## December 21, 2014

### Puzzle: Ring Oscillators

Ring Oscillators are very commonly used circuits in SoCs, where they find their use in Voltage Controlled Oscillators used inside the PLLs, and also used as Silicon odometer circuits- which are used to track various parameters of the device like variation of timing with ageing etc.

It is also a well-known fact that ring oscillators have odd number of inverters connected in form of a chain, as shown below:

And the frequency of oscillations is given by the expression:
f = 1/(2NT)
N= Number of inverters (odd)
T= Propagation delay of a single inverter

Can you comment on the below circuit? Maybe an expression for it's oscillation frequency? Or perhaps any analytical expression (without bothering about the intricacies of various transistor parameters) for the voltage? Assume the operating voltage to be 1V.

Please post your answers here. I'd be happy to share the solution and my thought process in a couple of days.

1. vout=vin=vm

bias generator

1. Yes! That is right!

2. Can you elaborate?

3. I surely will. However, I'd like to wait for a day or two to post it here. If you want, I can mail it to you.

4. plz send to remesh.manu0@gmail.com

5. functionally both the circuits are equal ... bt the later 1 ... ie ., the oscialtor with single invertor has highest frequency compared to any other oscilators using invertors with the given propagation delay.

I understood the above theory ... bt did not get vout=vin=vm ... pls elaborate in mail gautamireddy1990@gmail.com
Plz comment or mail to gautamireddy1990@gmail.com

6. vout=vin=vm ???... pls elaborate this and bias generator in mail prashantguptaengg@gmail.com

2. Vout = Vin = Vdd/2..?? half the bias voltage..

1. Yes, that is correct. No oscillator like function.

2. no, that's wrong.. read it again...

3. and not an oscillator like performance in achieved... I suppose

4. Hi Naman,

Can you please elaborate how Vout equals to Vin when an inverter is established in between input and output

5. And how the propagation delay of an inverter effects the above circuit

6. jkam273@gmail.com

7. for oscillation atleast three stages req. to satisfy Barkhausen criteria of oscilation. in which phase shift should above 180 degree. to get above one degree we need to connect three stages one inverter will give only 90. if we use two inverter 180 but even bcz of that no change in output and even formation of latchup.

single inverter wont provide any oscillation

8. Please mail me the explanation @ montu.bhavsar75@gmail.com

9. Hi,

10. hey,

11. hi

12. If I go by control theory the second circuit is only having a single pole (not a pair of complex/imaginary poles) as required for marginally stable systems. Hence the system will always settle immediately to a steady state value (likely tobe closure to the 50% threshold between high and low. thus frequency is 0, i.e a DC.

13. Hi,

shethketan30692@gmail.com