# Ring oscillator

A ring oscillator is an electronic oscillator circuit that is based on the transit time of amplifier components connected together to form a ring.

The ring oscillator starts to oscillate independently and does not require any reactance components such as capacitors or coils. Its frequency depends on voltage and temperature.

Circuit diagram of a three-stage ring oscillator
Experimental setup of four ring oscillators made of p-type MOSFETs on a silicon chip. This allows the influence of the transistor size on the frequency to be examined.
Ring oscillator made of three bipolar transistors

## principle

A closed series connection of an uneven number of inverters does not theoretically have a defined or permitted state, but an even number results in a flip-flop which always assumes a stable logic state. However, if the running time of the inverting components is taken into account, an uneven number results in a vibratory and self-exciting structure.

In the accompanying diagram are bipolar transistors in an emitter circuit as an inverter for a ring oscillator, any other odd number greater also oscillates. The fourth bipolar transistor in the circuit diagram only serves as an isolating stage for decoupling the signal. Due to the saturation of the bipolar transistors, this circuit oscillates significantly more slowly than a circuit made up of MOSFETs or logic gate inverters, even without capacitors .

In order for the circuit to oscillate at all, its loop gain must be greater than or equal to one. Their oscillation frequency then corresponds to the frequency at which the loop gain is equal to one. Since the circuit works in switching mode, the transistors do not have a constant current gain. With five transistors, the oscillation looks more rectangular than with three stages.

The amount of the phase difference between the individual steps is 360 ° / 3 = 120 ° with 3 steps, i.e. H. the frequency is just so great that this phase relationship exists. For more than three levels, accordingly less, until more than one period fits into the oscillator. Due to the inversion, the phase difference to the following stage is the next larger multiple of 120 ° that is greater than 180 °: 2 * 120 ° = + 240 ° = + 60 ° + 180 °. Since + 240 ° = −120 ° and since no effective direction can be seen from a periodic signal, one easily succumbs to the impression that the following inverter is running ahead of the driving one. The delay time per inverter corresponds to + 60 °.  ${\ displaystyle t_ {D} = {\ frac {60 ^ {\ circ} \ cdot T} {360 ^ {\ circ}}} = {\ frac {1} {6 \ cdot f}}}$

## Calculating the frequency

Because of the finite processing speed of an inverter, the input signal appears at the output after the transit time t D. With n inverters of the same type, the period of oscillation results

${\ displaystyle T = 2n \ cdot t_ {D}}$

and the frequency

${\ displaystyle f = {\ frac {1} {T}} = {\ frac {1} {2n \ cdot t_ {D}}}}$

If the ring  uses three common logic modules with t D ≈ 2 ns, then f ≈ 83 MHz.

## Applications

Integrated test circuits with ring oscillators are manufactured to evaluate and optimize manufacturing processes and technologies.

Ring oscillators are used in sensors to convert a change in capacitance into a change in frequency. These include sensors for acceleration, pressure , humidity and temperature.

Since the generated frequency depends on the temperature, ring oscillators are also used as thermometers on processor chips.