#452 CD4046 Mains-Linked PLL

A 50/60Hz oscillator locked to mains power frequency using a CD4046 PLL.

Build

Notes

The CD4046 is common starting point for learning about phase-locked loops. It is essentially a “toolkit” chip, comprising independent sub-systems including:

two types of phase detector
VCO

My objective here is to learn a bit about designing PLLs using the edge-controlled phase comparator in the CD4046. To spice things up a bit, I’ll use the circuit to produce a square wave locked in phase and frequency to the mains power supply - 230V 50Hz at home, but the circuit will work for 60Hz and lower voltages too.

About PLLs

#60: Basics of Phase Locked Loop Circuits and Frequency Synthesis, w2aew:

Circuit Design

AC pulse detector produces a 5V signal input to the phase comparator
CD4046 Phase Comparator II, compares phase of the input signal to the VCO output
Low-pass Filter to smooth and dampen the comparator output to driver the VCO
CD4046 VCO
CD4011 NAND is used as an inverting buffer for the VCO output

Mains Interface / AC Pulse Detector

A 4N35 opto-coupler is used as essentially a half-wave rectifier to convert the AC input signal to a low-voltage pulse train approaching a square wave.

A simplistic approach is possible because I’m not trying to tap the mains supply to also power the digital circuit:

a series of resistors to drop the voltage and limit current to around 2mA
4N35 opto-coupler
reverse-polarity diode across the opto-coupler, so that it only activates on half the cycle

I’m using a 12V AC power supply for testing purposes. For this supply, the voltage is dropped across a single 10kΩ resistor and produces a strong 60% duty cycle output on the opto-coupler.

In the final build a mains connection has the voltage is dropped across ~200kΩ (3 x 68kΩ resistors in series). I don’t have datasheets for my 1/4W resistors, and I suspect they may be fine with ~230V. But putting 3 resistors in series reduces the voltage across each individual resistor, and protects against any failing closed circuit.

Note: with these resistor values, I am driving the opto-coupler resonably hard so it turns “on” close to when the AC signal cross the zero-point. However there is at least a diode drop and rise time involved that corresponds to some lag, and this cascades through the PLL. So while the PLL output signal will be “locked” to the AC signal, it does have a fixed but non-zero phase offset that I haven’t designed out of the system.

Phase Comparator

CD4046 Phase Comparator II is used, which produces a tri-state output:

high when signal is leading the VCO output / comparator in
high impedance when signal is in phase with VCO output / comparator in
low when signal is lagging the VCO output / comparator in

VCO Configuration

VCO frequency range is controlled with the combination of C1, R1 amd R2.

R2 is left disconnected/high impedance, which sets the minimum frequency to 0 Hz.

Figure 5 in the CD4046 datasheet provides a rough guide for selecting C1 and R1. I chose C1 = 100nF and R1 = 100kΩ, which should correspond to a centre frequency of around 100Hz.

In practice, the range is 0 Hz to 166Hz. That’s a reasonable range for covering mains frequencies, expected to be 50/60Hz.

Some measurements to determine the actual VCO gain:

VCOin	Frequency
4.96 V	165.5 Hz
3.2 V	99.5 Hz
2.0 V	49.1 Hz

So very roughly a VCO gain, KVCO, of 247 radians/sec/volt.

Low-pass Filter

OK, this gets interesting and math-heavy. The CD4046 is notorious for not having a straight-forward LP filter configuration, especially with Phase Comparator II.

In section 9.29 of the Art of Electronics, there is a design example that I’m still trying to pull apart.

My design thinking so far:

Low-pass filter comprises C2, R3 and R4:

R3C2 time constant drives the response time (smoothing)
R4/R3 ratio influences the dampending

Given a 50 to 60 Hz mains frequency, choosing LP unity gain of around 2 Hz.

Choosing C2 = 2.2 µF and R4 = 220kΩ, zero/breakpoint of the LP filter is around 2πR4C2 = 0.33Hz

Using a starting guide that suggests R3 ~= 5 * R4, I choose R3 = 1MΩ.

So while I don’t have the full rigorous derivation of the filter, these component values turned out to produce a well-locked VCO signal that is stable and relatively immune to noise.