s11 reflection coefficient gamma

Do we have to connect resonator like ring or hair pin in negative resistance oscillator?
I have terminated the drain with 50ohm & adjusted gamma of load network >1.
Still i did not get oscillation.
I tried the same thing given in reflection oscillator tutorial on website
www.rfic.co.uk.

Can any one tell me the reason?
(My frequency of interest is 5.8/6.3GHz)

check the oscillator design procdures in Pozar book , and in gonzalez book
i think u need to adjust the negative resistance to be 2 to 3 time larger that Rl

khouly

Although many amplifier designers will attest that it is very easy to accidently design an oscillator, it is actually hard to deliberately design an oscillator!

You need a resonator to make an oscillator. Otherwise you would either have a reflection amplifier, or an oscillator that jumps around so much in frequency that it would be useless.

There are two basic criteria for oscillation to start up. 1)amplitude, and 2)phase.

1) You resonator has some loss. You can think of this in many ways, but lets keep it in terms of reflection coefficients. Lets say the resonator reflection coefficient, at the resonant frequency, has a reflection coefficient magnitude of 0.9.
That means for a wave amplitude of one traveling out towards the resonator, a reflected wave amplitude of 0.9 returns to the active device.

Lets now say that the active device reflection coefficient is 1.05. So lets look at a triple travel wave at oscillation start up. Some noise comes out of the active device and heads towards the resonator--lets say the amplitude of this initial noise is, arbitrarily, "1". It hits the resonator and reflects back, but now its amplitude is only 0.9 (you lost some power to heat up the resonator). This backwards traveling wave of 0.9 hits the active device, where it sees a reflection coefficient of 1.05. So the noise energy bounce back towards the resonator at 0.9 * 1.05 = 0.945.

This is too bad. Your 2nd reflection is smaller than the original noise amplitude, so the oscillations are not building up, but instead die out.

So you need a big enough reflection coefficient from the active device so that EVERY time something makes the round trip, the new wave amplitude is bigger than before.

In resistive terms, if the resonator had a loss equivalent resistance of Rres, then the negative resistance of the device had better be |Rdevice| > Rres.

2) But this is not enough. Since wave amplitudes behave like voltages, and voltages linearly add, one can see that the phase angle of the resonator and the active devices reflection coefficients have to be such that the round trip reflections add up to n*2*Π degrees. That is to say, you want any returning signal from the resonator to be in phase with the new signal bouncing off of the active device. In this way the earlier signal will vectorially combine with the present new bounce constructively, and the oscillation will grow.

In lumped element thinking, if the resonator has a reactance at resonance of X, then the reactance of the active device wants to be -X. This, in fact, is the main reason that an oscillator oscillates only at one frequency. At just one frequency do the two reactances cancel. At a slightly different frequency, there is not perfect reactance cancellation, and the round trip gain, after many thousands of bounces, is smaller that the true osillation frequency.

So, you need an active device reflection coefficient magnitude significantly greater than 1 to overcome resonator losses, and the round trip phase angles must be such to make the old and new signals combine constructively.

Thankk u biff44 & khouly for your suggestions.
I will design according to suggestions given by u.
Is there any criteria regarding setting the impedance of OsciTest probe in ADS?

You shuold use the harmonic balance to adjust until you get the oscilation . Ti takes long time for the beginner.
Experience :First you use the oscilator test in ADS. In order to easy get osicllation you try to adjust the S11 > 1 and phase ( S11) ~ 0 ( mean that the phase of S11 must cut( go through) the line 0 degree).
And then you try to connect oscillator port intead of oscillator test and use tuning tool.
In order to easily get oscillator you should matching the output .
You get S11 >1 ( gama in >1) . Then design output matching network like in the Gozalez book ( R in ~ -R load, X in ~ - X load). So the oscillator test ( S11) will have S11 >1 and phase S11 ~0.

Thanks BKD
I was really frustrated by doing calculations for gamma by calculator.
I was going by book method & it was taking lot of time.
books do not specify ,how to select gamma of terminating network from smith chart,
because almost all smith chart coordinates were available for gamma selection(because unstable region was inside the smith chart).
I will now try this HB method.

Added after 38 minutes:

should I use S parameter model or nonlinear model while simulation

u can begin ur design with S parameters of the active device , and then replace it with the nonlinear to check how ur frquqncy will shift due to nonlinearities in active device as the oscillation amplitude grows

khouly

I think you do not need to calculate gama. You can use ADS to do this automatically.
Gama here is reflection coefficent. You use the S11 port to connect in the output instead of 50 Ohm register and run simulation . Then you will observe the S11 easilly

Hi khouly
as u suggested I tried 1st S parameter model & adjusted the reflection coefficient.
Then I used nonlinear model to see the effect. Really nonlinearity changes the design.
Tunning must required when nonlinear model is used.
I did not get the expected frequency but still got the oscillation:D

yeah , sparameters are small signal , but in oscillator as the oscillation builds up the decive become more nonlinear as begins to saturate , the nonlinearity in the capacitances in the transistor changes , also the gain , the harmonics due nonlinearity will make ur output power is less

khouly