages meet the requirements for the linear mode for the o fet, you're done.
3. if not, then assume the o fet is in the saturated mode and repeat solving for all the voltages the same way.
For Vi = +2.5V and +5V the o fet has to be in either the linear or saturated mode.
For Vi = +1V it should be obvious what the mode of the o fet is.
Your simulation looks about right.
Remember you have Vd1 = Vs2 etc. The only unknown is Vd1 = Vs2.
P.S. an excel spreadsheet might be a good way to do this.

So what would be the Vgs of the O transistor seeing as how there is a Vgg tied to the O transistor

 

[rude man]

I will ty to do a computation for Vi = 5V and 1V, maybe 2.5V also. Later.

So what would be the Vgs of the O transistor seeing as how there is a Vgg tied to the O transistor

 

[rude man]

So what would be the Vgs of the O transistor seeing as how there is a Vgg tied to the O transistor

You mean Q_L, not "the O transistor", right? To avoid further confusion, I am using the subscript "1" for Q_o and "2" for Q_L henceforth:
You have every voltage except V_d1 which is also V_s2:
V_g1 = V_i (i.e. 1V, 2.5V and/or 5v)
V_g2 = +10V
V_d2 = +5V
V_s1 = 0
So, solve for V_d1 which is also V_s2.