phase/frequency noise from voltage noise

[Ken Smith]

In article <ceEGe.22172$Ag3.17873@newsfe4-gui.ntli.net>,
colin <no.spam.for.me@ntlworld.com> wrote:

"Ken Smith" <kensmith@green.rahul.net> wrote in message
news:dcel8g$fvl$1@blue.rahul.net...
In article <2UtGe.18947$Hd4.14395@newsfe2-gui.ntli.net>,
colin <no.spam.for.me@ntlworld.com> wrote:
[...]
No, mixing by multiplying makes equal side bands. The amplitude varies
but the frequency remains exactly the same. This is why I was suggesting
making sure that the amplifier is good to a much higher frequency than
needed. A distortion that acts only on the instantanious voltage, always
creates equal sidebands.

You would be correct if the circuit had a flat flat phase and balanced
amplitude response about its operating frequcncy but this isnt necessarily
so, it depends largly on the feedback topology.

I don't think you understood what I said (meant to say) so I'll try again.

Imagine that you have a little black box that contains the function that
creates the distortion. This box has an input and an output. If the
contents of that box produces an output that depends only on the
instantanious value of the input, that box must create balanced side
bands.

The filtering of the sidebands will only happen in the high Q tuned
circuit, assuming that we are trying to make a low drift oscillator. We
can also assume on that basis that the design is done such that the
effects of JFET parameters on tuning have been minimized. When this is
the case, the sidebands will remain balanced.

Although I cant say ive gone into the maths of how altering the
amplitude/phase of the sidebands affects the phase of the output in any
great detail, the modulation gets in there somehow, If you look at the
sidebands of a typical good oscilator the close in noise rises at 1/f^3 this
is due to 1/f noise and the 1/f^2 response of the resonant circuit.

When the upper and lower side band components are at 180 degrees to each
other, you have phase modulation. When they are in phase, you have
amplitude modulation. Any pair of side bands can be broken down into the
amplitude modulation component and the phase modulation component. Then
you can disregard the amplitude part.

Actually, the 1/F^3 rise continues into the part near the carrier where
the tuned circuit curve flattens. For that matter, there is often a
sudden increase in the slope at that point to well above the cubed factor.
A frequency drift will appear as a 1/F in the graph. A 1/F noise
modulation of a capacitance will appear as a sqrt(1/F)


[...]

I stated this happens and that, this again is why I suggested low AC
impedance nodes at the FET. This reduces the effect of any variation in
capacitance.

The ratio of parasitic capacitance seen by the tank circuit to capacitance
of the tank itself would determine how much this would afect the frequcncy.
If you have a high frequcncy oscilator you cant make this very large,
despite that the impedance would be quite low.

The OP is talking about a lowish frequency oscillator. Even at high
frequencies, the desire is to make the ratio higher. To make the ratio
higher you make the impedance even lower. The rule still applies it just
gets harder to follow.

also any noise will efectivly apear as a phase error if it is used in
highly
non linear mode, and a changing phase erroor = change frequcncy.

No, this is not true. Noise that is identical side to side WRT the
carrier does not effect the phase.

If it moves the operating point of the circuit then this may have an effect
on the delay through the amplifier and hence phase.

Once again I think you've misunderstood or perhaps I've misunderstood you.
Remember that I suggested that the amplifier section (FET) be one that has
a much higher band width than needed. This and the low terminal impedance
to to prevent the modulation of FET parameters from being a problem.

also non linearities
will efectivly make the noise no longer identical side to side of the
operating point.

Huh? Do you mean non-linearities in the phase or nonlinearities in the
more normal sense of the word.

If you mean in the more normal sense of the word then I disagree as stated
above. Non-linearities that operate on the instantanious value always
make equal sidebands.

No, this is not true. You can run a larger voltage on the inductor to
keep the voltage at the gate the same as you lower the impedance.

I dont see why you think this is not true, many RF FET datasheets specify
noise performance by using 50 ohm mathcing networks wich also step up the
voltage, this is how they arive at such spectacular noise figures.

This is a different case. The amplifier in an oscillator has its
terminals connected to the frequency determining circuit. The measurement
circuit does not.

If we take a perfectly impractical set of cases I think you will see:

Oscillator #1:

We use a simple 2 capacitor divider
Voltage on inductor = 20V RMS
Voltage from gate to source = 10VRMS

Oscillator #2:

We use the 3 capacitor divider
Voltage on the inductor = 10 billion VRms
Voltage from the gate to source = 10VRMS


Both have the same signal to noise at the gate of the FET but the second
one has about 10^12 less ability for the FET to control the frequency.

A very high Q tuned circuit has a high enough impedance that the noise
current of the FET starts to matter too.

Noise current of good FETs/MOSFETs is small, realy small, ... down to a few
fa/rt hz.

Lets say 10fA/sqrt(Hz) and few 100K impedance.

10fA/sqrt(Hz) * 100K = 1nV/sqrt(Hz) so we are in the same range as the
noise voltage of a low noise JFET. I have run into this fact in practical
circuits.

This is certainly not true. ALC style oscillators are what you use if you
want the most stable frequency. Clipping and distortion of any type
allows the noise components near the harmonics of the carrier to be
re-introduced as near carrier components. This reduces the performance a
great deal.

The harmonics will be greatly attenuated by the tank circuit before they can
be re introduced close to the carrier frequency.

No, the harmonics are in the noise voltage of the gate of the FET they do
not pass through the tuned circuit before they hit the non-linearity in
the FET.

Although im not too clear of the exact mechanism where they get introduced

It is fairly straight forward if you take a very simplified case:

Imagine we have an extremely non-linear amplifier. The amplifier is
assumed to be noiseless and the noise is in a generator, added to the
signal just before the amplifier. The input to output function of the
amplifier can be represented by a series. Lets just take the first few
terms:


Y = X + AX^2

Where:
X is the input
A is a constant
Y is the output

Now we consider X as the sum of (S)ignal and (N)oise.

Y = (S + N) + A(S + N)^2


Y = S + N + AS^2 + 2ANS + AN^2


It is the 2NS that does the dirty work. It will mix noise near the second
harmonic down to near the operating frequency. The more nonlinear things
are, the bigger A will be and the more 2nd harmoic noise gets shifted
down. The higher terms bring the higher frequencies down. As a result,
the more nonlinear the circuit is the noisier it is.

on this, look up "Oscillator Phase Noise Reduction Using Nonlinear Design
Techniques"

Reference left for later look up.


[...]

At the fequency of oscillation the gain of the total loop will be slightly
greater than 1 to sustain the oscillation frequcncy, any noise that gets
introduced that is close enough to the center frequcncy so that it is still
within the response of gain >1 will be amplified significantly.

Actually the gain must be exactly one if the amplitude is constant.

After all the oscilation frequency is in fact just the noise selectivly
amplified many many times by positive feedback, therfore what im saying is
that the close in noise in the output is much much greater than simply the
voltage noise at the input.

Thus keeping the gain as low as posible will ensure the bandwidth with gain
1 is also as low as posible.

The gain around the loop must be exactly one at the operating frequency.
The amplifier's gain does not effect the bandwidth of the system unless we
are taking the case of a poorly designed oscillator where the transistor
controls the frequency.

--
--
kensmith@rahul.net forging knowledge

 

colin wrote:

clicliclic@freenet.de> wrote in message
news:1122703400.428798.201810@g44g2000cwa.googlegroups.com...

Colin, what is the reasoning that makes you conclude that white noise
from within the bandwidth determined by the tank-circuit Q is no factor

for a simple self-limitimg FET oscillator like mine? How large could
that contribution to the frequency noise observed on a 10s scale be? I
have no clear idea how to estimate this. (The input-referred white
noise
level of the 2N3819 is around 3 nV/Hz^(1/2), my loop gain is only
moderately larger than one, f0 is near 60kHz, the unloaded Q is around
100, and the loaded Q around 20, maybe.)

The reasoning is that for a bandwidth of .1-10 hz the 1/f noise is several
orders of magnitude larger than the white noise, for a good device 100 times
larger wich from data sheets amounts to somthing in the order of ~0.1uv pk
to pk for bipolar and ~1uv pk to pk for FET, some device are well in exces
of 1000 times the white noise, some even more, most spec sheets for low
noise low freq devices dont even specify noise below 100hz, and its hard to
find specs at all for most devices for this f range, probably becuase it
looks embarising. some RF devices dont mention noise performance below
10mhz.

For the 2N3819, a junction FET, the ratio is 200nV/3nV - two orders of
magnitude (Vishay-Siliconix datasheet). But this may not really apply
to
my BF245, where I couldn't find any noise data below 1MHz ...

Even if the mechanism for modulating this noise onto the carrier is low it
is still quite likely to be high enough to allow it to become dominant

Although its not clear how much of this is due to modulating the parasitic
elements and how much is due to actualy mixing unless you examine a
particular circuit in detail, ive worked with xco wich are much higher
frequency and so you are limited to tens of pf, maybe your circuit baheves
diferently but with a Q of 20 compare to a Q of 20,000 for a crystal ...

This was my suspicion: that what appears to be a generally accepted
fact
for crystal oscillators might not equally apply to LC circuits with
their much smaller Q. The smaller Q allows a much wider band of white
noise to make it many times around the feedback loop. So, a
quantitative
estimate of its effect is needed, where the principles should apply to
both, LC and crystal oscillators. I had hoped the simplicity of my test

circuit might make this task easy, like it did for the low-frequency
flicker noise ...

Also as I mentioned the noise profile of the output its clearly dominated by
1/f noise very close into the carrrier as the noise rises at 1/f^3 where f
is the distance from the carrier. further out from the casrrier it returns
to 1/f^2 wich is white noise atenuated by the Q of the tank.

Also although your loop gain is marginaly larger than one this circuit has
positive feedback, therefore the actual closed loop gain is high, if you try
to work it out you will find it comes out as infinite, but it is limited as
when the output increases the gain falls.

If you get 2 identical oscilators in a PLL with the loop time constant of
less than 1 second you can see the phase noise from the output of the phase
detector on a scope, ... it jumps around a lot, when I first encountered
this I thought it was faulty components soldering or whatever etc, and
although vigourously cleaning of the flux helped sometimes even after
rebuilding them carfeuly with new components it was still there, I threw
away many a good oscillators in disgust before i cuaght on to this.

Sounds somehow familiar ...

There are some methods and programs wich estimate oscillator noise but these
are rather limited frtom what I can gather as it is an extremly complex
issue involving so many factors, especialy so for close in noise.

.... and this is bad news. But I don't believe it applies to a circuit
as
simple as mine ...

Also as has been mentioned before drift due to temperature etc will more
than dominate noise anyway.

Well, with 1ppm/deg TC compensation and styrofoam insulation, 10^-8 to
10^-9 frequency stability over 10 seconds is no problem for an LC
circuit. I am not yet able to see the 10^-10 arrived at for the FET
flicker noise - maybe for thermal stability, maybe for other reasons -
but what I am seeing could still be the unknown-so-far effect of white
noise from the vicinity of f0 ...

If you realy want a 60khz oscillator that remains totaly stable over a 10s
interval I sugest you consider a crystal oscilator and divide it down.

Colin =^.^=

I'm trying to understand how different noise contributions affect
oscillator circuits; I've no shortage of ideas for more stable
circuits.
Knowing which contributions matter under what circumstances (in
particular knowing how to estimate them beforehand) can be useful in
sifting good design ideas from bad ones.

Martin.

 

[Ken Smith]

In article <1122788724.797384.263770@g49g2000cwa.googlegroups.com>,
<clicliclic@freenet.de> wrote:
[...]

my BF245, where I couldn't find any noise data below 1MHz ...

I think you want to look up the LSK170 "improved" version of the 2SK170
for the frequencies you are working at.

This was my suspicion: that what appears to be a generally accepted
fact
for crystal oscillators might not equally apply to LC circuits with
their much smaller Q. The smaller Q allows a much wider band of white
noise to make it many times around the feedback loop. So, a
quantitative
estimate of its effect is needed, where the principles should apply to
both, LC and crystal oscillators.

IIRC:

White noise comes in as:

Y = A(B^2 + f^2)/f^2

Where:
Y is the phase noise in radians RMS at a given frequency offset
B is the 3dB bandwidth of the tuned circuit
f is the frequency offset from the carrier in radians
A is the noise at the input to the perfect part of the FET model

--
--
kensmith@rahul.net forging knowledge

 

Ken Smith wrote:

I think you want to look up the LSK170 "improved" version of the 2SK170
for the frequencies you are working at.

I knew the 2SK117 and 2SK170, but not this one. From the datasheets
(mostly read from the graphs and converted, hopefully correctly):

2SK117: 15mS 2.7nV/rtHz @ 10Hz 1.1nV/rtHz @ 1kHz (0.5mA, 10V)
2SK170: 22mS 3.0nV/rtHz @ 10Hz 1.0nV/rtHz @ 1kHz (1mA, 10V)
LSK170: 22mS 2.5nV/rtHz @ 10Hz 0.9nV/rtHz @ 1kHz (2mA, 10V)

I guess the LSK170 to be hard to obtain (particularly so in Europe);
the
2SK117 and 2SK170 are no problem.


Ken Smith wrote:

In article <1122788724.797384.263770@g49g2000cwa.googlegroups.com>,
clicliclic@freenet.de> wrote:
This was my suspicion: that what appears to be a generally accepted
fact
for crystal oscillators might not equally apply to LC circuits with
their much smaller Q. The smaller Q allows a much wider band of white
noise to make it many times around the feedback loop. So, a
quantitative
estimate of its effect is needed, where the principles should apply to
both, LC and crystal oscillators.

IIRC:

White noise comes in as:

Y = A(B^2 + f^2)/f^2

Where:
Y is the phase noise in radians RMS at a given frequency offset
B is the 3dB bandwidth of the tuned circuit
f is the frequency offset from the carrier in radians
A is the noise at the input to the perfect part of the FET model

--
--
kensmith@rahul.net forging knowledge

I'm not sure how to make use of this formula; it appears to be
independent
of the oscillation amplitude, in contrast to my naive expectation. Let
me
therefore propose the following derivation of frequency noise from
white
amplifier noise near the oscillator frequency f0:

Assume again an observational interval dt = 10s. Coherent "pulling"
action
over this interval can only be expected from a narrow range of noise
with
f0-df/2 < f < f0+df/2. Such noise has an approximate coherence time dt
=
4/dw = 2/(pi*df). Thus, for coherent action over 10s, we have df =
64mHz.

Guesstimating a white noise density of 6 nV/rtHz for my BF245A at
Id=1mA,
the coherent noise amplitude is B = 6nV/rtHz * sqrt(64mHz) = 1.5nV. On
the
other hand, my (measured) oscillation amplitude is A = 0.6V (across
each
of the tank capacitors).

If the noise happens to have the optimum 90deg phase for pulling, we
may write

A*sin(w0*t) + B*cos(w0*t) = sqrt(A^2+B^2) * sin(w0*t+arctan(B/A)).

That is, an extra phase shift dp = arctan(B/A) = B/A = 2.5*10^-9 is
introduced (for B << A, arctan(B/A) may be replaced by B/A). The
oscillator
will react to this phase shift by adjusting its frequency such that an
opposing shift arises in the tank circuit.

For a tank circuit with quality factor Q we have df0/f0 = dp/(2*Q)
around
resonance. Thus, for my Q of about 20, one arrives at df0/f0 =
6*10^-11.
This is about half of the effect from low-frequency flicker noise as
calculated earlier. It seems Colin was right, if by narrow a margin!

Any objections? Or endorsement?

Martin.

 

[Ken Smith]

In article <1122913173.746658.264600@g49g2000cwa.googlegroups.com>,
<clicliclic@freenet.de> wrote:

[...]

White noise comes in as:

Y = A(B^2 + f^2)/f^2

Where:
Y is the phase noise in radians RMS at a given frequency offset
B is the 3dB bandwidth of the tuned circuit
f is the frequency offset from the carrier in radians
A is the noise at the input to the perfect part of the FET model

[...]
I'm not sure how to make use of this formula; it appears to be
independent
of the oscillation amplitude,

You are right there is an error. "A" was supposed to be noise/signal.

[....]

the coherent noise amplitude is B = 6nV/rtHz * sqrt(64mHz) = 1.5nV. On
the
other hand, my (measured) oscillation amplitude is A = 0.6V (across
each
of the tank capacitors).

How non-linear is the FET being with a 0.6V swing. Remember that
frequencies near the harmonics will be mixed down to near the carrier by
any non-linear action.

[..]

This is about half of the effect from low-frequency flicker noise as
calculated earlier. It seems Colin was right, if by narrow a margin!

Colin may well be right he may also be wrong and just lucky. If you
change JFETs you may be able to settle the matter.



--
--
kensmith@rahul.net forging knowledge

 

No serious objections were raised, and I consider the question settled:

Over a 10 second interval, frequency deviations df0/f0 of the order
10^10 can be expected for my simple 60kHz oscillator from each, JFET
flicker noise at low frequency and JFET white noise near f0.

Thanks to everybody for having seen me through my labors with this
problem,

Martin.