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Oscillators With the addition of a capacitor and resistor, the Schmitt trigger can be turned into a simple oscillator. Technically, it’s known as an astable multivibrator. Before looking at the circuit, it is worth reviewing the transient response of a first order RC network.

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Transient Response and

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**is a separable first order differential equation.**

These are the easiest kind to solve! First, rearrange: and integrate each side: The constant, , is the value of VR when time=0, so:

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VC t VS VC(0) > VS VC(0) < VS NB. In either case, VC ® VS as t ® ¥. VC(¥) is known as the aiming potential.

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Oscillator Circuit The op-amp, R1 and R2 form an inverting Schmitt trigger As R1 = R2, threshold levels are ±VSAT/2 The output is fed-back to the inverting input via an RC network The aiming potential of the capacitor voltage will be either +VSAT or –VSAT

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Waveforms V VSAT t -VSAT

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Analysis To calculate the time-period, consider just one half-cycle of the oscillation. V VSAT t -VSAT

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**Analysis (cont) V t Half-cycle ends when VC reaches VSAT/2 VSAT -VSAT**

t -VSAT Full period of oscillation is 2 half cycles,

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Oscillator Summary Using only a couple of extra components, the Schmitt trigger can be converted into a simple oscillator R & C set the period of oscillation independently of VSAT Many square wave oscillators work using the same basic principles

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**Active Feedback Components**

There are two broad categories of non-linear op-amp circuits Those that exploit saturation Those that use active components in the feedback network We will concentrate on one example of the latter genre – the precision rectifier

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**Simple Half-Wave Rectifier**

IN OUT Ideal Output 1 1 0.5 0.5 Actual Output t t - 0.5 - 0.5 - 1 - 1

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**Precision rectifier Note that:**

The current through the diode (and therefore also through RL) can only flow in one direction The load voltage, VOUT, cannot, therefore, go below 0 V When the diode conducts, VOUT » V1 - ½

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**Analysis – Negative Input**

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**Analysis – Positive Input**

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Waveforms V V IN V 1 V OUT t t - V SAT

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**Other Non-Linear Applications**

Circuits that effectively change the saturation level(s) of the op-amp. Precision rectifier Limiters Circuits that use the exponential V-I curve of PN junctions. Log and antilog amplifiers Multipliers, squarers and dividers

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**Summary Non-Linear applications of op-amps Essentials**

Comparator Schmitt Trigger Precision Rectifier Additions for interest Limiters Log/antilog amps Multipliers etc.

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