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Phy si cs 173 / BGG N 266 P ri m er on Nonlinear OpAmp Circuits David Kleinfeld, Spring 2008 Si mple Osc illa to r This is a phase-shift oscillator. Four RC sections require 45° phase shift per section to reach a total, unstable shift of 180o. The total gain, RF/RG, must be sufficiently large to counter the collective loss from each RC divider or else the positive feedback is tool weak for an oscillation to occur. In particular, we want RF/RG > (1/√2)-4 = 4. Rather than have all of the gain in one step, as below, it can be distributed across each OpAmp. Sc hm itt Tri gger With positive feedback, Op-Amp circuits lose stability. The Schmitt trigger is one of them. H ere, the input voltage that causes a transition of the output from –VSS to R12 R Vss . Thus positive inputs must exceed 12 Vss and Rf Rf R negative inputs must be smaller than ! 12 Vss . Rf +VSS (or vice versa) is Vtrans = The addition of an offset to V- allows the band of 2 R12 Vss to be centered around Rf an arbitrary voltage and thus provides hysteresis. One application of Schmitt Trigger is to make the trigger level for an event immune to jitter, as may occur in physiological recording. Rectif ier(s) These can be used to take the magnitude of a signal when followed by a low-pass filter. Cu rren t Sou rc e This is used to drive a coil, or a high-power LED, with I = Vcontrol/R. The use of a FET as the current driver surmounts the typical 10 mA maximum current of an OpAmp. Hopfi eld Netwo rk ( mod ifi ed fo r s equ en tia l s tate generation) . Feedback links all Op-Amps to produce stable states that, through a second set of feedback connections that act on a slower time-scale (or after a delay), adiabatically switch the system between states. The flip-flop constructed from two OpAmps (4 with inverters) is the minimal manifestation.