Exploring the Cosine Wave Generator of the ESP32

1. Motivation

While browsing the extensive Technical Reference Manual for the ESP32, I came across the description of the Cosine Wave Generator. The many registers and cryptic designators soon put me off, but I thought surely someone had already done the hard work. The works of Krzysztof and Helmut were quickly found and these are therefore the basis for my contribution.

I packed up all the ideas and designed the CosineWaveGenerator (CWG) class and a simple command line interface (CLI) to explore the generator's capabilities.

2. Specification

3. Some Formulas

The frequency of the CWG depends on the operating frequency of the microcontroller and the contents of two registers. The common output frequency of both DAC channels is given by the formula:

  freq = dig_clk_rtc_freq / (1 + RTC_CNTL_CK8M_DIV_SEL) * SENS_SAR_SW_FSTEP / 65536
  dig_clk_rtc_freq = 8'000'000 Hz (assumed operating freq, no need to know it exactly, see below)
  SENS_SAR_SW_FSTEP     = 1..65535 (0x0001..0xffff) 

  If we set 
      SENS_SAR_SW_FSTEP     = 1
  we get      
      f0 = dig_clk_rtc_freq / 65536
  and with
      dig_clk_rtc_freq = 8000000
  we find
       f0 = 122.0703125 

If we measure another frequency, the operating frequency of our microcontroller is not exactly 8 MHz. Thats why we must first set the reference frequency f0 to our measured value.

4. User interface (CLI) and Operation

The user interface is a simple command line interface. The menu items are self-explanatory.

Command line interface

If we set a frequency of 200 Hz by pressing "b" and entering the value, we get the following output:

Setting 200 Hz with tolerance 10 ‰

The exact Frequency of 200 Hz cannot be set and the specified tolerance of 10 ‰ cannot be kept. Therefore, the best approximation is set and the found values are displayed.

Now we change the tolerance by pressing "t" and entering 20 followed by pressing "b" again and entering 200.

Setting 200 Hz with tolerance 20 ‰

We see that the best approximation is 203 Hz and that this frequency is also within the given tolerance.

Now we set a higher frequency, namely 50000 Hz. Afterwards we also press "p" to output the set values.

Setting 50000 Hz and pressing "p"

We see that with a divisor of 6, a deviation of only 2 HZ can be achieved. However, because a tolerance of 20% is acceptable, the smallest divisor is used to obtain the smoothest possible curve shape.

Let's have a look at the different modes of the two output channels.

CHN_1 in Mode 0, CHN_2 in Mode 1"

For the hobbyist, the two sinusoidal modes will probably be most useful.

CHN_1 in Mode 2, CHN_2 in Mode 3"

4. Program Code

The main program, is quite simple. Here only the menu structure and the main loop is shown, which consists only of the call to doMenu() if a character was entered on the serial interface.

  typedef struct { const char key; const char *txt; void (&action)(); } MenuItem;

  MenuItem menu[] = 
    { 'r', "[r] Set reference frequency f0",    setReferenceFrequency },
    { 'c', "[c] Toggle CHN_1 on/off",           toggleChannel1 },
    { 'C', "[C] Toggle CHN_2 on/off",           toggleChannel2 },
    { 'd', "[d] Set clock divisor 0..7",        setDivisor },
    { 's', "[s] Set step 1..65535",             setStep },
    { 'f', "[f] Set frequenz with set divisor", setFrequencyWithSetDivisor },
    { 'F', "[F] Set frequenz with set step",    setFrequencyWithSetStep },
    { 'b', "[b] Set frequency best match with set tolerance", setFrequencyBestMatch },
    { 't', "[t] Set tolerance for best match (1..999 °/oo)", setTolerance },
    { 'm', "[m] Set CHN_1 mode 0..3",           setMode1 },
    { 'M', "[M] Set CHN_2 mode 0..3",           setMode2 },
    { 'a', "[a] Set CHN_1 amplitude 0..3",      setScale1 },
    { 'A', "[A] Set CHN_2 amplitude 0..3",      setScale2 },  
    { 'o', "[o] Set CHN_1 offset 0..255",       setOffset1 },
    { 'O', "[o] Set CHN_2 offset 0..255",       setOffset2 },
    { 'p', "[p] Print current values",          printCurrentValues },
    { 'S', "[S] Show Menu",                     showMenu }
  constexpr uint8_t nbrMenuItems = sizeof(menu) / sizeof(menu[0]);
  void doMenu()
    char key = Serial.read();
    for (int i = 0; i < nbrMenuItems; i++)
      if (key == menu[i].key)

  void setup() 

  void loop() 

Interested? Please download the entire program code. The zip-file contains the complete PlatformIO project.

My programming environment is not the native Arduino™ IDE but PlatformIO™ on top of Microsoft's Visual Studio Code™. This combination offers many advantages and allows a much better structuring of the code into several modules especially when we adopt The Object Oriented way.