ring-oscillator frequency

[double_ramp]

Hi,

I have a ring-oscillator and I decrease its power supply, so the oscillation frequency decreases.

Well, I understand that with the decrease of Vdd the Vds decreases as well, etc. and the freq. changes.

But could somebody please explain me the exact physical reason why the oscillation frequency of the ring-oscillator gets lower, if I decrease the Vdd of the circuit?

Thx.

 

[malizevzek]

If you look at inverter as single stage, you can approximate it (to the first order) with RC circuit, that defines propagation delay. R is on-resistance of the transistor/inverter, that goes up as Vdd goes down. Having R increased, increases in turn propagation delay and decreases frequency.
Inverter capacitances are Vdd-sensitive as well, although not in the same way as Ron