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 $Z_{L}+Z_{C}=0$

Z_{L}=Z_{C}

\omega L={\frac {1}{\omega C}}

Solving for ω

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

Since ω = 2πf therefore

f = 1/2π ${\sqrt {\frac {1}{LC}}}$

This frequency is called Resonance Frequency and usually denoted as f_o

At Resonance Frequency

V_{L}=Z_{C}

V_{L}-Z_{C}=0

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 ${\sqrt {\frac {1}{LC}}}$

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

f_o = 1/2π ${\sqrt {\frac {1}{LC}}}$

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

f_o = 0.3 x 10^-½n

For RC Phase Shift

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

Therefore the frequency change through phase change is

f = 1/2π

{\sqrt {3}}{\frac {1}{RC}}

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

f_o = 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

f_o = 1/2π ${\sqrt {\frac {1}{(L_{1}+L_{2})C}}}$

2 series capacitors C₁ + C₂ in parallel to one inductor L

f_o = 1/2π ${\sqrt {\frac {1}{(C_{1}+C_{2})L}}}$

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.

f_o = n f_c

Reference

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