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" <[EMAIL PROTECTED]> To: <[email protected]> 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: [EMAIL PROTECTED] > Other mail: [EMAIL PROTECTED] > >
