Re: VCO design
For low frequencies, the required inductor and capacitor used for LC-VCO would be extremely large. You can try to calculate the required LC for 10Hz using f = sqrt(2*pi*L*C) and you'll see what I mean.
Also, LC-VCO can't achieve such wide band tuning range.
For ring oscillators, you can control the delay by controlling the number of stages and of delay per stage. Delay per stage can also be varied by varying current per stage or by varying the load.
However, ring oscillators suffer from much worse noise performance than their LC counterparts.