[time-nuts] Re: Collector current that minimizes BJT noise

[ghf at hoffmann-hochfrequenz.de]

Am 2022-09-18 21:28, schrieb Matt Huszagh via time-nuts:
> Hi,
> 
> In the the first edition of Low-Noise Electronic Design, Motchenbacher
> states that minimal noise for a BJT is attained at low collector
> currents (here we restrict ourselves to midband noise where 1/f noise
> and noise terms that are appreciable near the transition frequency can
> be neglected). To justify this, Motchenbacher gives the equation (eqn
> 4-23, for those with the text)
> 
> Fopt = 1 + sqrt(2rbb / (beta * re) + 1/beta)
> 
> However, this neglects the dependence of base-spreading resistance on
> collector current. At high quiescent current, the emitter current 
> crowds
> out the base current such that the base current travels a shorter
> distance through the base region, thus decreasing the effective base
> resistance (for references see eg the 1963 paper by Hauser).
> 
> The gummel-poon model quantifies this effect as
> 
> rbb = rbm + 3(rb - rbm) ((tan(z) - z) / (z tan^2(z)))
> z = (sqrt(1 + (12/pi)^2 * (ib / irb)) - 1) / (24/pi^2 * sqrt(ib/irb))
> 
> where rb is the zero-bias base resistance, rbm is the minimum base
> resistance (at high current) and irb is the base current at which rbb 
> is
> halfway between rb and rbm.
> 
> I ran calculations on several (fairly random) parameter combinations 
> and
> the collector current that minimizes noise depends on the values
> chosen. Does this rbb current dependence invalidate Motchenbacher's
> simple prescription, or is the practical behavior of BJTs such that
> minimizing collector current generally does minimize BJT noise
> contribution?

Not so sure about BJTs, but for FETs it is best to run them at
high drain current. Gain is proportional to the root of Id,
and voltage noise is proportional to 1/ sqrt(gain). So, things get
better with the 4th root of current. One hits the limits quite soon.
It is generally better to reduce Id and put more FETs in parallel.
Unless used at high temeratures, there is not much noise current,
but Cin hurts.

On BJTs , Ib * Rbb is the worst problem. A large Beta helps to
minimize that. But if you minimize Ic, beta may drop steeply
depending on the transistor. Then you may be worse off, over all.

> This raises the more general question: how do people find the minimum
> noise operating conditions for BJTs? Do you go straight to measurement,
> or do you first attempt to estimate it from datasheet and SPICE values?

I go to measurement with the intended circuit. There are other 
constraints
too, like supply voltage, required gain...
Spice models are seldom good wrt noise. Nobody seems to care.
A lot of these have historically been made with Orcad parts.exe.
They all seem to have the same RBB, be it 2N3055 or BC109.

> If so, can you shed some light on this process? I've attempted, for
> instance, to estimate rbb from SPICE models (using the equations above)
> and have had worse than bad success equating these to various measured
> results (from Art of Electronics and various papers). It's worth
> mentioning that measured results are also wildly different between
> sources, so this whole thing may be an exercise in futility anyway.

Since you mentioned AOE: their ribbon microphone preamp meets its
70 pV/rt Hz goal as promised. Of course, there is a lot of noise 
current.
OTOH, 70pV/rtHz makes only sense with a low impedance DUT.
It is a nice tool in front of the FFT analyzer.
I've built it in a single-ended version. That reduces the # of
transistors from 64 to 16. That costs a lot of input coupling capacitors
which is ugly, but then, most interesting signals ride on a DC
and a dc coupled differential input is no help then.
Vcc must be _really_ clean.

Cheers, Gerhard


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