ADCAndDAC < IoT_Course_English

---+ Exercise 9: Analogue to Digital (ADC) and Digital to Analogue (DAC) conversion
---++ Introduction

The ESP32 has two 12 bit SAR (<b>S</b>uccessive <b>A</b>pproximation <b>R</b>egister) <b>A</b>nalogue to <b>D</b>igital <b>C</b>onverters (ADCs) and two 8 bit <b>D</b>igital to <b>A</b>nalogue <b>C</b>onverters on chip. Checking for drivers in the !MicroPython manual I only find a [[https://docs.micropython.org/en/latest/esp32/quickref.html#adc-analog-to-digital-conversion][description of the ADC]]. Checking the !MicroPython source code however, I see that also the driver for the DACs is available.
---++ The ADC

ADC 2 is used for !WiFi and therefore not accessible to us. ADC 1 however has multiplexed input and 8 ADC channels are available for use (on Pins 32-39). The ADC has a range 0..1V but attenuators are available. If we set the attenuation to 11 DB we get a voltage range of approximately 0 .. 3.6 V. Pin 36 and pin 26 are available on the !WeMos D1 bus but pins on the ESP32 CPU card can also be used (e.g. pin 33, 34, 35).
---++ The DAC

The DACs are accessible on pins 25 and 26. Since there is no description in the manual, here is the way how to access the DAC:
<literal>&nbsp; from machine import Pin,DAC<br />from time import sleep_ms<br /><br />dac = DAC(Pin(26))<br />print("Running a triangular wave form with a frequency of ~ 1 Hz on pin 26")<br />while True:<br />&nbsp;&nbsp;&nbsp; for i in range(256):<br />&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; dac.write(i)<br />&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; sleep_ms(2)<br />&nbsp;&nbsp;&nbsp; for i in range(256):<br />&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; dac.write(256-i-1)<br />&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; sleep_ms(2)<br />&nbsp;&nbsp;&nbsp;</literal>

This will generate a slow triangular wave form that can be observed on a multi-meter.
---++ Checking linearity

If we connect the DAC output to the input of an ADC channel and we slowly ramp up the DAC value from 0 to its maximum and we read back the signal level with the ADC, then we expect a perfectly linear curve. This is true under the condition that both, the DAC and the ADC are perfectly linear.
| *linearity full range* | *linearity restricted range* |
| <img alt="linearity.png" height="598" src="%ATTACHURL%/linearity.png" title="linearity.png" width="662" /> | <img alt="restrictedLinearity.png" height="598" src="%ATTACHURL%/restrictedLinearity.png" title="restrictedLinearity.png" width="662" /> |
As we can see, the curve becomes very non-linear for values above 200 (3.3V * 200 / 256 ~ 2.6 V). Unfortunately we do not know if the ADC or the DAC is responsible for this non-linearity. We need an external ADC to check. We also see that the line does not pass though 0,0 as it should.
---++ Verifying linearity with an external ADS1115

The ADS1115 is a high precision 16 bit Sigma/Delta ADC with an !I2C interface. It can easily be connected to the !WeMos D1 bus as follows:
| ADS 1115 | !WeMos D1 bus and ESP32 | !WeMos D1 bus and ESP8266 |
| Vdd | 3.3V | 3.3V |
| Gnd | Gnd | Gnd |
| SCL | D1: GPIO 22 | D1: GPIO 5 |
| SDA | D2: GPIO 21 | D2: GPIO 4 |
| A0 | DAC 2: GPIO 26 | |
A driver !MicroPython driver for the ADS1115 is available making it very easy to perform the check: https://github.com/robert-hh/ads1x15. I copied the driver to /lib on the ESP32 using ampy and modified my ADC vs DAC program to use the ADS1115 instead of the ESP32 ADC. This is the result:

<img alt="linADS1115.png" height="598" src="%ATTACHURL%/linADS1115.png" title="linADS1115.png" width="662" />

Note the change in scale on the y axis. The ADS1115 is a 16 bit ADC while the ESP32 has only 12 bits. The maximum value on the y axis depends on the input voltage range selected.

This clearly shows that the ESP32 ADC is the culprit!
---++ Correcting the non-linearity

Now that we know that the DAC is nicely linear and it is the ADC introducing the non-linearity we can try to correct for it using our first DAC vs ADC measurement as calibration curve. If we can calculate the DAC value from the ADC output we can also calculate the corrected ADC value.

For this to work we must invert (replace x by y and vice versa) the function adc = y = f(x) where x is the DAC value. This is the function of the first plot. Then we fit a polynomial to the inverted curve and finally we use this polynomial to correct the values read from the ADC.

Here is a graph when fitting a polynomial of grade 5

<img alt="polynomial.png" height="55" src="%ATTACHURL%/polynomial.png" title="polynomial.png" width="277" />

<img alt="fit.png" height="596" src="%ATTACHURL%/fit.png" title="fit.png" width="660" />

The fit gives up the coefficients (a..e) of the polynomial and we can use this to correct for linearity. Instead of returning the raw ADC value we enter it into the polynomial and return the calculated value multiplied by 16 to get 0..4096 instead of 0..256.

Here is the DAC versus ADC measurement on the ESP32 ADC after correction:

<img alt="corrected.png" height="598" src="%ATTACHURL%/corrected.png" title="corrected.png" width="662" />

-- %USERSIG{UliRaich - 2020-07-26}%

---++ Comments

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Topic attachments
I	Attachment	History	Action	Size	Date	Who
png	corrected.png	r1	manage	37.6 K	2020-07-31 - 07:39	UliRaich
png	fit.png	r1	manage	31.7 K	2020-07-31 - 07:27	UliRaich
png	linADS1115.png	r1	manage	30.2 K	2020-07-30 - 13:30	UliRaich
png	linearity.png	r1	manage	31.6 K	2020-07-30 - 12:14	UliRaich
png	polynomial.png	r1	manage	3.5 K	2020-07-31 - 07:22	UliRaich
png	restrictedLinearity.png	r1	manage	29.2 K	2020-07-30 - 12:14	UliRaich
This topic: IoT_Course_English > WebHome > Exercises > ADCAndDAC
Topic revision: r4 - 2020-07-31 - UliRaich