AN2441

Oscillator theory

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Oscillator theory

An oscillator consists of an amplifier and a feedback network to provide frequency selection.

The following figure shows the block diagram of the basic principle.

Figure 1.

Oscillator principle

Where:

A(f) is the complex transfer function of the amplifier providing energy to the loop in

order to keep it oscillating.

B(f) is the complex transfer function of the feedback which is setting the oscillator

frequency.

To oscillate, the following Barkhausen conditions must be fulfilled. The closed loop gain

should be greater than 1 and the total phase shift of 360° is to be provided.

and

In order to get the oscillator to start up, it needs initial electrical energy. Power-up transients

as well as noise can supply the needed energy. However, the energy level should be high

enough to trigger oscillation at the required frequency. Mathematically, this is represented by

|A(w)|.|B(w)| >> 1 which means that the open loop gain should be much higher than 1. The

time until steady oscillations are reached depends on the open loop gain.

A(f)

B(f)

Active element

Passive feedback element

Vout

Af

()

Af

() e

jf

α f

()

⋅

=

Bf

()

Bf

() e

jf

β f

()

⋅

=

Af

()

Bf

()

1

≥

⋅

α f

() β f

()

+

2

π

=