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

[Bob kb8tq]

Hi

Typically, in the context of Time Nuts, the “noise” that is the issue is 
added phase noise when amplifying a fairly high level RF carrier. In 
that case, the 1/f noise of the device very much does matter. You also
need pretty significant collector current to provide the needed ( many 
dbm ….) power output. 

Oscillators are a bit different in terms of major collector current ( usually,
but not always …). They still are very sensitive to the 1/f noise in the
device.

Bob

> On Sep 18, 2022, at 2:28 PM, Matt Huszagh via time-nuts <time-nuts at lists.febo.com> wrote:
> 
> 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?
> 
> 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?
> 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.
> 
> As an aside, I feel this is on topic for this forum because BJT noise
> and base-spreading resistance are very relevant for low residual phase
> noise buffers, among other things. Additionally, I've seen some very
> good discussions of BJT noise on here. But, let me know if you feel this
> is off-topic and I can take this discussion elsewhere.
> 
> Matt
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