Oscillation: Design in terms of voltage or power?

[lamchidinh]

When we design an oscillator, sometimes we design in terms of voltage, then we have to satisfy the Barkhausen criterion: gain * feedback = 1. In this condition, feedback is mandatory.

But we also use the reflection coefficient to design an oscillator, in which case we have to satisfy the following:
Γin * Γs = 1. And usually in this condition, we don't have to worry about feedback at all, sometimes there is no feedback.

I am confused in which cases I should follow which conditions.

Can anybody help? :-|

 

[flashking]

I think the first one is the low frequency design equation where the circuit length is much smaller that the working wavelength

but when you move to high frequency (microwave) the transistors come with tables of S parameters vs. freq, where you can use this data to drive the transistor to unstability without using feedback.

 

[biff44]

"Γin * Γs = 1"

Where did you get that equation? And what do Γin and Γs mean, and why use the = sign?

If you had said something like Γactive device * Γresonator >> 1, then it would make some sense.

Also you have to realize that the equations of oscillation are different if you are using a one port or two port active device.

 

[flashking]

Γin is the reflection coofficient for the active device (eg. transistor) while Γs is the reflection coofficient for the tuning network ( the input side)

and Γin * Γs = 1 must hold to maintane oscillation

to prove it we assume a one port oscillator that has its own impedance Z connected to a tuning network with impedance Zt, we must have Z = -Zt for oscillation
then Γs = (Zt - Zo) / (Zt + Zo) = (-Z - Zo) / (-Z + Zo) = (Z + Zo ) / (Z - Zo) = 1/Γin, then Γin * Γs = 1

 

[lamchidinh]

Thank you for your comments!

I more agree with flashking.

However, we can also use the same formula to calculate reflection coefficients using impedances, instead of transmission lines. That means at low frequencies, we also have to consider reflection coefficients as well. Now if we want to design an oscillator, which equation should we use? Barkhausen or gamma?

Furthermore, when we build an oscillator in an IC environment at high frequencies, of course, reflection coefficients should be taken into consideration. However, in an IC, everything is so tiny that we can work in terms of voltage. I have seen some books that use the first equation to design, other books use the second one. Now, just why...?

 

[lamchidinh]

Repost so that people notice and help:

When we design an oscillator, sometimes we design in terms of voltage, then we have to satisfy the Barkhausen criterion: gain * feedback = 1. In this condition, feedback is mandatory.

But we also use the reflection coefficient to design an oscillator, in which case we have to satisfy the following:
Γin * Γs = 1. And usually in this condition, we don't have to worry about feedback at all, sometimes there is no feedback.

I am confused in which cases I should follow which conditions.

Can anybody help?

 

[pancho_hideboo]

When we design an oscillator, sometimes we design in terms of voltage,
then we have to satisfy the Barkhausen criterion: gain * feedback = 1.
In this condition, feedback is mandatory.

But we also use the reflection coefficient to design an oscillator,
in which case we have to satisfy the following:
Γin * Γs = 1.

Basically these are same mathematically.
Their differences are from different formulation for oscillation.

If we see oscillator as circuit having clear feedback, it is easy to adopt former formulation.
If we see oscillator as negative impedance generator, it is easy to adopt latter formulation.

However even for negative impedance generator, feedback is required to generate negative impedance component.
Vice Versa, we can treat clear feedback circuit as negative impedance generator.

And usually in this condition, we don't have to worry about feedback at all,
sometimes there is no feedback.

Wrong.
Simply it is difficult to identify clear feedback in oscillator based on negative impedance generator.

I am confused in which cases I should follow which conditions.

Again they are same mathematically.
The Designer's Guide Community Forum - Negative Impedance seeing Vdd node of Inverters
The Designer's Guide Community Forum - SP simulation and negative real Y
The Designer's Guide Community Forum - Bode Diagram of Conditionally Stable System

 

[lamchidinh]

@pancho: Simply great! Thanks!

Let me research more about it and will get back for more discussion!