# What is the difference between these ring oscillator topologies? How can I simulate one without "noise voltage?"

If I understand correctly, with ring oscillator, it adds the negative feedback back to the loop to make a supposedly infinite gain. With the first topology (NMOS inverter) the negative feedback adds to each stage delay because of transfer function H(w), adding infinity gain with each loop.

But I don't quite understand the other 2 design, the CMOS inverter and the differrential ring oscillator.

And does anyone know how to test the circuit? Do I have to add some "noise voltage" or is there anyway to make it work loop immediately and create oscillation without any activation voltage?

• As for each oscillator based on the oscillation crterion (Barkhausen) you need (1) negative feedback for DC (stable operating point), this is always fulfilled for an uneven number of inverting stages, and (2) positive feedback for the frequency of osciilation. For three stages, each stage must contribute -60 deg (due to the delay per stage) which - together with the inverting property (-180deg) gives -360 deg - identical to zero deg.
– LvW
Dec 5, 2019 at 13:54

Your "infinite gain" way of understanding only works for small signals. If that wasn't the case (it would always apply even when the signal is large) then the amplitude of the signal would reach infinity as well. Obviously, that's not what happens.

What does happen is that as the amplitude gets larger the amplifier stages start to saturate and because of that saturation their gain decreases. When a stable oscillation is in place, the loop gain will be equal to 1 (one).

The circuits that you don't quite understand aren't any different from the one you do understand. The only difference is in the implementation of each amplifier. The amplifiers simply use a different circuit. The differential circuit is also very similar only the signal isn't single ended (like in the other circuits) but differential. That means the signal has a copy that's the same but it has an inverted shape (180 degrees phase shift).

You ask about "noise voltage" but I think you're confused about the way how these circuits start in the real world. In the real world there's always noise present and that noise is enough to get the start up the oscillator.

In a simulation this is not the case, the simulator will be happy to find a stable solution where the circuit isn't oscillating. Like for the 3-inverter ring oscillator it will find that all signal nets are at a DC voltage close to Vdd/2 and that that is an OK solution. Theoretically it is but it does not work like that in the real world.

So to get the oscillation going in a simulator we need to "disturb" that wrong stable situation. I usually do that by inserting a pulsed source that can be a current source or a voltage source, it does not matter. I make that source deliver a small pulse like a 100 ns pulse of 1uA (or 10 mV). That will then start the oscillation.

Noise simulations (actually: Phasenoise) are the next step when you have fully understand how to simulate oscillators.

• Thanks for your comment. I understand the general idea but I don't understand how it exactly work to design. My teacher gave me a project to design .a Voltage Controlled Oscillator (VCO) Dec 5, 2019 at 13:19
• About the other 2 topologies,what I want to ask is With CMOS inverter,how does it gain? Because the Vout of each inverter is decided by Vdd and GND right? is Vdd/Vin the gain? With Differential, I see that they're usually used as Op-Amp and is used to for VCO, and I want to know how the circuit work, the I-V characteristic,how those transistor affect each others,.... Dec 5, 2019 at 13:22
• I suggest that you look up how a CMOS inverter works as an amplifier. Draw its small signal equivalent circuit. Note how it is just two common source amplifiers in parallel. No, the gain is not Vdd/Vin. It seems you want to know too much all at once, that never works. Pick one thing and fully understand that first. The differential amplifier is based on differential pairs, so go study that, it's a very common circuit just like the CMOS inverter. Dec 5, 2019 at 13:35
• Ok maybe I'll look more into differential amplifier. thks Dec 5, 2019 at 13:44