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Sigma-Delta Modulation (SDM)

Introduction

{IDF_TARGET_NAME} has a second-order sigma-delta modulator, which can generate independent PDM pulses to multiple channels. Please refer to the TRM to check how many hardware channels are available. [1]

Delta-sigma modulation converts an analog voltage signal into a pulse frequency, or pulse density, which can be understood as pulse-density modulation (PDM) (refer to Delta-sigma modulation on Wikipedia).

The main differences comparing to the PDM in I2S peripheral and DAC are:

  1. SDM has no clock signal, it just like the DAC mode of PDM;
  2. SDM has no DMA, and it can't change its output density continuously. If you have to, you can update the density in a timer's callback;
  3. Base on the former two points, an external active or passive filter is required to restore the analog wave (See :ref:`convert_to_analog_signal`);

Typically, a Sigma-Delta modulated channel can be used in scenarios like:

  • LED dimming
  • Simple DAC (8-bit), with the help of an active RC low-pass filter
  • Class D amplifier, with the help of a half-bridge or full-bridge circuit plus an LC low-pass filter

Functional Overview

The following sections of this document cover the typical steps to install and operate a SDM channel:

  • Resource Allocation - covers which parameters should be set up to get a channel handle and how to recycle the resources when it finishes working.
  • Enable and Disable Channel - covers how to enable and disable the channel.
  • Set Equivalent Duty Cycle - describes how to set the equivalent duty cycle of the PDM pulses.
  • Power Management - describes how different source clock selections can affect power consumption.
  • IRAM Safe - lists which functions are supposed to work even when the cache is disabled.
  • Thread Safety - lists which APIs are guaranteed to be thread safe by the driver.
  • Kconfig Options - lists the supported Kconfig options that can be used to make a different effect on driver behavior.

Resource Allocation

A SDM channel is represented by :cpp:type:`sdm_channel_handle_t`. Each channel is capable to output the binary, hardware generated signal with the sigma-delta modulation. The driver manages all available channels in a pool, so that users don't need to manually assign a fixed channel to a GPIO.

To install a SDM channel, you should call :cpp:func:`sdm_new_channel` to get a channel handle. Channel specific configurations are passed in the :cpp:type:`sdm_config_t` structure:

The function :cpp:func:`sdm_new_channel` can fail due to various errors such as insufficient memory, invalid arguments, etc. Specifically, when there are no more free channels (i.e. all hardware SDM channels have been used up), then :c:macro:`ESP_ERR_NOT_FOUND` will be returned.

If a previously created SDM channel is no longer required, you should recycle it by calling :cpp:func:`sdm_del_channel`. It allows the underlying HW channel to be used for other purposes. Before deleting a SDM channel handle, you should disable it by :cpp:func:`sdm_channel_disable` in advance or make sure it has not enabled yet by :cpp:func:`sdm_channel_enable`.

Creating a SDM Channel with Sample Rate of 1MHz

 sdm_channel_handle_t chan = NULL;
 sdm_config_t config = {
     .clk_src = SDM_CLK_SRC_DEFAULT,
     .sample_rate_hz = 1 * 1000 * 1000,
     .gpio_num = 0,
 };
ESP_ERROR_CHECK(sdm_new_channel(&config, &chan));

Enable and Disable Channel

Before doing further IO control to the SDM channel, you should enable it first, by calling :cpp:func:`sdm_channel_enable`. Internally, this function will:

  • switch the channel state from init to enable
  • acquire a proper power management lock is a specific clock source (e.g. APB clock) is selected. See also Power management for more information.

On the contrary, calling :cpp:func:`sdm_channel_disable` will do the opposite, that is, put the channel back to the init state and release the power management lock.

Set Pulse Density

For the output PDM signals, the pulse density decides the output analog voltage that restored by a low-pass filter. The restored analog voltage from the channel is calculated by Vout = VDD_IO / 256 * duty + VDD_IO / 2. The range of the quantized density input parameter of :cpp:func:`sdm_channel_set_pulse_density` is from -128 to 127 (eight-bit signed integer). For example, if a zero value is set, then the output signal's duty will be around 50%.

Power Management

When power management is enabled (i.e. :ref:`CONFIG_PM_ENABLE` is on), the system will adjust the APB frequency before going into light sleep, thus potentially changing the sample rate of the sigma-delta modulator.

However, the driver can prevent the system from changing APB frequency by acquiring a power management lock of type :cpp:enumerator:`ESP_PM_APB_FREQ_MAX`. Whenever the driver creates a SDM channel instance that has selected :cpp:enumerator:`SDM_CLK_SRC_APB` as its clock source, the driver will guarantee that the power management lock is acquired when enable the channel by :cpp:func:`sdm_channel_enable`. Likewise, the driver releases the lock when :cpp:func:`sdm_channel_disable` is called for that channel.

IRAM Safe

There's a Kconfig option :ref:`CONFIG_SDM_CTRL_FUNC_IN_IRAM` that can put commonly used IO control functions into IRAM as well. So that these functions can also be executable when the cache is disabled. These IO control functions are listed as follows:

Thread Safety

The factory function :cpp:func:`sdm_new_channel` is guaranteed to be thread safe by the driver, which means, user can call it from different RTOS tasks without protection by extra locks. The following functions are allowed to run under ISR context, the driver uses a critical section to prevent them being called concurrently in both task and ISR.

Other functions that take the :cpp:type:`sdm_channel_handle_t` as the first positional parameter, are not treated as thread safe. Which means the user should avoid calling them from multiple tasks.

Kconfig Options

Convert to analog signal (Optional)

Typically, if the sigma-delta signal is connected to an LED, you don't have to add any filter between them (because our eyes are a low pass filter naturally). However, if you want to check the real voltage or watch the analog waveform, you need to design an analog low pass filter. Also, it is recommended to use an active filter instead of a passive filter to gain better isolation and not lose too much voltage.

For example, you can take the following Sallen-Key topology Low Pass Filter as a reference.

Sallen-Key Low Pass Filter

Sallen-Key Low Pass Filter

Application Example

API Reference

.. include-build-file:: inc/sdm.inc

.. include-build-file:: inc/sdm_types.inc
[1]Different ESP chip series might have different numbers of SDM channels. Please refer to Chapter GPIO and IOMUX in {IDF_TARGET_NAME} Technical Reference Manual for more details. The driver won't forbid you from applying for more channels, but it will return error when all available hardware resources are used up. Please always check the return value when doing resource allocation (e.g. :cpp:func:`sdm_new_channel`).