The Designer's Guide Community Forum

The Designer's Guide Community Forum
https://designers-guide.org/forum/YaBB.pl
Design >> RF Design >> Hegazi's oscillator book
https://designers-guide.org/forum/YaBB.pl?num=1159800337

Message started by chenyan on Oct 2^nd, 2006, 7:45am

Title: Hegazi's oscillator book
Post by chenyan on Oct 2^nd, 2006, 7:45am

This book is named "The designer's guider to high-purity oscillator"

Because I am writing my disseration, I checked the phase noise in his book very carefully in order to use some of them in my disseration.

What I found (maybe I am wrong) is it seems that the author could finally get to the right formula only because he knew how the answer looked like.

For example, in his noise calculation of current biased oscillator, he assumed that the output voltage of VCO is a noiseless carrier plus AM sidebands and PM sidebands. But then in Colpitts analysis, he assumed that the output voltage is a noiseless carrier plus PM sidebands only, and said that the AM around carrier is negligble. Only with this assumption, could he reached the final formula.

To me, this does not make sense, please correct if I am wrong.

Title: Re: Hegazi's oscillator book
Post by emad on Oct 6^th, 2006, 6:33pm

The analysis on page 75 of the book says it all, I believe.

In the differential oscillator case, a full solution (AM + PM) is assumed. This is figuratively an assumption because this is the general solution anyway.
In the Colpitts oscillator case, and on p.75, equation 28 assumes a PM solution only for the gate-source voltage of the transistor. However, equation 29 assumes a general solution for the current in the transistor and the rest of the analysis goes on to validate that AM is very little. Now since the voltage on C1 is a filtered verion of the output voltage then its AM is also very small which validates our initial assumption.

So the analysis flows as follows:
1. Assume no AM on Vc1
2. Assume unknown AM on current pulse
3. Show current pulse AM is small
4. Vc1 AM is filtered version so also small

Note that assuming an AM component on Vc1 (equation 28) will not change the analysis at all. The reason is that equation 29 which calculates the current in the device already assumes an AM component. Therefore, you may modify equation 28 to the following:
Vc1 = V. exp(jwt) + a exp(jw_+ t) - a* exp(jw_- t) + b exp(jw_+ t) + b* exp(jw_- t) (28_mod)

Now the current waveform is merely the voltage given above by equation (28_mod) multiplied by the transconductance of the device which yields equation (29).

So why did we choose the write equation (28) the way it is? It cleans up the analysis to allow readers to follow. In fact, on p.78 we hint at this little inconsistency since we deduce a value for the component 'b' in equation (47) which we ignored in Vc1. However, the analysis will not change.

Cheers

Title: Re: Hegazi's oscillator book
Post by chenyan on Oct 7^th, 2006, 2:19pm

Thanks for the explanation. BTW, sorry I was so judgemental, after all this book is by far the best on cmos oscillator.

But still I cannot agree with your analysis on page 75.

First I checked your analysis flow, if I do it the other way. I assume that a(PM) on Vc1 is negligible, only b(AM) exists. Then with the same analysis I will get a very small a(PM) compared with b(AM), but that doesnot have to mean that my assumption about small a(PM) is right. Beacuse a(PM) and b(AM) are interchangeable in this analysis method.

Then I use 28_mod instead, then with this method, it turns out a=b, that is quite a different result.