[1]
You kept talking about decreasing the peaked part of the response.

In some of my examples I have shown that - depending on component selection - the peaking could be reduced without touching the capabilty of the circuit to oscillate. Can you really not imagine why I have mentioned this?
Because it was YOU who has stated that such a peaking is typical for this kind of oscillator.
Quote (your post#22): "Here are some facts:
1. When i do a hand analysis i get a bandpass with fairly sharp response.
2. When i do a simulation i get a bandpass with fairly sharp response."
Don`t you remember?
Both of your "facts" are totally wrong!

[2]
This 'surprising value' has been cleared up but you didnt seem to read that.

Where has it "cleared up". I have asked you for a verification of the 10 Ohm resistor. Are you kidding me?
Where is your answer? If it is "cleared up" - can you tell me where (in which of your answers)?

[3]
The three types of electrical resonance.
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I'll have to try to find this paper again or else you can look for it on the web.

Ah I see.....(nothing else to say).

[4]
The relationship to a bandpass function that i see is because of the peaked amplitude response.
The phase shift is better understood by the low pass function as you pointed out.

...."better understood" ? IT IS A LOWPASS ! What is the real meaning of these two sentences?

[5]
:::::::::::::::::::::::::::::
But in this regard you have not yet answered my question about resonance and the formula for the
oscillation frequency of this oscillator (in the first post in this thread). The formula for this
is the same as a formula for resonance. Why do you think that is so. Is it just a conincidence.

The answer is simple. We only have to remember some parts of the system theory.
When we have to analyze a certain network there are always some different methods.
Some are more involved and some others are somewhat simpler.
In our case we are speaking about the denominator of the transfer function - and in particular about the pole frequency.
As we know, an RLC combination can be used as a (a) highpass or (b) lowpass or (c) bandpass.
The response does depend only on the selected nodes for input and output.
And it is important to note that the denominator of the transfer function in all 3 cases is the same - in particular the pole frequency wp=SQRT(1/LC).
In case of a bandpass this pole frequency is identical to the resonant frequency (zero phase at wp=wo) and in case of lowpass or highpass the phase shift at this pole frequency is 90 deg. This illustrates the relationship between the three transfer functions which can be allocated to the same network.

To answer in detail your question about the oscillation frequency (see first line,item [5] above):
In your post#19 you wrote:
„the frequency appears to be: f=1/(2*pi*sqrt(L*C)) where C is the series combination of the two caps across the inductor.“

However, it must be noted that this applies only when the circuit is not loaded.
In fact, the circuit is connected to the base of the transistor (some kOhms).
Here is the correct calculation:
From the lowpass function (setting the imaginary part equal to zero) we can get the frequency for 180 deg phase shift:
wo=SQRT[1/L*C + L/ro*r1*C]
with ro=output res. atthe collector; r1=input res. at the base and C=C1C2/(C1+C2).

 

The reality is that there are many circuits that will oscillate, including quite a few that are not intended to oscillate. And there have been posted several that are challenging to explain how they oscillate, when the feedback scheme is both poorly defined and very poorly executed. The "slayer" oscillator is one such assemblage of parts that for some folks will oscillate, but not for others.
And the more common description of an LC oscillator without much of a peak is usually "An unstable oscillator".

 

The reality is that there are many circuits that will oscillate, including quite a few that are not intended to oscillate. And there have been posted several that are challenging to explain how they oscillate, when the feedback scheme is both poorly defined and very poorly executed. The "slayer" oscillator is one such assemblage of parts that for some folks will oscillate, but not for others.
And the more common description of an LC oscillator without much of a peak is usually "An unstable oscillator".

Yes, I agree to you - with one exception: Could you please explain what you mean with "unstable oscillator"?
In system theory the term "dynamic stability" (in case of sysytems with feedback) is clearly defined (Nyquist theorem).
And, as far as I know, there are two types of instability : (a) without or (b) with continuous (self-sustained) oscillation.
Case (a) leads to saturation of the system.

By the way - I think that the "slayer" type does not belong to the class of feedback systems we are discussing in this thread.

 

Hello again,

I am going to have to defer a more complete reply for now this is getting too time consuming for such a simple circuit.

The simple explanation is that we need to see a pole on the jw axis and the only way to get that is with at least a 2nd order response that has imaginary solutions.
Since the transfer function can be shown to be in the form:
K/((s+a)*(s^2+b*s+c))

we can see that 2nd order response part in the s^2+b*s+c part of the denominator. This part must have imaginary solutions and this is the part that produces the peaked response part. That would be an underdamped response. The solution for the oscillation frequency is reminiscent of a resonant response, and that's the reason for bringing the concept of resonance into the discussion, although resonance like that is a typical way that the oscillation is explained in various texts.
There is also the negative resistance feedback explanation for the oscillation, but i think that's a side issue because it does not really bring in voltage and/or current responses which i think many of us are looking for at least part of the explanation. That does seem to be a requirement for oscillation quoted in literature, although i have not looked into that myself.

As a side note, resonance comes in various forms. To say that inductive reactance equals capacitive reactance is just ONE way of describing that and that is referred to as "physical resonance". In short, it is possible to call any peaked response resonance even though it is not physical resonance, but the more exact definition is a response that causes an extreme change for an input that is nothing more than a typical forcing function. That means that when we apply a drive signal to a filter type circuit that is not extreme yet we get some extreme response to that regular signal that could be called resonance. That would be typical in a tuned circuit that does not exhibit physical resonance yet has a peaked or dipped response. An example may be a twin tee notch filter. I dont think we see any physical resonance there but we see a very very extreme response to a very very regular input signal. In fact, in theory the output dip could be zero which is very extreme compared to the response at other frequencies. If we had to form a ratio of input to output we would see that the input is non zero but the output is zero so the ratio would approach infinity (k/0). That's probably one of the most extreme responses to a drive signal, yet this could be called resonance even though it is not physical resonance.
What may be even more interesting when we investigate resonance is if we use that circuit as the feedback in an op amp circuit, we get an extreme response at the output of the op amp which strongly resembles a band pass function. Is it really a band pass function? Probably not a band pass proper, but it for sure is something special which has a response that is very similar to a band pass function because it passes one frequency with much more amplitude than other frequencies which a band pass proper is known for.

In conclusion, i find all these things interesting and very useful and if you dont that's your choice and that's ok with me.

 

An "Unstable Oscillator" is an oscillating circuit that allows the frequency to vary more than is acceptable, from external changes that are not part of the design, nor intended to be part of the resonance frequency control portion of the system. Those changing variables could include supply voltage, active device gain, element resistance change, small temperature changes, external capacitance variations, and component position relative to other component positions. Such an oscillator may also change frequency when there is no obvious change in any element of the system.

 

Hello again,
..........................
There is also the negative resistance feedback explanation for the oscillation, but i think that's a side issue because it does not really bring in voltage and/or current responses which i think many of us are looking for at least part of the explanation. That does seem to be a requirement for oscillation quoted in literature, although i have not looked into that myself.
........................
In conclusion, i find all these things interesting and very useful and if you dont that's your choice and that's ok with me.

I have to admit that I don't know how to react to this post - it largely contains long known basics.
One sentence on the subject of "negative resistance". It is possible to explain every oscillator working according to the feedback principle also according to the "negative resistance principle". In this case, a negative and a positive resistor compensate each other at the interface between feedback and amplifier input.

Finally, I believe that a continuation of this discussion cannot bring any new insights.
Regards
LvW

 

An "Unstable Oscillator" is an oscillating circuit that allows the frequency to vary more than is acceptable, from external changes that are not part of the design, nor intended to be part of the resonance frequency control portion of the system. Those changing variables could include supply voltage, active device gain, element resistance change, small temperature changes, external capacitance variations, and component position relative to other component positions. Such an oscillator may also change frequency when there is no obvious change in any element of the system.

OK - now I know what you mean. Thank you. Of course, I agree.

 

An "Unstable Oscillator" is an oscillating circuit that allows the frequency to vary more than is acceptable, from external changes that are not part of the design, nor intended to be part of the resonance frequency control portion of the system. Those changing variables could include supply voltage, active device gain, element resistance change, small temperature changes, external capacitance variations, and component position relative to other component positions. Such an oscillator may also change frequency when there is no obvious change in any element of the system.

Yes that's a good explanation.
To that end i submit that a phase shift oscillator is NOT a Colpitts oscillator, even though that also requires a phase shift. In addition to some kind of phase shift we also need amplitude control, and that happens also in a Colpitts oscillator.
If i can find the time i'll write up some math on this point. The first would be an actual phase shift oscillator that has very well know characteristics. For one, the feedback network is a passive phase shift network with plenty of losses that needs amplification to keep oscillating alive an not veering off to one rail or another. In feedback jargon, this would mean the pole can not veer off to the left of the jw axis or the oscillation damps out, and it can not veer off to the right of the jw axis or the oscillation amplitude increases without limit ... either of which does not come out to be an actual stable oscillator.

The phase shift math is so simple maybe i'll proceed with that, then just modify it into the Colpitts and then we will see the difference. It will be impossible to misinterpret that.

The work on resonance was done by a guy i think his name was Antonov. He went on to explain resonance in it's fullest possible forms. His papers discuss this much more than i can here. His basic premise is that a response can be called resonant if a small change in input causes an large change in output, and this is most likely a statement about frequency. if you change the frequency by 1 percent and nothing much changes on the output, then you change it by another 1 percent and nothing happens, then change it a third time by 1 percent and the output amplitude changes greatly, then that could be called resonance also, especially if later as you keep changing the input frequency the output goes back to being fairly typical without much changing, although there is also the possibility, of course, that you may encounter another point where resonance occurs. A crystal is an interesting example i think.

 

To that end i submit that a phase shift oscillator is NOT a Colpitts oscillator, even though that also requires a phase shift. In addition to some kind of phase shift we also need amplitude control, and that happens also in a Colpitts oscillator.
If i can find the time i'll write up some math on this point.
::::::::::::::::::::::::::::::::::::::::::
The phase shift math is so simple maybe i'll proceed with that, then just modify it into the Colpitts and then we will see the difference.

I think, the math for these two oscillator types can be found in each relevant textbook, in many, many internet contributions - and it was discussed already intensively also in this forum.

 

(Slightly off topic) It would be really interesting to see an attempt at creating the formulas for the "Slayer" oscillator circuit, or even a description of how it functions..

 

(Slightly off topic) It would be really interesting to see an attempt at creating the formulas for the "Slayer" oscillator circuit, or even a description of how it functions..

I can give you details on several versions for lowpass-/highpass-/bandpass-/band-reject and allpass oscillators, as well as on GIC- and integrator-based quadratur oscillators - but not on the "slayer" oscillator.
I suppose it does not belong to the class of "amplifier with feedback"-oscillators. Correct?

 

The slayer oscillator has feedback through the capacitance between a large area conductor at the top of the secondary and ground. The frequency is presumably due to the tank circuit formed by the secondary and that stray capacitance.

 

The slayer oscillator has feedback through the capacitance between a large area conductor at the top of the secondary and ground. The frequency is presumably due to the tank circuit formed by the secondary and that stray capacitance.

You have a schematic or drawings of some kind?

 

Hello again,


Here is what the math reveals about the Colpitts and the RC High Pass Phase Shift proper oscillators.

The root locus of these two show how the roots approach the jw axis in different ways.
For the RC oscillator the approach is steep and it varies on either side of the jw axis. For a small change in gain the frequency seems to change more than we might like to see.
For the Colpitts the approach is more smooth and it varies in the same way on either side of the jw axis. Thus for a small change in gain the frequency stays relatively constant.

For the RC oscillator the feedback network form is:
K/((s+a)*(s+b)*(s+c))

which shows all real roots.

For the Colpitts it is:
K/((s+a)*(s^2+b*s+c))

where the second degree term has complex roots.

I think it is clear to see that if we try to get rid of the second degree term in the Colpitts we and up with real roots, which then defaults to a phase shift oscillator but also of interest is then the gain need to be increased by a factor of 29 in order to get any oscillation.

So the phase shift oscillator is quite a bit different than the Colpitts.

 

I think it is clear to see that if we try to get rid of the second degree term in the Colpitts we and up with real roots, which then defaults to a phase shift oscillator ..........
........................
So the phase shift oscillator is quite a bit different than the Colpitts.

I think, if we "try to get rid of the second degree term in the Colpitts" we end up with ONE SINGLE REAL ROOT.
The resulting circuitis not a phase shift oscillator - it cannot oscillate.

 

I think, if we "try to get rid of the second degree term in the Colpitts" we end up with ONE SINGLE REAL ROOT.
The resulting circuitis not a phase shift oscillator - it cannot oscillate.

Here's what i said exactly:
" I think it is clear to see that if we try to get rid of the second degree term in the Colpitts we and up with real roots "

Notice i said "roots" (plural) while you said "ROOT" (singular).
You can not "get rid of" the second degree term entirely and end up with 'roots' because then there would be only one root, which is not what i stated.
You can in fact "get rid of" the second degree term entirely and then end up with one 'root' but that's not what i said, that's what you said.

If you want to be critical, it's really the second degree 'factor' in the denominator not the second degree 'term'

That's not the main issue anyway though.

Here are the two root locus plots.