# negative feedback and oscillations?

#### Mathematics!

Joined Jul 21, 2008
1,022
Ok , their are 2 ways to create an ossilator using either negative/positive feedback or with an op-amp and the gain of 1 condition , phase condition forgot what it was called etc ....

Leaving off the op-amp way

Their are main ways to make ossilators based on negative/positive feedback..
i.e
Clapp oscillator
Colpitts oscillator
Costas loop
Hartley oscillator

to name a few ( all of then use the same method except use either more inductors then capacitors in parrell or series ...etc)
But what I want to know is
http://en.wikipedia.org/wiki/File:Cb_colp.svg
http://en.wikipedia.org/wiki/Clapp_oscillator
...etc

In these ossilator circuits basically the name of the game is to cancel out the resistance that dampers out the LC resonanting circuit...

I am wonder how adding just a transistor like in the case of
http://en.wikipedia.org/wiki/Clapp_oscillator
to a LC circuit makes it so the transistor supplies the exact negative or positive feedback to keep it's LC tank resonanting....?

Because as I look at these ossilator circuit they are just LC tank circuits with a transistor the only difference is some of them use more inductors or capacitor then others but this can all be reduced down to 1 L and 1C using series/parrellal circuit analysis. Still doesn't quite make since how the transistor feedsback the exact amount.... kind of like magic

Just wondering how the transistor gives the exact feedback need to keep it ossilating forever...

I guess I don't see how the transistor is going to close/open at the correct time to give the correct negative or postive feedback

Is the reason why the transistor is put their leg between 2 cap's for basing or something ....
If this is the case then at least one of the caps would have to be a specific fix value for basing but the other one could vary to be used to give different carrier frequencies or ossilations.

Also in this clapps ossilator must it be a specific type of transistor or could you use NPN or PNP ?

Thanks for any clarity
enough said I am repeating myself but by now you get the question

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#### steveb

Joined Jul 3, 2008
2,431
...
Just wondering how the transistor gives the exact feedback need to keep it ossilating forever...

I guess I don't see how the transistor is going to close/open at the correct time to give the correct negative or postive feedback...

Also in this clapps ossilator must it be a specific type of transistor or could you use NPN or PNP ?

Thanks for any clarity
enough said I am repeating myself but by now you get the question
Without going into detail of any particular design, you need to have unity gain and a multiple of 360 degree phase shift to have oscillation. These conditions must be precisely met. The transistor provides gain that offsets any losses in the system, but it must do so to create unity round trip gain. The mystery of how the trasistor provides the exact condition is related to gain saturation, or nonlinearity. A perfectly linear circuit is very difficult to have oscillation because, like you said, it takes magic to perfectly create the exact oscillation condition. However, nonlinearity allow the gain to saturate so that there is a particular output amplitude that creates the proper gain match.

A similar issue occurs with frequency and phase. How do you get the exact frequency you want to have 360 degrees shift? Basically you can't, but you can design a circuit that gets close. The circuit will automatically select the frequency that has exactly 360 degree round trip phase shift.

Basically, the output amplitude and internal gain are related, and the output frequency and internal phase shift are related. Proper control of gain/nonlinearity and selection of frequency band (with filters) allows high quality controlled oscillations.

As an exercise, take any oscillator design and try to identify the mechanism by which gain saturation occurs.

By the way, in general, either NPN or PNP transistors can be used for oscillators.

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#### Mathematics!

Joined Jul 21, 2008
1,022
Ok , so I understand how to create a carrier of any frequency using any of these ossilator schematics but I still don't see how the transistor provides gain of unity and 360 degrees phase???

Won't this change if you change the L , C's values in the schematic?
Take for instance Clapp oscillator circuit if I use random L and C values for the components of this schematic to make a specific carrier frequency based on the formula given on that page....
How is the transistor given only a gain of 1 and 360 phase condition?
I can see since we used the same battery source for base and emitter/collector then the gain should be always one since you are not amplifying anything if you are using only one source voltage to began with. Correct me if I am wrong but an transistor that has the same supply voltage for the base and emitter/collector would have a gain of 1 because it is not amplifying anything....?

But I don't understand what this 360 phase condition is coming from.
And I still don't get why these 2 conditions imply that it will cancel out the resistance with the correct amount of feedback...IS THEIR A PROOF ON THIS SOMEWhere ?

On second though the gain 1 condition I think I got it wrong ....

You spoke of the transistor being a nonlinear device but a diode is also nonlinear but I don't think I can use just any nonlinear device to provide the feedback I need because I cann't see a diode being used to do it like a transistor does?
So why can some nonlinear device just work for the feedback "transistors "? It all boils down to the condition you mention so I am still wondering how the transistor works and the proof of this condition implying continous ossilation forever..?

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#### steveb

Joined Jul 3, 2008
2,431
Ok , so I understand how to create a carrier of any frequency using any of these ossilator schematics but I still don't see how the transistor provides gain of unity and 360 degrees phase???
Transistors are able provide current gain or voltage gain, either of which (depending on the design) can allow compensation of system losses and create a net gain of unity. Note that the entire system (not just the transistor) must be considered. The output signal gets fed back to the input with an effective gain and phase shift. The phase shift usually comes mostly from the external filtering components, although the transistor's limited bandwidth can add to the net phase shift at high frequency.

A gain and phase analysis requires a small signal AC understanding of the circuit. However, the saturation effects require a nonlinear AC analysis. You really need to dive into the mathematics to fully understand the answers to your questions.

Won't this change if you change the L , C's values in the schematic?
....Correct me if I am wrong but an transistor that has the same supply voltage for the base and emitter/collector would have a gain of 1 because it is not amplifying anything....?..?
The component values do change everything. These components form a filter which selects the frequencies that will achieve the unity gain and 360 degree phase shift. The transistor is amplifying something. It amplifies noise and only the noise that is at the right frequency gets amplified and builds up until if forms a signal that saturates the transistor circuit gain.

You spoke of the transistor being a nonlinear device but a diode is also nonlinear but I don't think I can use just any nonlinear device to provide the feedback I need because I cann't see a diode being used to do it like a transistor does?
So why can some nonlinear device just work for the feedback "transistors "? It all boils down to the condition you mention so I am still wondering how the transistor works and the proof of this condition implying continous ossilation forever..?
A diode will not amplify a signal, but a transistor can amplify a signal with the correct circuit.

Before you can understand the oscillator, you need to understand the transistor amplfier by itself. Once you understand a small signal amplfier and note the effects of distortion and gain saturation as the AC signal becomes large, then you can begin to understand the oscillator circuits.