In a traditional oscillator, oscillation is achieved by providing a loop-gain greater than unity and a phase-shift of \(0^o\) at some \(f_{osc}\). However, in the case of a relaxation oscillator, oscillation is achieved by switching between two discrete states. Often a relaxation oscillator is constructed with a non-linear circuit element which can provide 2 threshold voltage levels to define two discrete states. One non-linear circuit element which is commonly employed in a relaxation oscillator is a schmitt trigger.

Due to the hysteresis developed internal to the schmitt trigger, two trigger thresholds are realized, namely \(V_N\) and \(V_P\). Where \(V_N\) is the negative threshold voltage and \(V_P\) is the positive threshold voltage. The hysteresis voltage is then,

$$ V_H = V_P – V_N $$

Ideally, the thresholds \(V_N\) and \(V_P\) would be centered around mid-supply (\(V_{dd}/2\)), however in practice this is only approximately true.

A minimal component count relaxation oscillator is shown in the figure below.

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