By Austin Blaquiere (Auth.)
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LINEARITY AND NONLINEARITY Η ω F I G . 24. Jump phenomenon. W h e n ω is alternately increased a n d decreased over t h e range [α/, ω"], point Ρ describes t h e so-called hysteresis cycle BG'DGB. O n t h e other h a n d , it may easily be seen that if ω is prescribed a n d F is continuously increased, the j u m p p h e n o m e n o n again occurs, as a c o n s e q u e n c e of t h e c o n t i n u o u s deformation of t h e resonance curve. 4. Rauscher's Method 1 R a u s c h e r ' s m e t h o d may be applied to systems whose equations have t h e form χ + f(x) — F sin wt (85) w h e r e f(x) is a c o n t i n u o u s function of x.
Accordingly, representation of Γ and Φ by differential operators is m o r e general and, in any case, it is the only one which can be applied to typical nonlinear systems, in which t h e superposition p r o p e r t y does not hold. I n this case (15) is a nonlinear differential equation. L a t e r we shall see that, in m a n y practical weakly nonlinear examples, Γ can be considered a slowly varying function of t h e a m p l i t u d e a of t h e i n p u t voltage, while Φ is a constant (or possibly a n o t h e r slowly varying function of a ).
When impedances Z , Ζ , 0 λ 1 Colpitt's oscillator. 3. Negative Resistance. Threshold Condition Again we find a negative d a m p i n g t e r m in (18), —LS (C jC )x which will be responsible for t h e g r o w t h of oscillations. It expresses t h e fact t h a t t h e oscillator is receiving energy from an outside source, whereas positive d a m p i n g is the c o n s e q u e n c e of energy losses. I n d e e d in (18) energy losses are also taken into account, in connection with t h e t e r m rCx.
Nonlinear System Analysis by Austin Blaquiere (Auth.)