Collector current that minimizes BJT noise
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
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
I confess to sloppy wording:
In the FET section, replace gain by gm.
Now that I send the correction: Bob Widlar did not like
JFETs too much. He designed a bipolar opamp with bias
currents better than the FET ones at high temperatures.
(LM108 IIRC)
I've played a bit in LTspice with his input circuit.
He ran the input transistors with Vce abt= Vbe. That results
in small bias currents and allows the use of super-beta
transistors that cannot withstand much voltage.
I was surprised by the good low noise properties.
The circuit at the top left creates a noisy Vcc to see
how much noise can be tolerated there. Q4 and Q5 are parked
there only for quick exchange.
Gerhard
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@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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Thanks for the reply Bob.
Bob kb8tq kb8tq@n1k.org writes:
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.
No disagreement there. To be clear, the purpose of ignoring 1/f noise
was to focus the discussion somewhat, as this is quite a large topic.
You also need pretty significant collector current to provide the
needed ( many dbm ….) power output.
Of course. But, there are still cases where low collector current might
be relevant. For instance, in a multi-stage amplifier (eg to achieve
higher reverse isolation) you might set a higher input impedance for the
second stage and run the first stage at lower collector current. I'm not
sure yet if you'd want to do this, but it is conceivable.
Matt
Hi Gerhard, thanks for the thoughts.
Gerhard Hoffmann via time-nuts time-nuts@lists.febo.com writes:
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.
I'd neglected beta's dependence on collector current; thanks for the
reminder.
As for the base shot noise, Motchenbacher includes this in the complete
noise formulation and then discards it for his simplified voltage noise
expression, leaving just collector shot noise and base thermal noise. He
claims these are the two quantities limiting noise performance at
midband frequencies.
After running some numbers I'm inclined to agree. The base thermal noise
is proportional to the root of the base resistance whereas base shot
noise is proportional to the first power of base resistance. For T=300,
ic=10mA, beta=100, the base shot noise doesn't catch up to base thermal
noise until rbb hits about 500ohms. That should be well out of low-noise
BJT territory. Even with lower beta the equalizing rbb is still pretty
high.
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.
Ah, yeah I was worried about something like that. The fact that
datasheets barely provide any information about noise performance didn't
bode well. Are people not designing low-noise first stages with
discrete transistors?
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.
I'd come across that but not given it a detailed look yet. I'll look
closer. I think that's confined to audio frequencies, though, whereas
the prompt for this question was looking at Bruce Griffith's
common-emitter Norton buffer amplifier for distributing a clean 10 MHz
source.
I've been investigating alternative transistors to posssibly lower the
noise further. I also wanted to add a second stage to increase the
reverse isolation. That raised the possibility of running the first
stage at lower collector current.
I've been going around in circles a bit trying to use datasheet and
spice values in calculations. It sounds like I need to just build a few
variations and test them at this point. The only problem is that I'm not
sure I have a test setup sensitive enough to measure the difference...
Matt
Moin, moin,
On Sun, 18 Sep 2022 12:28:36 -0700
Matt Huszagh via time-nuts time-nuts@lists.febo.com wrote:
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.
I would like to expand here a bit on what other people wrote:
Spice models, especially of older transistors, were designed to
meet the datasheet. If you are lucky, someone measured the
four-quadrant graph paramters of the transistor (instead of looking
at the datasheet) and adjusted the model to match those values.
This means that the Spice model does not match the physical realities
of the transistor but rather matches the measured parameters. That
works well for DC simulations, but only approximately for AC and
(fast) transient simulations. Noise simulations are derived from
those DC parameters, but because nobody measures noise parameters,
the spice model is not checked for accurate noise modeling.
I.e. it usually does not match the device's actual behaviour.
Which means, if you want to use Spice for noise modeling, then you
have to measure the transistor parameters yourself and adjust the
model until it matches those.
This also gets compounded by the fact that the noise simulation
system in Spice is rather crude and ignores many factors that come
into play.
Thus it's usually more accurate to take some measured noise parameters
of transistors (e.g. Art of Electronics 3rd ed) and then calculate
the noise through the system by hand.
I would also recommend to look at [1] instead of Motchenbacher, as it
is not only more up to date, but quite a bit more extensive in its
coverage of noise modeling of devices.
Additionally, in my experience, the intrinsic noise of the transistor
can be ignored in most applications where a low noise architecture/device
is being used. The up and down-conversion of noise due to non-linearities
are much more of a problem than shot noise and Rbb noise, which is usually
lower than the input noise in our type of applications. In particular flicker
noise performance is, due to above mentioned up/down conversion, directly
connected to the amplifier's IP2 performance. Which gets especially important
when you are using multi-stage amplifiers.
If flicker noise is a limiting factor in your application, then the way to
go is to use a system that actively stabilizes the collector current.
Using a push-pull architecture where even harmonics cancel out (gives usually
between 6 and 20dB of even harmonic cancelation, more when transistors are
matched) also minimizes flicker noise.
If you are using a differntial pair or similar architecture, ensure that
the base voltage bias is adjusted for each branch individually. A good
substitute for measuring collector current is the output DC bias, which
should be zero for two identical transistors. I.e. you can use that to
steer the base voltage of one transistor to minimize output DC bias
and thus even mode harmonics.
And last but not least: Don't trust any model you have not verified.
I.e. after you've done your calulations and simulations, build the
device and see whether it matches what you expect. Then build a second
prototype with slightly different choices and verify that it still
matches the model/calculation and is indeed worse than your first prototype.
That is, unless your first prototype is good enough and you don't
want to optimize it further.
Attila Kinali
[1] "Electronic Noise and Interfering Signals", by Vasilescu, 1st ed, 2005
--
In science if you know what you are doing you should not be doing it.
In engineering if you do not know what you are doing you should not be doing it.
-- Richard W. Hamming, The Art of Doing Science and Engineering
On 9/26/22 5:28 AM, Attila Kinali via time-nuts wrote:
Moin, moin,
On Sun, 18 Sep 2022 12:28:36 -0700
Matt Huszagh via time-nuts time-nuts@lists.febo.com wrote:
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.
I would like to expand here a bit on what other people wrote:
Spice models, especially of older transistors, were designed to
meet the datasheet. If you are lucky, someone measured the
four-quadrant graph paramters of the transistor (instead of looking
at the datasheet) and adjusted the model to match those values.
This means that the Spice model does not match the physical realities
of the transistor but rather matches the measured parameters. That
works well for DC simulations, but only approximately for AC and
(fast) transient simulations. Noise simulations are derived from
those DC parameters, but because nobody measures noise parameters,
the spice model is not checked for accurate noise modeling.
I.e. it usually does not match the device's actual behaviour.
Which means, if you want to use Spice for noise modeling, then you
have to measure the transistor parameters yourself and adjust the
model until it matches those.
What has been the list's experience with noise models in SPICE for ICs
(e.g. Analog Devices provides SPICE models for low noise op-amps)
We've been hand calculating using the datasheet values, and then
measuring in the circuit, and as expected, we get comparable
measurements (perhaps a bit better than data sheet performance).
On Mon, 26 Sep 2022 08:53:26 -0700
"Lux, Jim via time-nuts" time-nuts@lists.febo.com wrote:
What has been the list's experience with noise models in SPICE for ICs
(e.g. Analog Devices provides SPICE models for low noise op-amps)
We've been hand calculating using the datasheet values, and then
measuring in the circuit, and as expected, we get comparable
measurements (perhaps a bit better than data sheet performance).
As far as I can tell, ADI's models are quite accurate for noise.
Though I have not extensively tested them. Neither have I operated
any of the devices at the limits of the specifications. I.e. I have
only ever exercised the models in the region of most common use.
And it seems like since ADI switched to encypted device models, that
they even have gotten more accurate. Might be that they don't fear
to expose device internals anymore.
But my comment on non-linearity and its effects not being modeled
by Spice remain. They are just less important for the low frequencies
where most opamps are operated at. I have not done, neither have I
seen comparison of Spice simulations with measurements of high-speed
opamps operating in the MHz range.
Attila Kinali
--
In science if you know what you are doing you should not be doing it.
In engineering if you do not know what you are doing you should not be doing it.
-- Richard W. Hamming, The Art of Doing Science and Engineering