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]
