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Sigma-Delta Modulation (SDM)

:link_to_translation:zh_CN:[中文]

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 I2S PDM mode and DAC peripheral are:

  1. SDM has no clock signal, it is just like the DAC mode of PDM;
  2. SDM has no DMA, and it can not change its output density continuously. If you have to, you can update the density in a timer's callback;
  3. Based on the former two points, unlike the DAC peripheral, an external active or passive low-pass filter is required additionally to restore the analog wave (See 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 an SDM channel:

  • sdm-resource-allocation - covers how to initialize and configure an SDM channel and how to recycle the resources when it finishes working.
  • sdm-enable-and-disable-channel - covers how to enable and disable the channel.
  • sdm-set-equivalent-duty-cycle - describes how to set the equivalent duty cycle of the PDM pulses.
  • sdm-power-management - describes how different source clock selections can affect power consumption.
  • sdm-iram-safe - lists which functions are supposed to work even when the cache is disabled.
  • sdm-thread-safety - lists which APIs are guaranteed to be thread-safe by the driver.
  • sdm-kconfig-options - lists the supported Kconfig options that can be used to make a different effect on driver behavior.

Resource Allocation

In ESP-IDF, the information and attributes of SDM channels are managed and accessed through specific data structures, where the data structure is called :cppsdm_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 there is no need to manually assign a fixed channel to a GPIO.

To install an SDM channel, you should call :cppsdm_new_channel to get a channel handle. Channel-specific configurations are passed in the :cppsdm_config_t structure:

  • :cppsdm_config_t::gpio_num sets the GPIO that the PDM pulses output from.
  • :cppsdm_config_t::clk_src selects the source clock for the SDM module. Note that, all channels should select the same clock source.
  • :cppsdm_config_t::sample_rate_hz sets the sample rate of the SDM module.
  • :cppsdm_config_t::invert_out sets whether to invert the output signal.
  • :cppsdm_config_t::io_loop_back is for debugging purposes only. It enables both the GPIO's input and output ability through the GPIO matrix peripheral.

The function :cppsdm_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), :cESP_ERR_NOT_FOUND will be returned.

If a previously created SDM channel is no longer required, you should recycle it by calling :cppsdm_del_channel. It allows the underlying HW channel to be used for other purposes. Before deleting an SDM channel handle, you should disable it by :cppsdm_channel_disable in advance or make sure it has not been enabled yet by :cppsdm_channel_enable.

Creating an SDM Channel with a Sample Rate of 1 MHz

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 :cppsdm_channel_enable. Internally, this function:

  • switches the channel state from init to enable
  • acquires a proper power management lock if a specific clock source (e.g., APB clock) is selected. See also sdm-power-management for more information.

On the contrary, calling :cppsdm_channel_disable does the opposite, that is, put the channel back to the init state and releases the power management lock.

Set Pulse Density

For the output PDM signals, the pulse density decides the output analog voltage that is 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 :cppsdm_channel_set_pulse_density is from -128 to 127 (8-bit signed integer). Depending on the value of the density parameter, the duty cycle of the output signal will be changed accordingly. 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., 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 :cppESP_PM_APB_FREQ_MAX. Whenever the driver creates an SDM channel instance that has selected :cppSDM_CLK_SRC_APB as its clock source, the driver guarantees that the power management lock is acquired when enabling the channel by :cppsdm_channel_enable. Likewise, the driver releases the lock when :cppsdm_channel_disable is called for that channel.

IRAM Safe

There is a Kconfig option 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:

  • :cppsdm_channel_set_pulse_density

Thread Safety

The factory function :cppsdm_new_channel is guaranteed to be thread-safe by the driver, which means, the 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.

  • :cppsdm_channel_set_pulse_density

Other functions that take the :cppsdm_channel_handle_t as the first positional parameter, are not treated as thread-safe. This means the user should avoid calling them from multiple tasks.

Kconfig Options

  • CONFIG_SDM_CTRL_FUNC_IN_IRAM controls where to place the SDM channel control functions (IRAM or Flash), see sdm-iram-safe for more information.
  • CONFIG_SDM_ENABLE_DEBUG_LOG is used to enable the debug log output. Enabling this option increases the firmware binary size.

Convert to an Analog Signal (Optional)

Typically, if a Sigma-Delta signal is connected to an LED to adjust the brightness, you do not have to add any filter between them, because our eyes have their own low-pass filters for changes in light intensity. 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

  • 100 Hz sine wave that is modulated with Sigma-Delta: peripherals/sigma_delta/sdm_dac.
  • LED driven by a GPIO that is modulated with Sigma-Delta: peripherals/sigma_delta/sdm_led.

API Reference

inc/sdm.inc

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 does not forbid you from applying for more channels, but it will return an error when all available hardware resources are used up. Please always check the return value when doing resource allocation (e.g., :cppsdm_new_channel).↩