# How can I derive the period of oscillation for a relaxation oscillator?

• limofunder
In summary, the conversation discusses a problem on relaxation oscillators and the derivation of a relationship for the period of oscillation in terms of R1, R2, RC, VCC, and VEE. The individual mentions knowledge of V=IR and C=Q/V, as well as the equation dq/dt = I. They then make deductions and use the voltage divider formula to try and relate V_out with the current from above. A question is also posed about the latex code not appearing properly.

## Homework Statement

I am having a bit of trouble with a homework problem on relaxation oscillators, the schematic is shown below:

https://webspace.utexas.edu/sz233/Relaxation%20Oscillator.png [Broken]

The original problem states:
derive a relationship for the period of oscillation for a relaxation oscillator in terms of R1, R2, RC, VCC
and VEE.

## Homework Equations

So I know from E&M that
V=IR, and C=Q/V.
also, I know that dq/dt = I

## The Attempt at a Solution

from this, I deduce, possibly erroneously, that
$$V_- = IR +\frac{1}{C} \int I(t)dt$$
so
$$0 = R \frac{dI}{dt} + \frac{1}{C} * I(t)$$
then
$$\frac{dI}{I} = - \frac{1}{RC} dt$$
it follows that
I = I0Exp[-t/RC]

given that current doesn't change at the + or - poles on the amplifier, then this should be the same current that goes through V+ thus using the voltage divider formula,
$$V_out = V_+ * \frac{R_2}{R_1 + R_2}$$
Now, how do I relate the Vout here with the current from above?

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Is there a reason for which the latex code doesn't appear? I pulled the notation direct from the sigma reference in the tool box menu

thanks a bunch guys

## 1. What is a relaxation oscillator?

A relaxation oscillator is an electronic circuit that produces repetitive, non-sinusoidal waveforms, such as square, triangular, or sawtooth waves. It uses a combination of a capacitor, resistor, and a non-linear element to create a self-sustaining oscillation.

## 2. How does a relaxation oscillator work?

A relaxation oscillator works by charging and discharging a capacitor through a resistor. As the capacitor charges, the voltage across it increases until it reaches a threshold value, at which point the non-linear element triggers and discharges the capacitor. This process repeats, creating a continuous oscillation.

## 3. What are the applications of relaxation oscillators?

Relaxation oscillators have many applications, including generating clock signals in electronic devices, generating sound in musical instruments, and producing periodic signals for timing circuits. They are also used in relaxation oscillation timers, pulse generators, and voltage-controlled oscillators.

## 4. What is the difference between a relaxation oscillator and a harmonic oscillator?

The main difference between a relaxation oscillator and a harmonic oscillator is the type of waveform they produce. A relaxation oscillator produces non-sinusoidal waveforms, while a harmonic oscillator produces sinusoidal waveforms. Additionally, a relaxation oscillator does not require a resonant circuit, unlike a harmonic oscillator.

## 5. Can a relaxation oscillator be used in digital circuits?

Yes, relaxation oscillators can be used in digital circuits as they can generate square waves, which are commonly used in digital systems. They can also be used to generate clock signals for microcontrollers, timers, and other digital devices.