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Re: gEDA-user: ngspice shot noise

Karel Kulhavy wrote: 
Hello

Does ngspice noise model also work for operation of BJT with extremely
small collector current?

I got an idea to make low-noise amplifier by taking some 25GHz
transistor and powering it with so small collector current that its
transition frequency would drop down to 300MHz and then using it in
Ronja preamplifier instead of 2N3904. As second or even first stage
of the preamp.

Why use an RF transistor? The only reason I'd see for this is if thermal noise due to base resistance were your limiting factor.

How can one calculate shot noise in BJT?
Some papers say that shot and thermal noise are the same phenomenon,


they are not.

You'll have thermal noise due to the base resistance (not the small signal (kT/q)/Ibase but rather the actual resistance associated with getting to the base-emitter junction. You'll also have shot noise due to collector current and shot noise due to base current. So to model this, you'd take your normal bipolar small signal circuit model and add:

- a voltage source in series with the base with spectral density
4 k T rb V^2/Hz (k= Boltzmann's constant, T = temperature, rb = base resistance)

- a current source in parallel with the base-emitter junction with spectral density
2 q Ib A^2/Hz (q = electron charge, Ib = DC base current)

- a current source in parallel with the collector-emitter with spectral density
2 q Ic A^2/Hz (q = electron charge, Ic = DC collector current)

This ignores flicker noise and burst noise. If you want to add flicker noise, you can add
K1 Ib^a / f A^2/Hz to the base current spectral density. K1 will be a parameter related to the particular device.

These 3 noise sources are uncorrelated.

Now, if you convert to equivalent input voltage and current noise sources, you'll find that the input voltage noise source gets worse at lower currents but the input current noise source gets better at lower currents. Be careful because at higher frequencies where your current gain is falling off, these 2 equivalent sources are not completely uncorrelated. The best operating point from a noise point of view will be different depending on whats driving your circuit.

See something like the Gray and Meyer text which has long been the standard for an intro to analog design.

I think the danger with running a device way out from its typical operating range is that when the models were extracted, they may not have paid attention to that operating point. In other words if you have a transistor which is usually run with a 1 to 10 mA collector current because people are making 50 ohm LNA's with it, running at 10 uA may not be as well modeled. For example, as you go to very low collector currents, the dc current gain starts to fall off as sqrt(Ic) due to recombination of carriers in the base-emitter depletion region. dc current gain matters because it effects base current and hence shot noise.

In general I think you're better off with a device more targeted to where you're going to operate it.

-Dan