Electronics · Ch 6 — Oscillators

Introduction

6.1

Introduction

An oscillator is an electronic circuit that converts DC energy into AC energy of a desired frequency. The AC sources it produces range from a few hertz to several gigahertz, which is why oscillators sit at the heart of radios, TV transmitters and receivers, radar sets, computers and many other electronic devices.

Classification of oscillators

Oscillators are grouped in two ways:

By the shape of the waveform they generate — (i) sinusoidal oscillators and (ii) non-sinusoidal oscillators.
By the components used in the feedback circuit — sinusoidal oscillators are further divided into (i) LC oscillators, (ii) RC oscillators and (iii) crystal oscillators.

Sinusoidal (harmonic) oscillator. When the output is a smooth sine wave of constant amplitude the circuit is a sinusoidal, or harmonic, oscillator (Figure 6.1.1).

Non-sinusoidal oscillator. When the output is some other repeating shape — square, rectangular, triangular or saw-tooth — the circuit is a non-sinusoidal oscillator (Figure 6.1.2).

Damped and un-damped oscillations

Damped oscillations are electrical oscillations whose amplitude keeps decreasing with time while the frequency stays the same (Figure 6.1.3). Un-damped (sustained) oscillations are oscillations whose amplitude stays constant with time — both amplitude and frequency remain unchanged (Figure 6.1.4). A useful oscillator must deliver sustained oscillations, so the whole design problem is to keep the amplitude from decaying.

Basic principle of an oscillator

An oscillator is an amplifier with positive feedback. Feedback is positive when the feedback voltage returned to the input is in phase with the input signal. Consider the amplifier-plus-feedback arrangement of Figure 6.1.5, where the loop is drawn with 0 degrees phase shift in both the forward and feedback paths.

The open-loop gain of the amplifier is $A = \dfrac{V_o}{V_i}$ . After positive feedback the overall gain is $A_f = \dfrac{V_o}{V_s}$ . Because the amplifier input is the sum of the source and feedback voltages, $V_i = V_s + V_f$ , and the feedback voltage is $V_f = \beta V_o$ , we get $V_s = V_i - \beta V_o$ . Substituting and dividing numerator and denominator by $V_i$ gives the closed-loop gain

A_f = \dfrac{A}{1 - A\beta}

Here $A\beta$ is called the loop gain and $\beta$ is the feedback ratio.

Stabilization of oscillations

The expression $A_f = \dfrac{A}{1 - A\beta}$ contains the necessary condition for sustained oscillations. If the loop gain reaches $A\beta = 1$ , the denominator becomes zero and $A_f = \infty$ : the circuit produces an output with no input applied. In other words, the amplifier has become an oscillator.

Start-up oscillations and start-up conditions

Where does the very first signal come from if there is no input? The starting voltage is provided by noise — the random thermal movement of free electrons in the circuit resistors at room temperature. When power is switched on, this tiny noise voltage is amplified, drives the feedback network, and returns to the input. If the feedback network is designed so that the total loop phase shift is 0 degrees (equivalently 360 degrees), the signal reinforces itself at one frequency and grows into a steady oscillation.

In a typical transistor oscillator the inverting amplifier contributes 180 degrees and the feedback network contributes another 180 degrees, giving 360 degrees around the loop (Figure 6.1.6). At switch-on the loop gain $A\beta$ is deliberately greater than 1, so the oscillations build up; as the amplitude rises the amplifier gain falls until $A\beta$ settles at exactly 1, giving a constant-amplitude output.

Treating a fictitious input $V_i$ applied to the amplifier: the output is $V_o = A V_i$ and the feedback voltage $V_f = \beta V_o = A\beta V_i$ . For a true oscillator the external source is removed ( $V_s = 0$ ), so the feedback voltage alone sustains the input, $V_f = V_i$ , which requires $|A\beta| = 1$ with $V_f$ in phase with $V_i$ .

Barkhausen criterion

The two conditions above are summarised as the Barkhausen criterion for sustained oscillations:

The total phase shift around the closed loop must be 0 degrees (or 360 degrees).
The magnitude of the loop gain must be unity, $|A\beta| = 1$ .

The value of the loop gain decides the nature of the oscillations: …

Definition 1Oscillator

An oscillator is an electronic circuit that converts DC energy into AC energy of a desired frequency, producing an AC output (a few Hz up to several GHz) with no externally applied AC input. It is an amplifier with positive feedback that draws energy from a DC supply and delivers a continuous AC waveform, which is why oscillators …

Definition 2Sinusoidal (harmonic) oscillator

A sinusoidal or harmonic oscillator produces an output that is a continuous sine wave of constant amplitude and single frequency. Its waveform is a smooth, un-damped sine wave, and by the components used in the feedback network these harmonic oscillators are …

Figure 3Constant-amplitude sinusoidal waveform of an oscillator plotted as voltage V against time t