Obtaining gm and u by simulating CMOS transistor on

[gcmarimon]

Heya!
Im trying to find out how to, for a given technology, calculate the values of gm and µ, by simulating a transistor on Hspice. I know theres a command line wich will give me the value! But thats not what im searching. Im looking for a technique to, by simulating a dc Voltage through the drain-source and gate-source gates, make some math calculations and find the values of gm and µ. Thats because im about to try to extract these values from a real one in the lab, but first i gotta make an algoritm which i will follow when i finish the simulations.

Hope you can help me!
thanks a lot!
best regards,
Gabriel Marimon

 

[Lucyfer]

Re: Obtaining gm and µ by simulating CMOS transisto

hey guys, still waiting for some help!
thanks

 

[geinstein337]

Get the following curves:
1) ID vs. VGS (short gate and source terminal)
2) sqrt(ID) vs. VGS
3) slope or derivative of #2 above

Let ID = β/2 * (VGS-VTH)^2
Then sqrt(ID) = sqrt(β/2) * (VGS-VTH)
where β=u*Cox*W/L

The slope or derivative in graph#3 will show sqrt(β/2) vs. VGS. So the y-value at any VGS for graph#3 can be squared and the multiplied by 2 to get β. The u can derived if you know Cox and W/L.

gm is sqrt(ID*β*2). The expression can be derived from taking the derivative of ID = β/2 * (VGS-VTH)^2.

-Gerry D.

 

[Lucyfer]

Ok, here is the .m command lines

"

clc

clear all

close all

%gm extraction%

%1 - Ids x Vgs%

ids2=[-5.403e-10

-6.989e-10

-9.038e-10

-1.169e-09

-1.510e-09

-1.951e-09

-2.520e-09

-3.253e-09

-4.197e-09

-5.412e-09

-6.975e-09

-8.981e-09

-1.156e-08

-1.485e-08

-1.907e-08

-2.447e-08

-3.134e-08

-4.010e-08

-5.122e-08

-6.531e-08

-8.314e-08

-1.056e-07

-1.339e-07

-1.693e-07

-2.135e-07

-2.686e-07

-3.370e-07

-4.214e-07

-5.253e-07

-6.526e-07

-8.079e-07

-9.963e-07

-1.224e-06

-1.497e-06

-1.823e-06

-2.210e-06

-2.665e-06

-3.195e-06

-3.809e-06

-4.512e-06

-5.309e-06

-6.203e-06

-7.195e-06

-8.283e-06

-9.463e-06

-1.073e-05

-1.207e-05

-1.347e-05

-1.492e-05

-1.642e-05

-1.794e-05

-1.948e-05

-2.102e-05

-2.255e-05

-2.406e-05

-2.556e-05

-2.702e-05

-2.845e-05

-2.985e-05

-3.120e-05

-3.251e-05

-3.378e-05

-3.500e-05

-3.618e-05

-3.732e-05

-3.841e-05

-3.947e-05

-4.048e-05

-4.146e-05

-4.240e-05

-4.330e-05

-4.417e-05

-4.501e-05

-4.582e-05

-4.659e-05

-4.734e-05

-4.806e-05

-4.876e-05

-4.943e-05

-5.007e-05

-5.070e-05

-5.130e-05

-5.188e-05

-5.245e-05

-5.299e-05

-5.352e-05

-5.403e-05

-5.453e-05

-5.500e-05

-5.547e-05

-5.592e-05

-5.635e-05

-5.678e-05

-5.719e-05

-5.759e-05

-5.797e-05

-5.835e-05

-5.872e-05

-5.907e-05

-5.942e-05

-5.975e-05

-6.008e-05

-6.040e-05

-6.071e-05

-6.101e-05

-6.131e-05

-6.159e-05

-6.187e-05

-6.215e-05

-6.241e-05

-6.267e-05

-6.292e-05

-6.317e-05

-6.341e-05

-6.365e-05

-6.388e-05

-6.410e-05

-6.432e-05

-6.453e-05

-6.474e-05

-6.494e-05

-6.514e-05

-6.534e-05

-6.553e-05

-6.572e-05

-6.590e-05

-6.608e-05

-6.625e-05

-6.642e-05

-6.659e-05

-6.675e-05

-6.691e-05

-6.707e-05

-6.722e-05

-6.737e-05

-6.752e-05

-6.766e-05

-6.780e-05

-6.794e-05

-6.808e-05

-6.821e-05

-6.834e-05

-6.847e-05

-6.859e-05

-6.871e-05

-6.883e-05

-6.895e-05

-6.907e-05

-6.918e-05

-6.929e-05

-6.940e-05

-6.950e-05

-6.961e-05

-6.971e-05

-6.981e-05

-6.991e-05

-7.001e-05

-7.010e-05

-7.019e-05

-7.028e-05

-7.037e-05

-7.046e-05

-7.055e-05

-7.063e-05

-7.071e-05

-7.079e-05

-7.087e-05

-7.095e-05

-7.103e-05

-7.110e-05

-7.117e-05

-7.125e-05

-7.132e-05

-7.138e-05

-7.145e-05

-7.152e-05

-7.158e-05

-7.165e-05

-7.171e-05

-7.177e-05

-7.183e-05

-7.188e-05

-7.194e-05

-7.200e-05

-7.205e-05

-7.210e-05

-7.215e-05

-7.220e-05

-7.225e-05

-7.230e-05

-7.235e-05

-7.239e-05

-7.244e-05

-7.248e-05

-7.252e-05

-7.256e-05

-7.260e-05

-7.264e-05

-7.267e-05

-7.271e-05

-7.274e-05

-7.277e-05

-7.281e-05

-7.284e-05

-7.286e-05

-7.289e-05

-7.292e-05

-7.294e-05

-7.296e-05

-7.299e-05

-7.301e-05

-7.302e-05

-7.304e-05

-7.306e-05

-7.307e-05

-7.308e-05

-7.309e-05

-7.310e-05

-7.311e-05

-7.312e-05

-7.312e-05

-7.312e-05

-7.312e-05

-7.312e-05

-7.312e-05

-7.311e-05

-7.311e-05

-7.310e-05

-7.308e-05

-7.307e-05

-7.305e-05

-7.303e-05

-7.301e-05

-7.299e-05

-7.296e-05

-7.293e-05

-7.290e-05

-7.286e-05

-7.282e-05

-7.278e-05

-7.274e-05

-7.269e-05

-7.264e-05

-7.258e-05

-7.252e-05

-7.246e-05

-7.239e-05

-7.232e-05

-7.224e-05

-7.216e-05

-7.208e-05];





vgs=(0:0.01:1.5);

ids=-ids2(1:length(vgs));



%2 - sqrt(Ids) x Vgs%

sqrtIds= sqrt(ids);



%3 - diff de #2 e plot%

dIds=diff(sqrtIds);

dVgs=diff(vgs);

for i=1:length(vgs)-1

vgsd(i)=(vgs(i)+vgs(i+1))/2;

end



%4 - calculating gain%

ganho=2*sqrt(dVgs);



%5 - gm%

gm=sqrt(ids*ganho*2);









figure(1)

hold on

subplot(3,1,1);

plot(ids,vgs);

xlabel('ids');

ylabel('vgs');

subplot(3,1,2);

plot(sqrtIds, vgs);

xlabel('sqrtIds');

ylabel('vgs');

subplot(3,1,3);

plot(dIds, dVgs);

xlabel('dIds');

ylabel('dVgs');

subplot(3,2,1);

plot(ganho,vgsd);

xlabel('ganho');

ylabel('Vgs');

subplot(3,2,2);

plot(gm,ids);

xlabel('gm');

ylabel('Ids');

hold off


"

does this curve seems correct ?
thanks
regards

i know this post is kinda consufing cause of the large amount of data, but i was not sure about how many steps should i take from the simulation.

 

[Lucyfer]

Doesn't Gm equals d( Id)/d (Vg) ??
what kind of operating mode we use for this simulation ? does it gives a diferent curve if we change the operating mode ?
please link papers as well. Thx a lot

Regards