# Simple circuit suits quadrature detection

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**Originally published in the August 22, 1985, issue of**

*EDN*

The circuit in **Figure 1** generates
an output voltage that you can
measure to determine whether two sine
waves have a quadrature relationship. If
the output voltage is 0V, the inputs (ϕ1
and ϕ2) are exactly in quadrature. If the
inputs are other than 90° out of phase,
a dc voltage appears at the circuit’s output. The voltage is proportional to the
number of degrees that the input signals
are out of quadrature. The polarity of
the voltage is positive for phase angles
of less than 90° and negative for angles
of greater than 90°.

The signals **A** and **B** in **Figure 2**
are in quadrature. When **A**’s signal
is applied to the ϕ1 input, a bilateral
CMOS switch turns on during the
positive half cycle and turns off during
the negative half cycle. If **B**’s signal is
applied to ϕ2 simultaneously, an output
similar to that of **C** appears at pin 2.
Note that the areas above and below
ground are equal. The integrating network,
R_{5}C_{1} in **Figure 1**, produces a net
voltage of 0V.

If the phase angle is >90°, the area
above ground is larger than the area
below ground, and
the output voltage
is positive (**D**). If
the phase angle
is <90°, a negative
output voltage
results (**E**). If the 4016 triggers at a value other than 0V,
the detector’s accuracy will not change.

R_{3}, D_{1}, and D_{2} provide input protection
for the IC. The performance
of the R_{4}/R_{5}/C_{1} integrator depends on
the frequency of the input signals and
the impedance of the network at pin
1. If you choose 8.2 kΩ for R_{1} and 2.2
kΩ for R_{2}, the values 8.2Ω, 4.7 kΩ, and
3.2 μF for R_{4}, R_{5}, and C_{1}, respectively,
yield good performance at 25 kHz. These
values will accommodate a 24V p-p
swing at the ϕ2 input. The values of V_{DD}
and V_{SS} must be large enough to accommodate
the input swings at the 4016. For
example, an input swing of ±3V would
call for 5V for V_{DD} and −5V for V_{SS}.

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