[moved] How to get fixed current density?

Hi,

I am working on a design using CMOS. I do a Vgg sweep to observe current density, and now want to plot Zopt vs device size with fixed current density.

Do you know how I should do that?

Thanks,

Zopt = ???

Hi,

Zopt is about 60ohm...

Do I need to consider Zopt to get fixed current density?

I meant that I did not understand the meaning of "Zopt".
Output impedance? Optimum impedance? Something else?

Zopt is the optimum impedance for noise matching.

Hi,

I suppose the optimum impedance you are writing about is your optimum source impedance. If you are trying to do something at HF, things are done in a different way than what I'm writing about and you will have to consider line lengths and impedance transformations for noise matching. Let's assume you are using a common-source configuration.

In a MOSFET design the optimum source impedance is usually somewhere in the Megohm range so you'll probably have a less-than-perfect source impedance.

A bipolar transistor's contribution to a circuit's noise can be divided up into an equivalent input noise voltage and an equivalent input noise current:
The equivalent input noise voltage gets smaller when the collector current rises. Additionally, there is a contribution by the base-spreading resistance that is independent of your operating point.
The equivalent input noise current flows into the base terminal. You could also say it flows out of the base terminal as it's not signed. It causes a voltage drop across the resistance that's connected to the base terminal. The voltage drop goes up as base current rises.

So with a bipolar transistor you will have an optimum point when your collector current is high enough to cause a small noise voltage and low enough not to cause an excessive voltage drop over your source impedance. This optimum point depends on the value of your source impedance as the source impedance will determine the voltage drop.

With MOSFETS, at moderate frequencies the equivalent noise current only depends on the gate leakage current and will be extremely low. Your optimum source resistance will be several orders of magnitude higher than the 60 Ohms you seem to be aiming for.

Having said that, I enjoy seeing the noise figures a MOSFET can yield at source resistances that are much lower than the optimum. Try to get the highest gm you can get away with. If you are happy with your noise figure you'll be fine, otherwise increase the transistor's width or the drain current until you are.

If you're still not happy, use a bipolar transistor if that's available in your technology. The equivalent input noise and optimum source resistance for a BPT can be calculated fairly easily so you'll only need a simulation as a sanity check after finding your optimum point through calculation. It might be tricky to find a device with a base-spreading resistance of less than 60 Ohms, though.

I don't know which circuit simulation tool you're using. It will probably have a way of displaying total input related noise. Set up your input signal source and output node in your circuit file. Choose a bandwidth that's well above your system bandwidth.
Do various runs with the source impedance you've chosen and either vary your operating point or vary your source impedance. Find out if your tool displays the source resistor's noise voltage density or the square of the noise voltage density (the quantity displayed varies from simulator to simulator). Display or calculate the total source resistor noise. Calculate the noise figure. See if it gets better or worse as you change your bias or source resistance.

Some simulators let you vary a parameter and display the noise density at a specified frequency as a function of that parameter. If your simulator can do that and you want to go that route, choose your frequency wisely.

Don't be shocked if your total input noise voltage goes up when you choose a higher source impedance. That's normal. Aim for a minimum noise figure. But don't try to improve the noise figure by increasing the source impedance if you have a voltage-type signal source. Increase your transistor's gm.