4096 counts

One period, 4096 counts

The PCA9685 has one counter for all sixteen channels. It counts from 0 to 4095 once per period and starts again. Each channel holds two numbers: the count at which its output goes HIGH, and the count at which it goes LOW. For a servo the first is 0 and the second is the pulse width.

The counter's speed comes from the chip's 25 MHz oscillator divided by a prescaler. The datasheet's formula for it is:

prescale = round(25 000 000 / (4096 × frequency)) − 1

For 50 Hz that is 121. The period is then 20.0 ms (50.03 Hz), and one count is 122 / 25 MHz, about 4.88 µs. So:

writeMicroseconds() in the Adafruit library does exactly this division and writes the result. Between the two conventional ends there are about 205 steps.

One frequency for all sixteen

There is one prescaler, so every channel runs at the same frequency. The range is 24 Hz (prescale 255) to 1526 Hz (prescale 3). At power-up the prescaler is 30, which is 200 Hz.

The chip also powers up asleep, with its oscillator off, and the prescaler can only be changed while it sleeps. After waking it needs 500 µs before the outputs are right. The library's setPWMFreq() handles all three: sleep, write, wake, wait.

The number nobody can know for you

Every figure on this page assumed the oscillator runs at exactly 25 MHz. The datasheet says 25 MHz typical and gives no tolerance. If the chip runs fast or slow, every pulse on every channel is stretched or shrunk by the same ratio.

Adafruit's servo example passes 27 MHz to setOscillatorFrequency(). That is what Adafruit's example assumes, not a property of this board, and this book does not claim either number for yours. How far off it can matter: were a chip really at 27 MHz while the sketch assumed 25, a command of 1500 µs would come out at about 1390 µs.

Measuring your own chip

Set one channel to a known frequency and measure its period with an oscilloscope or a logic analyser, on the PWM pin and GND. Then:

oscillator = measured_Hz × 4096 × (prescale + 1)

Use the prescale the chip is actually running, which is 121 for a sketch that assumed 25 MHz and asked for 50 Hz. As an example, a reading of 53.0 Hz there means the oscillator is 53.0 × 4096 × 122, about 26.48 MHz. Put that number in the sketch's setOscillatorFrequency() and every channel is corrected at once.

Each chip has its own oscillator, so a board measured once keeps its number. Two boards in one project may need two.