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

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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
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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 ) [ ] 0 2 v ( t ) = 0 [ VdP-1 ] where ϖ 0 2 = LC ( 29 -1 . If α is small, it is reasonable to take v ( t ) = 1 2 V ( t ) exp - i ϖ 0 t ( 29 + c . c . [ VdP-2 ] Then Equation [ VdP-1 ] becomes without approximation 1 2 0 2 V ( t ) - i 2 ϖ 0 ˙ V ( t ) + ˙ ˙ V ( t ) [ ] exp - i ϖ 0 t ( 29 + c . c . - α-
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vanderpol - The van der Pol Negative Resistance Oscillator...

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