vanderpol

# vanderpol - The van der Pol Negative Resistance Oscillator...

This preview shows pages 1–3. Sign up to view the full content.

The van der Pol Negative Resistance Oscillator Van der Pol’s analysis 1 of “negative resistance” ( e.g., tunnel diode) oscillators prides a valuable framework for treating relative simplicity important features of oscillatory systems. The characteristic curve of a “negative resistance” device Consider the following negative resistance oscillatory circuit: By simple circuit analysis, it is a straightforword proposition to find the following simple circuit equation which is the fundamental van der Pol oscillator equation: 1 B. van der Pol, Radio Rev. 1 , 704-754, 1920 and B. van der Pol, Phil. Mag. 3 , 65, 1927

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
The van der Pol Negative Resistance Oscillator Page R. Victor Jones, March 16, 2000 2 d 2 d t 2 v ( t ) d d t α v ( t ) β v 3 ( t ) [ ] + ω 0 2 v ( t ) = 0 [ VdP-1 ] where ω 0 2 = LC ( ) -1 . If α is small, it is reasonable to take v ( t ) = 1 2 V ( t ) exp i ω 0 t ( ) + c . c . [ VdP-2 ] Then Equation [ VdP-1 ] becomes without approximation 1 2 −ω 0 2 V ( t ) i 2 ω 0 ˙ V ( t ) + ˙ ˙ V ( t ) [ ] exp i ω 0 t
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 02/29/2012 for the course PHYSICS 216 taught by Professor Staff during the Fall '11 term at BU.

### Page1 / 5

vanderpol - The van der Pol Negative Resistance Oscillator...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online