How 3-capacitor sine generator works really?

[RodionGork]

Hi Friends!

Schematic / simulation in "Falstad online simulator":
https://tinyurl.com/23hcg8np

This is probably very old and widely known schematic of single-transistor
generator which
requires no inductance, but instead uses three capacitors - actually it
seems a chain
of high-pass single-stage filters with transistor serving as feedback from
output to input.

One can find it, for example, in classic stylophone schematic (the part
creating low-frequency
oscillations for "vibratto" effect).

I teach it to my pupils for years probably and I always thought I less or
more understood what
is happening inside - each filter stage gives shift in phase and hence when
amplifying feedback
is added there happen harmonic oscillations.

However on the schematic given above I added 4 scopes over the length of
the filter (potentials
at the points A, B, C, D according to labels - here A and B are potentials
at points between capacitors, C is at the base and D at collector) - I
suddenly found that intermediate voltages are
not pretty harmonic! They could be distorted by the current drawn into
transistor base though. And
I'm not sure the output is exactly sine now. Though probably it is a matter
of adding some resistor to improve input impedance of transistor cascade?

Regretfully I can't find any thorough explanation of the schematic
(probably due to keywords being too general and I don't know if this design
has fancy proper name). So I would be grateful either
for links or for verbal clarifications.

[Bill Sloman]

Post by RodionGork
Hi Friends!
https://tinyurl.com/23hcg8np
This is probably very old and widely known schematic of single-transistor
generator which requires no inductance, but instead uses three capacitors - actually it seems to be a chain
of high-pass single-stage filters with transistor serving as feedback from output to input.
One can find it, for example, in classic stylophone schematic (the part creating low-frequency
oscillations for "vibratto" effect).
I teach it to my pupils for years probably and I always thought I less or
more understood what is happening inside - each filter stage gives shift in phase and hence when
amplifying feedback is added you get harmonic oscillations.
However on the schematic given above I added 4 scopes over the length of
the filter (potentials
at the points A, B, C, D according to labels - here A and B are potentials
at points between capacitors, C is at the base and D at collector) - I
suddenly found that intermediate voltages are
not pretty harmonic! They could be distorted by the current drawn into
transistor base though. And
I'm not sure the output is exactly sine now. Though probably it is a matter
of adding some resistor  to improve input impedance of transistor cascade?
Regretfully I can't find any thorough explanation of the schematic
(probably due to keywords being too general and I don't know if this design
has fancy proper name). So I would be grateful either
for links or for verbal clarifications.

It's a phase shift oscillator - one of many.

https://en.wikipedia.org/wiki/Phase-shift_oscillator

The amplitude is limited by clipping in the single transistor amplifier.
If you model it with LTSpice, you can get the program to produce a
Fourier transform of the output waveform and it is going to have all the
harmonics out to the cut-off frequency of the transistor.

You can do better, but it takes more components.

Here's a solution I came up with back in 1986, developed as a retrofit
to excite a linear variable differential transformer used to measure the
progressively increasing mass of a single crystal of gallium arsenide
(GaAs) being grown in the Metals Research GaAs Liquid-Encapsulated
Czochralski (LEC) crystal puller. The circuit it replaced had been
developed a decade earlier and used components that had become obsolete
in 1986. The new circuit replaced it in new machines and was retrofitted
to some older machines.

Only about 50% of the power fed into the oscillator ends up in the load,
rather than the better than 90% transfer you can get with a classic
Class-D oscillator – but it’s quite a lot more efficient than any of the
low distortion oscillators I know about, and it lends itself to very
precise control of the output amplitude. I’ve generated quite a few
Spice models of various implementations of the idea, but I’ve yet to get
around to building a current version of the real circuit – the 1986
version worked fine, but at that time I wasn’t aware how good the
circuit could be and didn’t have any reason to check out its performance
in detail.

Here's a proof-of-principle simulation - which doesn't have anything in
common with the 1986 circuit.

http://sophia-electronica.com/BillsBaxandall.html

[RodionGork]

Post by Bill Sloman
It's a phase shift oscillator - one of many.

Thanks a lot, so the "keywords" were on the surface, I just missed. It
could be googled by
phase shift or even by RC-oscillator. Great!

Post by Bill Sloman
Here's a solution I came up with back in 1986

Wow, thanks for curious story. I haven't yet went to school then :) Golden
age of electronics!

Post by Bill Sloman
For oscillation you need to put the output back in phase to the input.

The tansistor gives 180 degrees phese shift

Thanks, I see I was mistaken thinking that each stage "shifts" phase by 90
degrees (obviously I forgotten university lectures) and that confused me.

Post by Bill Sloman
and as gain is >1 it wil oscillate

supposedly, it is about overall gain - transistor gain multiplied by (less
than 1) gains of filter stages - it seems they "eat" quite a lot of an
amplitude.

Post by Bill Sloman
The 100K base resistor was probably selected to match the

beta of the transistor

please note here is some cheat - resistor is connected not to the positive
supply but to the collector - it reduces the pull-up effect, but allows for
wider range of resistance (effectively removing necessity of adding proper
pull-down resistor at the base and small another one at emitter).

Post by Bill Sloman
The lesson for your students is more general

Thanks, it is a good lesson for myself - as for the students, they are a
bit too beginners to
get into such depth of idea, but I'll try to communicate your explanations
:)

Post by Bill Sloman
Another phase-shift osc form uses three RC integrators

That's curious, I'll look for this variant.

[Jan Panteltje]

On a sunny day (Fri, 3 May 2024 06:14:54 +0000) it happened RodionGork

Post by RodionGork
Hi Friends!
https://tinyurl.com/23hcg8np
This is probably very old and widely known schematic of single-transistor
generator which
requires no inductance, but instead uses three capacitors - actually it
seems a chain
of high-pass single-stage filters with transistor serving as feedback from
output to input.
One can find it, for example, in classic stylophone schematic (the part
creating low-frequency
oscillations for "vibratto" effect).
I teach it to my pupils for years probably and I always thought I less or
more understood what
is happening inside - each filter stage gives shift in phase and hence when
amplifying feedback
is added there happen harmonic oscillations.
However on the schematic given above I added 4 scopes over the length of
the filter (potentials
at the points A, B, C, D according to labels - here A and B are potentials
at points between capacitors, C is at the base and D at collector) - I
suddenly found that intermediate voltages are
not pretty harmonic! They could be distorted by the current drawn into
transistor base though. And
I'm not sure the output is exactly sine now. Though probably it is a matter
of adding some resistor to improve input impedance of transistor cascade?
Regretfully I can't find any thorough explanation of the schematic
(probably due to keywords being too general and I don't know if this design
has fancy proper name). So I would be grateful either
for links or for verbal clarifications.

For oscillation you need to put the output back in phase to the input.
The tansistor gives 180 degrees phese shift
(when base goes up the collector goes down)
the RC networks that follow give together an other 180 degrees at some specific frequency.
so at the base now the feedback is in phase
and as gain is >1 it wil oscillate at that frequency set by the R and C values.

[John Larkin]

Post by RodionGork
Hi Friends!
https://tinyurl.com/23hcg8np
This is probably very old and widely known schematic of single-transistor
generator which
requires no inductance, but instead uses three capacitors - actually it
seems a chain
of high-pass single-stage filters with transistor serving as feedback from
output to input.
One can find it, for example, in classic stylophone schematic (the part
creating low-frequency
oscillations for "vibratto" effect).
I teach it to my pupils for years probably and I always thought I less or
more understood what
is happening inside - each filter stage gives shift in phase and hence when
amplifying feedback
is added there happen harmonic oscillations.
However on the schematic given above I added 4 scopes over the length of
the filter (potentials
at the points A, B, C, D according to labels - here A and B are potentials
at points between capacitors, C is at the base and D at collector) - I
suddenly found that intermediate voltages are
not pretty harmonic! They could be distorted by the current drawn into
transistor base though. And
I'm not sure the output is exactly sine now. Though probably it is a matter
of adding some resistor to improve input impedance of transistor cascade?
Regretfully I can't find any thorough explanation of the schematic
(probably due to keywords being too general and I don't know if this design
has fancy proper name). So I would be grateful either
for links or for verbal clarifications.

That sim makes a suspiciously nice sine wave, for a phase-shift
oscillator. The 100K base resistor was probably selected to match the
beta of the transistor, and if so it wouldn't be as good in
production, where betas vary.

If that resistor is too big or too small, it won't oscillate. Try
varying it.

There is some AGC effect from base rectification biasing the transisor
off, which increases beta tolerance.

The lesson for your students is more general: the amplitide of a
linear oscillator increases exponentially until something nonlinear
kicks in to reduce the overall gain to unity. The nonlinearity makes
distortion.

Your phase shifter is three differentiators, so magnifies harmonics.
Another phase-shift osc form uses three RC integrators, so can
attenuate harmonics and make a better sine.

Another lesson for students is that a hand-selected set of values may
not be a reproducible, sellable circuit.

[a***@spenarnc.xs4all.nl]

Post by John Larkin

Post by RodionGork
Hi Friends!
https://tinyurl.com/23hcg8np
This is probably very old and widely known schematic of single-transistor
generator which
requires no inductance, but instead uses three capacitors - actually it
seems a chain
of high-pass single-stage filters with transistor serving as feedback from
output to input.
One can find it, for example, in classic stylophone schematic (the part
creating low-frequency
oscillations for "vibratto" effect).
I teach it to my pupils for years probably and I always thought I less or
more understood what
is happening inside - each filter stage gives shift in phase and hence when
amplifying feedback
is added there happen harmonic oscillations.
However on the schematic given above I added 4 scopes over the length of
the filter (potentials
at the points A, B, C, D according to labels - here A and B are potentials
at points between capacitors, C is at the base and D at collector) - I
suddenly found that intermediate voltages are
not pretty harmonic! They could be distorted by the current drawn into
transistor base though. And
I'm not sure the output is exactly sine now. Though probably it is a matter
of adding some resistor to improve input impedance of transistor cascade?
Regretfully I can't find any thorough explanation of the schematic
(probably due to keywords being too general and I don't know if this design
has fancy proper name). So I would be grateful either
for links or for verbal clarifications.

That sim makes a suspiciously nice sine wave, for a phase-shift
oscillator. The 100K base resistor was probably selected to match the
beta of the transistor, and if so it wouldn't be as good in
production, where betas vary.
If that resistor is too big or too small, it won't oscillate. Try
varying it.
There is some AGC effect from base rectification biasing the transisor
off, which increases beta tolerance.
The lesson for your students is more general: the amplitide of a
linear oscillator increases exponentially until something nonlinear
kicks in to reduce the overall gain to unity. The nonlinearity makes
distortion.
Your phase shifter is three differentiators, so magnifies harmonics.
Another phase-shift osc form uses three RC integrators, so can
attenuate harmonics and make a better sine.
Another lesson for students is that a hand-selected set of values may
not be a reproducible, sellable circuit.

On the other hand restricting amplification with a ptc resistor,
or a 50 ma 6 V incandescent light bulb could result in a decent
(less that 1% distortion) sine wave.

Groetjes Albert