# Practical Electronics/Generators/Oscillators

## Intro

An oscillator is a circuit which generates a repetitive electric signal of given waveform (for example a sinewave).

## Electronic Oscillation

Electronic Oscillator is an electronics circuit that generates oscillation when circuit is in resonance a natural process when all the frequency components cancel out . Commonly found in LC and RC Phase Shift

In electronics, oscillation occurs when the following conditions are met

• Output voltage is equal to input voltage and inverted
• The Phase Angle difference between input and output voltage must be 180

### Passive Oscillation

With Series LC or Parallel LC . At Resonance, the frequency dependent components will cancel out ie impedance of inductor will cancel impedance of capacitor ${\displaystyle Z_{L}+Z_{C}=0}$

${\displaystyle Z_{L}=Z_{C}}$
${\displaystyle \omega L={\frac {1}{\omega C}}}$

Solving for ω

${\displaystyle \omega ={\sqrt {\frac {1}{LC}}}}$

Since ω = 2πf therefore

f = 1/2π${\displaystyle {\sqrt {\frac {1}{LC}}}}$

This frequency is called Resonance Frequency and usually denoted as fo

At Resonance Frequency

${\displaystyle V_{L}=Z_{C}}$ or ${\displaystyle V_{L}-Z_{C}=0}$ or ${\displaystyle V_{C}=-Z_{L}}$

The voltage of the series LC keeps oscillating between inductor's voltage and capacitor's voltage between phase angle 0 - 180

In LC circuit, oscillation occurs at the resonance frequency
f = 1/2π${\displaystyle {\sqrt {\frac {1}{LC}}}}$

### Active Oscillation

#### Fixed Frequency Oscialltor

For active cicuit, to meet the requirement for oscillation require

An Inverter that has output voltage equals to input voltage and inverted . So any Transistor or Op Amp Amplifier can be configured to act as an Inverter
A Feedback circuit between input and output that provides 180 degree difference in phase angle . This can be achieved through Resonant Tuned LC circuit or three stage of RC Phase Shift with each stage has a phase shift of 60

For Resonant Tuned LC circuit, the oscialltion frequency is equal to the resonant frequency

fo = 1/2π${\displaystyle {\sqrt {\frac {1}{LC}}}}$

When choosing the value of ${\displaystyle {\sqrt {\frac {1}{LC}}}}$ in power of 10 so that ${\displaystyle {\sqrt {\frac {1}{LC}}}}$ is equivalent to 10-½n then the oscillating frequency can be calculated by

fo = 0.3 x 10-½n

For RC Phase Shift

Tanθ = 1/2π f ${\displaystyle {\frac {1}{RC}}}$
Tan 60 = Sin 60 / Cos 60 = ${\displaystyle {\frac {\frac {\sqrt {3}}{2}}{\frac {1}{2}}}={\sqrt {3}}}$

Therefore the frequency change through phase change is

f = 1/2π ${\displaystyle {\sqrt {3}}{\frac {1}{RC}}}$

When choosing the value of ${\displaystyle {\frac {1}{CR}}}$ in power of 10 so that ${\displaystyle {\frac {1}{CR}}}$ is equivalent to 10-n then the oscillating frequency can be calculated by

fo = 0.33 x 10-n

#### Variable Frequency Oscialltor

Variable Frequency Oscialltor can be achieved through inverter with feedback circuit of

• 2 series inductors L1 + L2 in parallel to one capacitor C
fo = 1/2π ${\displaystyle {\sqrt {\frac {1}{(L_{1}+L_{2})C}}}}$
• 2 series capacitors C1 + C2 in parallel to one inductor L
fo = 1/2π ${\displaystyle {\sqrt {\frac {1}{(C_{1}+C_{2})L}}}}$
• 2 series capacitors C1 + C2 in parallel to a tuned LC

## Electro-Mechanical Oscillation

### Crystal Oscillator

A crystal oscillator is an electronic circuit that uses the mechanical resonance of a vibrating crystal of piezoelectric material to create an electrical signal with a very precise frequency.

fo = n fc