# Sigma-Delta Modulation (SDM)

[中文]

## Introduction

ESP32-S2 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).

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:

- Resource Allocation - covers how to initialize and configure an SDM channel and how to recycle the resources when it finishes working.

- Enable and Disable Channel - covers how to enable and disable the channel.

- Set Pulse Density - 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

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

To install an SDM channel, you should call `sdm_new_channel()` to get a channel handle. Channel-specific configurations are passed in the `sdm_config_t` structure:

- `sdm_config_t::gpio_num` sets the GPIO that the PDM pulses output from.

- `sdm_config_t::clk_src` selects the source clock for the SDM module. Note that, all channels should select the same clock source.

- `sdm_config_t::sample_rate_hz` sets the sample rate of the SDM module. A higher sample rate can help to output signals with higher SNR (Signal to Noise Ratio), and easier to restore the original signal after the filter.

- `sdm_config_t::invert_out` sets whether to invert the output signal.

The function `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), `ESP_ERR_NOT_FOUND` will be returned.

If a previously created SDM channel is no longer required, you should recycle it by calling `sdm_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 `sdm_channel_disable()` in advance or make sure it has not been enabled yet by `sdm_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 `sdm_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 Power Management for more information.

On the contrary, calling `sdm_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 `sdm_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 `ESP_PM_APB_FREQ_MAX`. Whenever the driver creates an SDM channel instance that has selected `SDM_CLK_SRC_APB` as its clock source, the driver guarantees that the power management lock is acquired when enabling the channel by `sdm_channel_enable()`. Likewise, the driver releases the lock when `sdm_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:

- `sdm_channel_set_pulse_density()`

### Thread Safety

The driver uses critical sections to ensure atomic operations on registers. Key members in the driver handle are also protected by critical sections. The driver's internal state machine uses atomic instructions to ensure thread safety, with state checks preventing certain invalid concurrent operations (e.g., conflicts between enable and delete). Therefore, SDM driver APIs can be used in a multi-threaded environment without extra locking.

The following functions can also be used in an interrupt context:

- `sdm_channel_set_pulse_density()`

### Kconfig Options

- CONFIG_SDM_CTRL_FUNC_IN_IRAM controls where to place the SDM channel control functions (IRAM or Flash), see 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

(Refer to peripherals/sigma_delta/sdm_dac/README.md to see the waveforms before and after filtering.)

## Application Examples

- peripherals/sigma_delta/sdm_dac demonstrates how to use the sigma-delta driver to act as an 8-bit DAC, and output a 100 Hz sine wave.

- peripherals/sigma_delta/sdm_led demonstrates how to use the sigma-delta driver to control the brightness of an LED or LCD backlight.

## API Reference

### Header File

- components/esp_driver_sdm/include/driver/sdm.h

- This header file can be included with:

  >     #include "driver/sdm.h"

- This header file is a part of the API provided by the `esp_driver_sdm` component. To declare that your component depends on `esp_driver_sdm`, add the following to your CMakeLists.txt:

  >     REQUIRES esp_driver_sdm

  > or

  >     PRIV_REQUIRES esp_driver_sdm

### Functions

esp_err_t sdm_new_channel(const sdm_config_t *config, sdm_channel_handle_t *ret_chan)

  Create a new Sigma Delta channel.

  Parameters:

    - config -- [in] SDM configuration

    - ret_chan -- [out] Returned SDM channel handle

  Returns:

    - ESP_OK: Create SDM channel successfully

    - ESP_ERR_INVALID_ARG: Create SDM channel failed because of invalid argument

    - ESP_ERR_NO_MEM: Create SDM channel failed because out of memory

    - ESP_ERR_NOT_FOUND: Create SDM channel failed because all channels are used up and no more free one

    - ESP_FAIL: Create SDM channel failed because of other error

esp_err_t sdm_del_channel(sdm_channel_handle_t chan)

  Delete the Sigma Delta channel.

  Parameters:

    chan -- [in] SDM channel created by `sdm_new_channel`

  Returns:

    - ESP_OK: Delete the SDM channel successfully

    - ESP_ERR_INVALID_ARG: Delete the SDM channel failed because of invalid argument

    - ESP_ERR_INVALID_STATE: Delete the SDM channel failed because the channel is not in init state

    - ESP_FAIL: Delete the SDM channel failed because of other error

esp_err_t sdm_channel_enable(sdm_channel_handle_t chan)

  Enable the Sigma Delta channel.

  Note

  This function will transit the channel state from init to enable.

  Note

  This function will acquire a PM lock, if a specific source clock (e.g. APB) is selected in the `sdm_config_t`, while `CONFIG_PM_ENABLE` is enabled.

  Parameters:

    chan -- [in] SDM channel created by `sdm_new_channel`

  Returns:

    - ESP_OK: Enable SDM channel successfully

    - ESP_ERR_INVALID_ARG: Enable SDM channel failed because of invalid argument

    - ESP_ERR_INVALID_STATE: Enable SDM channel failed because the channel is already enabled

    - ESP_FAIL: Enable SDM channel failed because of other error

esp_err_t sdm_channel_disable(sdm_channel_handle_t chan)

  Disable the Sigma Delta channel.

  Note

  This function will do the opposite work to the `sdm_channel_enable()`

  Parameters:

    chan -- [in] SDM channel created by `sdm_new_channel`

  Returns:

    - ESP_OK: Disable SDM channel successfully

    - ESP_ERR_INVALID_ARG: Disable SDM channel failed because of invalid argument

    - ESP_ERR_INVALID_STATE: Disable SDM channel failed because the channel is not enabled yet

    - ESP_FAIL: Disable SDM channel failed because of other error

esp_err_t sdm_channel_set_pulse_density(sdm_channel_handle_t chan, int8_t density)

  Set the pulse density of the PDM output signal.

  Note

  The raw output signal requires a low-pass filter to restore it into analog voltage, the restored analog output voltage could be Vout = VDD_IO / 256 * density + VDD_IO / 2

  Note

  This function is allowed to run within ISR context

  Note

  This function will be placed into IRAM if `CONFIG_SDM_CTRL_FUNC_IN_IRAM` is on, so that it's allowed to be executed when Cache is disabled

  Parameters:

    - chan -- [in] SDM channel created by `sdm_new_channel`

    - density -- [in] Quantized pulse density of the PDM output signal, ranges from -128 to 127. But the range of [-90, 90] can provide a better randomness.

  Returns:

    - ESP_OK: Set pulse density successfully

    - ESP_ERR_INVALID_ARG: Set pulse density failed because of invalid argument

    - ESP_FAIL: Set pulse density failed because of other error

### Structures

struct sdm_config_t

  Sigma Delta channel configuration.

  Public Members

  gpio_num_t gpio_num

    GPIO number

  sdm_clock_source_t clk_src

    Clock source

  uint32_t sample_rate_hz

    Over sample rate in Hz, it determines the frequency of the carrier pulses

  uint32_t invert_out

    Whether to invert the output signal

  uint32_t allow_pd

    If set, driver allows the power domain to be powered off when system enters sleep mode. This can save power, but at the expense of more RAM being consumed to save register context.

  struct sdm_config_t flags

    Extra flags

### Type Definitions

typedef struct sdm_channel_t *sdm_channel_handle_t

  Type of Sigma Delta channel handle.

### Header File

- components/esp_hal_gpio/include/hal/sdm_types.h

- This header file can be included with:

  >     #include "hal/sdm_types.h"

- This header file is a part of the API provided by the `esp_hal_gpio` component. To declare that your component depends on `esp_hal_gpio`, add the following to your CMakeLists.txt:

  >     REQUIRES esp_hal_gpio

  > or

  >     PRIV_REQUIRES esp_hal_gpio

### Type Definitions

typedef soc_periph_sdm_clk_src_t sdm_clock_source_t

[1]

Different ESP chip series might have different numbers of SDM channels. Please refer to Chapter GPIO and IOMUX in ESP32-S2 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., `sdm_new_channel()`).

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