AN2867 datasheet(8/41 Pages) STMICROELECTRONICS

8 / 41 page

Oscillator theory

AN2867

8/41

DocID15287 Rev 9

Oscillator theory

Oscillators are one of the backbone components of modern digital ICs. They can be

classified into different sub-families depending on their topology and operating principles. To

each oscillator sub-family corresponds a more suitable mathematical model that can be

used to study the oscillator behavior and theoretically determine its performance.

This section deals only with harmonic oscillators (relaxation oscillators are not within the

scope of this application note) with a particular focus on Pierce-oscillator topology (see

Section 3: Pierce oscillator design for details). This restricted scope is due to the fact that all

the oscillators embedded in STM32 microcontrollers covered by this document that require

external passive components (external resonator, load capacitors, etc.) are of the previously

mentioned type and topology.

The harmonic oscillator family can be divided into two main sub-families:

•

Negative-resistance oscillators

•

Positive-feedback oscillators.

These two sub-families of oscillators are similar for what regards the output waveform. They

deliver an oscillating waveform at the desired frequency. This waveform is typically

composed of a fundamental sine-waveform at the desired frequency plus a sum of overtone

harmonics (at frequencies multiple of the fundamental one) due to the nonlinearity of some

components of the oscillation loop.

These two sub-families differ in their operating principles. This difference also implies a

different mathematical model to describe and analyze each sub-family.

Positive-feedback oscillators are generally modeled using the famous Barkhausen model

where an oscillator should fulfill the Barkhausen criterion to be able to maintain a stable

oscillation at the desired frequency.

Negative-resistance oscillators could be described by the Barkhausen model. However this

approach is not adequate. The most suitable approach to analyze a negative-resistance

oscillator is by using the negative-resistance model as described in E. Vittoz’s paper ([1]).

Since STM32 low-speed external (LSE) oscillator and high-speed external (HSE) oscillators

were both designed following the negative-resistance principle, this section focuses on the

presentation of the negative-resistance model.

2.1

Negative resistance

Theoretically speaking, a negative resistance would be a dipole that absorbs heat and

converts the energy into an electrical current proportional to the applied voltage but flowing

in the opposite direction (exactly the opposite mechanism of an electrical resistance). In the

real word such a dipole does not exist.

In fact the term “negative resistance” is a misnomer of the “negative transresistance” which

is defined by the ratio of a given voltage variation (∆V) divided by the induced current

variation (∆I). Unlike the resistance which is always positive, the transresistance (also

known as differential resistance) can be either positive or negative. Figure 3 gives the

current-voltage curve for a dipole that shows a negative transresistance region. It is obvious

that the V/I ratio is always positive. However this is not the case for the ∆V/∆I ratio

AN2867 Datasheet(PDF) 8 Page - STMicroelectronics

AN2867 Datasheet(HTML) 8 Page - STMicroelectronics

Html Pages

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

Datasheet Download

Link URL