The Designer's Guide Community Forum

The Designer's Guide Community Forum
https://designers-guide.org/forum/YaBB.pl
Design >> Analog Design >> gm initially increases with W and then gets const?
https://designers-guide.org/forum/YaBB.pl?num=1175263334

Message started by Alm on Mar 30^th, 2007, 7:02am

Title: gm initially increases with W and then gets const?
Post by Alm on Mar 30^th, 2007, 7:02am

Hi,

I am tryin to understand the following behavior:

In the attached circuit of a simple 5 transistor diff-amp, the bias voltage Vb is held constant.

Now I am increasing the width of the pair w1-w2. As width increases, initally gm of those mosfets increase in proportion to sqrt(w1).
I believe this is because as current is const, due to const Vb,

gm = sqrt(2 * Mn * Cox * W/L * Id)

However, after a point even when the Width of the mosfet pair increases, gm1 remains constant (see attached figure).

Could anyone help me understand why does gm1 become constant.

Is this the so called 'strong inversion' where gm gets poor?

-Alm

Title: Re: gm initially increases with W and then gets co
Post by monte78 on Mar 30^th, 2007, 9:29am

Hi!

If you increase W you are reducing the effective gate-source voltage of transistor M1. This mean that M1 will work in strong inversion region until Vgs-Vth becomes comparable to vt=26mV at room temperature. If you increase W, your transistor will work in weak inversion, where gm=Ibias/(n vt), so gm will be constant (if you don't modify bias current) also if you increase W (and linearly dependent by the current).
Weak inversion is the region where you obtain the maximum gain with a fixed bias current, compared to the strong inversion where gm=2 Ibias/Veff and there is a square root dependence by the current.

However if you take a look to a good microelectronic book you'll find a more accurate analysis on the operating region of mosfet.

With particular regards to the curve you show here, I don't know why the gm stabilize at a lower level, I expected that gm should be constant beyond a certain W value.
I think it's better if you plot the id - vds characteristic of a single transistor circuit without a differential amplifier structure to understand the correct behaviour of the MOSFET.

Bye!

Monte

Title: Re: gm initially increases with W and then gets co
Post by vivkr on Apr 2^nd, 2007, 12:29am

Hi,

The gm of a MOS will never be larger than the gm of a BJT for a given current consumption.
If you consider this fact, you will realize automatically that increasing W/L will not fetch you
more gm beyond a point. This is an erroneous result of applying the square-law model. For very large
W/L, your MOS is in weak inversion where its gm flattens out and is controlled only by the current.

For a good analysis of these issues, try the JSSC paper by Jespers & Silveira.

Regards
Vivek