# Low-component-count zero-crossing detector is low power

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There are many circuits published showing zero-crossing detectors for use with 50- and 60-Hz power lines. Though the circuit variations are plentiful, many have shortcomings. This Design Idea shows a circuit that uses only a few commonly available parts and provides good performance with low power consumption.

In the circuit shown in **Figure
1**, a waveform is produced at V_{O}
with rising edges that are synchronized
with the zero crossings of the
line voltage, V_{AC}. The circuit can
be easily modified so that it produces
a falling-edge waveform that
is synchronized with V_{AC}.

**Figure 1** The zero-crossing detector uses few components and consumes very little power. The V_{O} signal has a rising edge that is coincident with each zero crossing of the line voltage, V_{AC}.

The circuit operates as follows.
At the zero crossings of V_{AC}, the current through the capacitor
and the LED of the HCPL-4701 optocoupler satisfies
**Equation 1** below. **Equation 2** shows the standard conversion
between radians per second and hertz; it also shows
the derivation and explanation for v_{i}(t). **Equations 3** and
**4** show the simplification used in **Equation 1**. Because the
voltage across the LED is close to constant, differentiation
of that value with respect to time results in a zero value.

The peak value of the current through the LED is a function
of the capacitor, C, so you must choose a value for C
under the constraint that at the initial time (t=0) and for a given minimum supply-voltage value, the intensity exceeds
the triggering threshold value for the optocoupler. In the case
of the HCPL-4701, it is I_{F(ON)}=40 μA.

Diode D_{1} not only allows for the capacitor to discharge
but also prevents the application of a reverse voltage on the
LED. The maximum reverse input voltage of the HCPL-4701 is 2.5V.

Resistor R_{1} is included in order to discharge the energy
stored in the capacitor in the latter portion of each cycle of
v_{i}(t) when i_{c}(t)<0 (**Figure 1**). Its maximum value is limited
by the capacitor, by the peak value of the supply voltage
(V_{AC-PEAK}), and by the maximum acceptable time delay of
the current rising edges through the LED with respect to
the corresponding ac-voltage zero crossing (**Figure 2**). Its
minimum value is limited by the maximum allowable power
dissipation in R_{1} ([V_{AC-RMS}]^{2}/R_{1}). A practical compromise has
to be reached.

**Figure 2** The relationship between v_{i}(t) and I_{LED}(t) is a function of the value of R_{1}. The time delay between the zero crossing and the LED current is shown.

**Table 1** shows the time delay (t_{DELAY}) of the current rising
edges through the LED and the power dissipation for three
different values of R_{1}. Notice that the time delay of the rising
edges of V_{O} with respect to the zero crossings of V_{AC} must include an additional delay for the optocoupler’s propagation
time delay. The HCPL-4701 has a typical propagation
time delay of 70 μsec.

Based on the previous information, the following practical
values for C and R_{1} are obtained:

- For V
_{AC}=230V_{RMS}±20% (**Figure 3**): C=0.5 nF/400V (MKT-HQ 370 polyester metallized, MKT series), R_{1}=560 kΩ/0.25W, t_{DELAY}=114 μsec (the time delay in the rising edges of V_{O}with respect to the zero crossings of V_{AC}), and P≈100 mW (average power from the ac line). - For V
_{AC}=115V_{RMS}±20% (**Figure 4**): C=1 nF/200V, R_{1}=220 kΩ/0.25W, t_{DELAY}=130 μsec (time delay in the rising edges of V_{O}with respect to the zero crossings of V_{AC}), and P≈65 mW (average power from the ac line). - For operation from 80 to 280V
_{RMS}: C=1 nF/400V and R_{1}=330 kΩ/0.25W.

**Figure 3**Empirical results are shown for V

_{AC}=230V

_{RMS}, C=0.5 nF, and R

_{1}=560 kΩ.

**Figure 4**Empirical results are shown for V

_{AC}=115V

_{RMS}, C=1 nF, and R

_{1}=220 kΩ.

Empirical results are shown for V_{AC}=267V_{RMS}, C1=1 nF,
and R_{1}=220 kΩ (**Figure 5**). See **Figures 6 **and** 7** for additional empirical results.

**Figure 5** Empirical results are shown for V_{AC}=267V_{RMS}, C=1 nF, and R_{1}=220 kΩ.

**Figure 6** Empirical results are shown for V_{AC}=114V_{RMS}, C=1 nF, and R_{1}=560 kΩ.

**Figure 7** Empirical results are shown for V_{AC}=228V_{RMS}, C=1 nF, and R_{1}=560 kΩ.

Note that as with any device connected directly to the mains, exercise extreme caution while bench testing the circuit. Follow proper guidelines when laying out a printed circuit board.

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