Working

Before going into further detail, let’s first define what base signal should be generated and repeated by the PWM peripheral. Consider the signal shown in the figure below.

Following variables define the base signal,

• $t_H$ is the time period of the base signal for which the signal is HIGH.
• $t_L$ is the time period of the base signal for which the signal is LOW.
• $p = t_H + t_L$ represents the time period of the base signal. The inverse of $p$, i.e. $1/p$, is the frequency of the PWM signal, $f_{PWM}$.
• The ratio of $t_H$ to $p$ is known as the duty cycle, $D = \frac{t_H}{p} \cdot 100\% $

Most of the PWM peripheral implementations allow the configuration of the base signal through 3 values. For the RP2040 μC, the three values are called

• Clock Divider value, DIV
• Counter Wrap value, TOP
• Counter Compare value, CC

The terminology might be slightly different in each μC’s datasheet although the operation is pretty similar.

Clock Divider Value DIV

As discussed previously, every μC relies on a clock signal, referred to as system clock in this section, to function correctly. The clock signal frequency for RP2040 is set to 125MHz by default. The Clock Divider in PWM peripheral takes in this high frequency signal and divides it with a certain number to generate a lower frequency signal, referred to as frequency divided clock in this section. This number is the DIV value that can be specified through software. For RP2040, this value is split into an 8-bit integer part, $1 \leq$DIVi$\leq 255$, and a 4-bit fractional part, $0 \leq$DIVf$\leq 15$. Thus, the DIV value is defined as

\[\begin{equation*} \mathtt{DIV} = \mathtt{DIV}_{\mathtt{i}} + \frac{\mathtt{DIV}_{\mathtt{f}}}{16} \leq 255 \frac{15}{16} \end{equation*}\]

And, the frequency of the output clock is

\[\begin{equation*} f_{div} = \frac{f_{sys}}{\mathtt{DIV}_{\mathtt{i}} + \frac{\mathtt{DIV}_{\mathtt{f}}}{16}} \end{equation*}\]

Let’s take an example. Following animation show the output signal from the clock divider if the integer part is set to 7 and the fractional part is set to 9. Basically, 7.5625 cycles of the system clock make one cycle of the frequency divided clock.

Clock
Divider
7⁹⁄₁₆

Counter Wrap Value TOP

The number of cycles, of the frequency divided clock, generated by the clock divider is counted and stored as a CTR value. However, this value can only reach TOP value, after which the CTR value falls back to 0 and starts increasing again.

CTR

≤

TOP

It takes one clock cycle for the `CTR` value to fall back to 0.

The time it takes for the CTR value to start from 0, reach the TOP value, and then fall back to 0, is the time period $p$ of the PWM base signal. It can be defined as

\[\begin{equation*} p = \frac{\mathtt{TOP} + 1}{f_{div}} \end{equation*}\]

The TOP value is a 16-bit number, i.e. 0 $\leq$ TOP $\leq$ 65535.

Counter Compare Value CC

Now that the time period of the base signal is defined, all that is remaining is to define for how long the signal will be HIGH or LOW. This is done using the counter compare value. The GPIO, that is being controlled by the PWM peripheral, is set to HIGH when the CTR value starts increasing from 0. This HIGH state is maintained until the CTR value becomes equal to the CC value. The GPIO is set to LOW when this happens.

CC

CTR

TOP

This defines both the duty cycle, $D$, and the HIGH time, $t_H$, of the base signal as given below

\[\begin{gather*} D = \frac{\mathtt{CC}}{\mathtt{TOP} + 1} \cdot 100\% \\ t_H = \frac{\mathtt{CC}}{f_{sys}} \cdot \mathtt{DIV} \end{gather*}\]

The CC value is also a 16-bit number, i.e. $0 \leq$ CC $\leq 65535$. Also note that if CC is 0 then the PWM output is always LOW and if CC > TOP then the PWM output is always HIGH.

Next

hardware_pwm Library Functions

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