*Ferran Bayes*

*EDN*

A previous design idea is reminiscent of a similar but somewhat simpler circuit (see [1]). This circuit delivers a rectangular signal with duty cycle varying between 0 and 100% in response to an input signal varying from 0 to 5 V dc (Figure 1). As with the above-mentioned circuit, the frequency is not constant (Figure 2), but the circuit is so simple that it can be useful in certain applications. In response to the hysteresis R_{2} provides and the time constant R_{3}C_{1}, the comparator delivers the rectangular wave (Figure 3). The voltage V– at the inverting input swings between the two threshold levels, V_{TH} and V_{TL}. If you assume that R_{2} >> R_{1}, then V+ is always very close to V_{IN}. R_{3}C_{1} averages the signal at V_{OUT}, and the dc voltage at V– is proportional to the duty cycle of V_{OUT}. The closed feedback loop tries to make V– equal to V+; therefore, the duty cycle at V_{OUT} is proportional to V_{IN}.

Figure 1. |
This voltage-controlled PWM circuit is simplicity personified. |

Figure 2. |
Output frequency is a nonlinear function of the input voltage. |

Figure 3. |
The voltage at the inverting input follows a linear ramp. |

The voltage at V_{OH} determines both the output signal's high level and the full-scale range of V_{IN}. It can have any value, insofar as it does not surpass the common-mode input range of the comparator. The mathematical analysis of the circuit is easy if we assume that, because V_{TH} – V_{TL}is small, we can approximate the exponential charge and discharge of C_{1} to assume the characteristic stemming from a constant-current source/sink. During the charging phase, the current is approximately (V_{OH} – V_{IN})/3, so:

Similarly, during the discharge phase, we can assume the current is V_{IN}/3, and

Matching the two equations yields

and the duty cycle, D, is

You can see that the duty cycle is directly proportional to V_{IN}: 0% for V_{IN} = 0 V and 100% for V_{IN} = V_{OH}. Moreover, the duty cycle is essentially independent of the component values, with the constraint that R_{2} >> R_{1} to keep hysteresis small. An inverse relationship between duty cycle and V_{OH} can be useful in some applications, so consider V_{OH} as an additional input. The output frequency follows the relationship

reaching its maximum at V_{IN} = V_{OH}/2.

Tests with a TLC393 CMOS comparator and a bipolar LM393 reveal that the TLC393 performs better at low values of V_{IN}, because of its lower V_{OL}. Avoid loading the comparator's output; buffer it if necessary, because the loading can degrade the switching levels.

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