CMOS relaxation oscillator Design ...

[LvW]

Khaled, I completely agree with you - and I really appreciate your approach to find a rough estimate for the circuit´s behaviuor with the aim to get a feeling for electronic circuits.
And believe me, I was not very happy with my answer "too involved".
But in this particular case I am afraid I cannot help you - also with respect to the time needed to analyze the circuit (including the most important parasitics).

For example, don´t forget: It is not a simple task to solve only a 3rd order linear equation by hand.

Let me give you another example: There are some linear oscillator circuits called "R-oscillator" with no extra capacitors. That means the only reactive element is the frequency-dependence of the opamps (at least two units).
In order to be able to analyze such a circuit and to roughly approximate its behaviour the opamp gaim is approximated by a simple integrating functio (1/sT). That`s the only way to estimate the oscillating frequency and to derive practical formulas. But in reality - because of the simplifications (and because of the uncertainties connected with the value of T) the oscillating frequency will largely deviate from the calculated value.

Good luck and regards
LvW

 

[Milad-D]

The first attachment for sure can satisfy the sine wave oscillation conditions. From one port modeling of cross-coupled transistor s with cap is a negative resistor in series with negative capacitor. -2/gm-1/cs, and negative capacitors acts like a n inductor.

Recently, this circuit has been used in combination with FBARS with very low power and good phase noise.

 

[saro_k_82]

Hi Saro,
It has been long time since i posted this message. I have quick doubt here. Since it is a relaxation oscillator without the crystal, i want the check the Barkhausen criteria for this circuit .
Redrawing the above circuit as


i) To satisfy the phase criteria of 360° each stage has to provide 180° of phase shift. Each stage contains one left hand zero and two left hand poles.How can a left hand zero and two left hand poles give 180° phase shift ?.

ii) What is the DC closed loop gain (Positive feedback or Negative feedback) ?

Thanks
Hari.

Hi Hari,
I was off for a long time. Hope you have found answers. Anyways here are my observations on your questions.

1. Each stage has to provide 180 deg phase shift to work as an oscillator. Yes. But since each are inverting stages, they provide just that at dc. THe circuit resolves to one of the states quickly and then it relaxes. Recall that this is how a simple astable multivibrator works.
I wrote the equation for the loop gain for the complete loop and found that it has a pole at the origin, double pole along negative real axis and a single pole on negative real axis. There are 3 zeros and all of them will be in the negative plane if CA is lesser than a critical value. If CA is higher, it pushes 2 zeros to the left half plane allowing the circuit to oscillate. This confirms what is said in the paper and the root-locus (barkhausen) criteria for oscillation.

2. Positive feedback

- Saro

 

[sunny.sunny]

Re: Crystal oscillator: How to simulate the equivalent negative
Hi friends
I have a basic question..why do u want to include crystal's shunt capacitance while measuring negative resistance.

my second clarification is:
I need to run an ac analysis & at the frequency of interest I need to checkout impedance of input source. am I right ?
& then I can tune my load cap to get a negative resistance X5 times of ESR of crystal so as to meet safety margin requirements.

please clarify.

~sunny