# [time-nuts] Square to sine wave symmetrical conversion (part 2)

Mon Jul 27 21:58:03 EDT 2015

```Bob, I think you meant to write: "Hook a 100 pf cap from emitter
to ground."

Also remember that the feedback loop can use multiple active devices.
You can design a crystal oscillator which has only linear loading on the
crystal but which has nonlinear characteristics somewhere in the
feedback loop. Some oscillators use a filter to insure that only a
linear signal is fed back from a very nonlinear amplifier in the loop.
The output can be taken from various places in the feedback loop, and
the harmonic content varies depending on that location.

One idea is to only add energy to the crystal at the peak of the
sinewave voltage, when the derivative of the voltage is zero. If a short
pulse is added at the peak the amplitude is increased without
significantly affecting the phase. But if the pulse is added at the
middle "zero crossing" of the sinewave (with resepect to the peak-to-
peak swing) where the derivative is large, the phase can be affected by
the feedback. Ideally you want to add just enough energy each cycle to
overcome the energy lost in the crystal due to limited Q.

If the feedback loop is linear, then the noise generated by the active
and passive devices is continuously fed back to the crystal, generating
amplitude noise. Due to the angle of the feedback (described above) and
AM to PM conversion due to device characteristics (junction capacitance
changes with voltage), some of the amplitude noise gets converted to
phase noise. The total resulting noise sidebands (made up of both
ampitude and phase noise) is what everyone wants to minimize.

You could also use a feedback loop which was very nonlinear by using an
active switch with a low ON resistance (so hopefully a low noise figure
when closed) to send spikes back to the crystal resonator at the peak of
the voltage waveform. If you could arrange the circuit so that the duty
cycle of this switch was low, the residual noise would only be amplified
and fed back to the crystal resonator over a small portion of each
cycle, reducing the average noise figure of the oscillator. If the
feedback circuit is highly nonlinear the amplitude noise might be
clipped and reduced. Of course, the jitter in the feedback circuit is
important.

The active devices need to be well bypassed at audio frequencies so that
low frequency shot noise isn't amplified with high efficiency. Since the
junction capacitance (and other AM to PM conversion sources) in
downstream amplifiers can be affected by audio frequency noise, I think
that it's very important that such noise isn't allowed to phase modulate
the desired RF signal.

--
Bill Byrom N5BB

On Mon, Jul 27, 2015, at 05:39 PM, Bob Camp wrote:
> Hi
>
>
>> On Jul 27, 2015, at 11:52 AM, jerry shirᴀr <radio.n9xr at gmail.com> wrote:
>>
>> Here's the rub Bob. I have been trying to find a way or have you explain
>> how a high harmonic oscillator stage
>
> You are confusing the current through the crystal with the current in the
> oscillator transistor.
> So:
>
> Connect a 2N918 with the collector to +12V through a 50 ohm resistor. AC
> couple that resistor to your spectrum analyzer.
> Connect the base of the transistor with a 10K to +12 and a 10K to ground
> Connect a 1K ohm resistor from the emitter of the transistor to ground
> Hook a 100 pf cap from base to emitter
> Hook a 100 pf cap from emitter to base
> Hook a 10.0 MHz fundamental crystal with a resistance of < 10 ohms  to
> the base of the transistor.
> Hook a 32 pf cap from the other side of the crystal to ground
>
> I **hope** that’s specific enough for you.
>
> That circuit **will** oscillate.
>
> Look at the current on the 50 ohm resistor. It’s got plenty of harmonics.
>
> With me so far or is this still to theoretical?
>
> Now, this **does** get a bit exciting, but it’s the way this circuit has
> been analyzed since the 1930’s (when it used a tube):
>
> You shift the ground to the emitter for the purposes of seeing what’s
> going on. You now have an “input side” and an “output side” to
> the active stage. This lets you break the loop for analysis.
>
> In this format, the current in the collector is more clearly flowing
> through the 1K resistor and one of the 100 pf caps.
> The current that passes through the crystal flows through the other 100
> pf cap (and the base) to ground.
>
> The current in the oscillator stage is every bit as nonlinear as you saw
> before.
>
> Since this is an oscillator, the current flows in a loop. There is no
> independent current in any one leg. They all are related.
> If you want to see this, hook up an oscilloscope to the collector
> resistor and apply power to the oscillator. The output does not
> go instantly to a full output. It slowly builds up to the full value. The
> current circulates around the loop **many** times as the
> stage oscillates.
>
> Now:
>
> Break the circuit (AC) at any of the connection points. It stops
> oscillating. (A DC break also does the same thing, but that’s cheating).
> Without everything hooked in a loop, you do not have oscillation.
>
> Next:
>
> Charles posted a long list of interesting transistors a few messages
> back. Try them one at a time and look at phase noise at 20 KHz offset.
> You will find that some are better than others. Take a look at the
> harmonics in the collector. They don’t correlate with the phase noise…
>
> So, unless you are looking at the crystal as being the oscillator (which
> it is not), there’s not much way to say that there are no harmonics
> running around in this circuit.
>
> Is that simple enough?
>
>> is even possible and zip. You don't
>> know and I certainly don't know. So there's that.
>
> **IF** your desire is for an explanation, offensive comments probably are
> not a good idea….
>
> Bob
>
>>
>> Jerry
>> On Jul 27, 2015 9:33 AM, "Bob Camp" <kb8tq at n1k.org> wrote:
>>
>>> Hi
>>>
>>> Here’s the basic point:
>>>
>>> What is **required** for low phase noise?
>>>
>>> If you can build **one** oscillator that violates a “law” then that “law” is
>>> not
>>> valid. In tis case the question is “do you **need** low harmonics in the
>>> oscillator
>>> stage to get low phase noise?”
>>>
>>> Here on the list, we get obsessed about all sorts of stuff. That’s fine.
>>> It’s fun.
>>> We learn things taking stuff past “the limit”. The gotcha is that can make
>>> it
>>> hard to keep track of “what is necessary ”.
>>>
>>>> On Jul 27, 2015, at 12:47 AM, jerry shirᴀr <radio.n9xr at gmail.com> wrote:
>>>>
>>>> Thanks Tim.  I love reading these papers.  However my copy states "In
>>> fact,
>>>> were it not for this slight non-linearity, it would be virtually
>>>> impossible to build a simple lamp-stabilized RC oscillator with good
>>>> envelope stability over a wide frequency range." rather than "In fact,
>>> were
>>>> it not for [amplifier] nonlinearity, it would be impossible to build a
>>>> simple oscillator with good envelope stability."  The meaning changes a
>>>> little bit.
>>>>
>>>> Thanks Bob,
>>>>
>>>> Even looking at Tim's article, they are talking about a low degree of
>>>> distortion with an RC oscillator.  I am assuming that the Q of the RC
>>> would
>>>> be quite low with respect to the overtone crystals you speak, and yet the
>>>> RC oscillator described here has low distortion from the oscillator
>>> stage.
>>>
>>> The objective of an RC lab oscillator design **is** low harmonic distortion.
>>> They
>>> have awful phase noise.
>>>
>>>>
>>>> Putting a filter in the feedback path with the high Q crystal seems like
>>>> you would be de-Q-ing the crystal and losing the high Q characteristics
>>> of
>>>> the crystal.
>>>
>>> The oscillator must be a closed loop to operate. There will **always** be
>>> things
>>> “in series” with the crystal.
>>>
>>>> Any changes of filter components over time seems like it
>>>> would necessarily add drift to the oscillator.
>>>
>>> Since you **must** tune the oscillator on frequency and you **must** select
>>> the overtone, you will have caps and inductors in the loop.
>>>
>>>> What do you think?  Of
>>>> course I am not saying that you can't put filters in the crystal circuit
>>>> but rather that is something I would never recommend doing that in a
>>>> precision oscillator design.
>>>
>>> Except you have to do it. Since you have to do it, every example out there
>>> of a low phase noise oscillator has at least some caps in series with the
>>> crystal. The vast majority have both coils and caps.
>>>
>>>>
>>>> I realize what the impedance plot looks like of AT-cut and SC-cut
>>> crystals
>>>> but my question was specifically about harmonics.  That is the topic of
>>>> this thread.  Are you thinking that crystals are rich in harmonics?  I am
>>>> not really seeing an idea of where you are saying the harmonic components
>>>> come from in these high precision oscillators in the oscillator circuit.
>>>
>>> The limiting action in the oscillator device creates harmonics.
>>>
>>>>
>>>> What are the "impedance properties" of the crystal?
>>>
>>> There are literally thousands of papers on this. The simple answer is that
>>> they have **many** resonant modes.
>>>
>>>> Why use a crystal
>>>> rather than slapping a cap and a coil in there to get your desired
>>>> frequency?
>>>
>>> 1) Because it’s Q is higher
>>> 2) Because it’s more stable
>>>
>>>>
>>>> When you "pick off" the collector current, wouldn't that include the
>>>> amplified base to emitter junction noise inherent in simple transistor
>>>> oscillator circuits?
>>>
>>> Again, it’s a loop. The current goes around in circles. There is no magic
>>> “clean here” current. If you are looking at an OCXO that doubles the
>>> crystal
>>> before the output is created, it’s a really good bet they pulled the signal
>>> off the collector of the oscillator. The net result is still a low phase
>>> noise
>>> oscillator.
>>>
>>>> Would that be the same as the crystal current?
>>>
>>> You can’t have an oscillator with just a crystal. You also need other
>>> “stuff”….
>>>
>>> Bob
>>>
>>>>
>>>> Thanks.
>>>>
>>>> Jerry
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