Re: gEDA-user: ngspice shot noise

["Greg Cunningham" <greg@xxxxxxxxxxxxxxxxxxxx>]

I'm not an engineer, but I recollect years ago Elekto mag published a very
lo-noise mic amp by parallelling a dozen-or-so gp bipolars.  Their argument
was that the randomness of the noise sources produced cancellation, while
summing the in-phase signals added.
-- 
Greg
----- Original Message ----- 
From: "John Doty" <jpd@xxxxxxxxxxxxx>
To: <geda-user@xxxxxxxx>
Sent: Friday, September 30, 2005 3:04 AM
Subject: Re: gEDA-user: ngspice shot noise


> On Wed, 28 Sep 2005, Karel Kulhavy wrote:
>
> > Does ngspice noise model also work for operation of BJT with extremely
> > small collector current?
>
> Should work just fine.
>
> > 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.
>
> First stage looks at a photodiode, right? You'll generally find it better
> to use a FET there: base current noise will kill you with a BJT. Get the
> impedance down with a FET front end. Use a BJT for the second stage: a
> well chosen BJT in a well designed circuit will generally be quieter than
> a FET at moderate impedance. There's a good discussion of this in Horowitz
> and Hill.
>
> Your idea to use fast transistors to achieve low noise is good. For
> interface to a capacitive sensor, a good procedure for choosing a front
> end FET is to choose a transistor technology that maximizes sqrt(gm)/Cin,
> and then choose a transistor whose input capacitance, Cin, matches the
> sensor capactance This will generally get you close to optimum from a
> noise perspective if you've done your homework on the rest of the circuit.
>
> For the second stage, operating a BJT at low current density will minimize
> noise due to parasitic resistances, but again you'll want a relatively
> fast transistor to do this. There's a tradeoff though: high beta will
> reduce base current noise, but really high beta transistors are generally
> not really fast. So, there's some art here.
>
> Always remember that noise is a system issue: choosing "low
> noise" components is no guarantee that you'll wind up with a low noise
> system. For a photoelectric detector, you probably want to start by
> calculating the shot noise in the detector output current (dark current +
> photocurrent): if the input-referred noise of your amplifier is more than
> a factor of two or three lower there's little to be gained by sweating the
> amplifier design.
>
> >
> > How can one calculate shot noise in BJT?
> > Some papers say that shot and thermal noise are the same phenomenon,
> > some are talking about partition noise, some say that shot noise in
> > base actually doesn't exist, some say that the shot noise is modelled
> > as two independent noise currents, one for BC and other for BE junction,
> > some say that the previous papers aren't true, and if I try to imagine
> > a transistor, I have a feeling that there should be one shot noise
> > current source connected with it's pins to B and E with
> > DC current given by base current, and another between E and C with
> > "steering" with DC current given by collector current.
> >
> > I get crazy from that. Does anyone know the truth?
>
> Start with an ideal semiconductor diode. I = Is*exp(V*q/(k*T)) - Is. Now
> what, exactly, is that magic parameter Is? The diode junction represents a
> potential barrier. Thermal energy will occasionally excite a charge
> carrier over the barrier, at a rate given by Is. Since the excitation of a
> carrier over the barrier is a random event, independent of other such
> events, the result is shot noise.
>
> At zero applied volts, the net current is zero (as thermodynamics
> requires), but from a noise standpoint it actually makes more sense to
> consider it as two currents, of magnitude Is, crossing the junction in
> opposite directions.
>
> For shot noise in a current I of charges of magnitude q measured over a
> bandwidth B, the current variance In^2 = 2*q*I*B. Plug in 2*Is for the
> current, you get 4*q*Is*B. But there's another point of view.
>
> The conductance, g = dI/dV = Is*q/(k*T)*exp(V*q/(k*T)). For zero bias,
> it's Is*q/(k*T). Now, the thermal (Johnson) noise current variance
> associated with an ohmic conductange g is In^2 = 4*k*T*g*B: plug in the
> above expression for g at zero bias, and you get 4*q*Is*B, the very same
> result we got from shot noise! Again, thermodynamics requires
> this: otherwise you could base a perpetual motion machine around a diode.
>
> At nonzero bias, things are just a little more complicated. For I>>Is,
> there's only significant noise current associated with the forward
> current. The result is that the noise variance is half of the Johnson
> noise for conductance g: the forward biased diode, as a noise source,
> behaves as if it's at half its physical temperature. This isn't a problem
> for thermodynamics as the bias supply is a source of free energy. Still,
> the noise current variance scales with temperature at a fixed g, so one
> might reasonably consider it thermal.
>
> So, is diode current thermal or shot noise? Since the conduction mechanism
> is thermal, but involves individual carriers, it's impossible to draw such
> a distinction.
>
> Of course a real diode also has parasitic resistances that make ordinary
> thermal noise. Ngspice takes these into account. However ngspice computes
> the junction noise as shot noise based on net current, which isn't right
> around zero bias, but in most cases parasitic leakage dominates the noise
> there anyway.
>
> For a BJT, the base-emitter junction acts like a diode, with the same
> noise current. The collector current follows a similar equation based on
> the base-emitter voltage (at least away from saturation). A good model is
> a  shot noise current based on the collector current, uncorrelated with
> the base current noise. Alternatively, you can consider it Johnson noise
> generated by the transconductance, but at half its physical temperature,
> just like a diode.
>
> Of course, the Johnson noise associated with parasitic resistances also
> matters. Base "spreading" resistance is often an important noise source.
>
> For situations where the emitter current is controlled externally (as in
> the upper transistor of a cascode pair) it is sensible to consider the
> noise as partition noise between the base and collector currents. Again,
> however, this yields the same answers as the shot noise and thermal
> approaches. The only advantage is computational: in the other models
> emitter-base voltage fluctuations work through gm to cancel part of the
> collector noise in this case, while the partition noise model doesn't
> require you to consider them (as they don't, by definition, affect the
> emitter current in this special case).
>
> John Doty          "You can't confuse me, that's my job."
> MIT-related mail:                       jpd@xxxxxxxxxxxxx
> Other mail:                             jpd@xxxxxxxxxxxxx
>
>