Comparator as a Duty Cycle Controller

In this comparator the input voltage to be compared is applied to non-inverting terminal of op-amp. The reference voltage can be changed by connecting a potential divider arrangement as shown below.

Comp12

Consider the following non-inverting open loop comparator as shown below in the circuit diagram. The input applied is a sine wave of peak amplitude 6V.The reference voltage is generated from a potential divider as shown in circuit diagram below.

Comp13

The reference voltage is calculated as
Comp14
Operation:
The operation of the circuit can be explained with following two conditions
1. When Vin>Vref    then Vo=+V_sat
2. When Vin<Vref    then Vo=-V_sat

Comp15

From the output waveforms shown above, input signal crosses the reference point of 3V at two points in the positive half cycle of input signal. Therefore at the two crossing points we can have the equation
Comp16
Thus at θ = 30̊, input signal crosses the reference point. Since there are two reference points in the positive half cycle of input signal and both are symmetric from both the ends. So we get two angles corresponding to two crossings as follows,

Comp17

Thus between θ1 = 30̊  to θ2 = 150̊  output voltage is high (+Vsat). The complete cycle of input signal corresponds to θ = 360̊.
Thus the duty cycle of the output square wave can be represented as follows,
Comp18
Thus the duty cycle of the output square wave is 33.33%
If now input signal is changed to have amplitude of 10V peak, the duty cycle calculations are becomes
10sinθ=3
sinθ= 3/10
∴θ= sin^(-1)⁡(0.3)
∴θ=17.45°
So the two angles corresponding to two crossings are calculated as follows
θ1=17.45°-0°       θ2=180°-17.45°
θ1=17.45°              θ2=162.55°
Thus between θ1 = 17.45° to θ2 = 162.55° output voltage is high (+Vsat). The complete cycle of input signal corresponds to θ = 360̊.
Thus the duty cycle of the output square wave can be represented as follows
D= TON/T
∴D= (θ2-θ1)/θ
∴D= (162.55° -17.45°)/(360°)
∴D= (145.10°)/(360°)
∴D= 0.4030
∴D= 40.30 %
Thus the duty cycle of the output square wave is 40.30 %
Thus as the magnitude of the input signal increases, the duty cycle of the output square wave is also increases. Hence the comparator acts as a duty cycle controller.

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