From db876151d61298b092524050743c92a4b5ffdedd Mon Sep 17 00:00:00 2001
From: Leon Krieg <info@madcow.dev>
Date: Fri, 20 Sep 2024 01:07:31 +0200
Subject: [PATCH] Implement alternate voltage divider equation

---
 src/bus/i2c.c     |  2 +-
 src/common/math.c | 62 ++++++++++++++++++++++++++++++++---------------
 2 files changed, 44 insertions(+), 20 deletions(-)

diff --git a/src/bus/i2c.c b/src/bus/i2c.c
index e5764ee..9e76913 100644
--- a/src/bus/i2c.c
+++ b/src/bus/i2c.c
@@ -525,7 +525,7 @@ word I2C_ADS1115_ReadRaw(int channel)
 	// 110  |  ±0.256 V
 	// 111  |  ±0.256 V
 
-	gain = 0x0000; // 6.144 V      |  00000100 00000000
+	gain = 0x0000; // 6.144 V      |  00000000 00000000
 
 	// Input multiplexer configuration: These bits
 	// configure the input multiplexer.
diff --git a/src/common/math.c b/src/common/math.c
index e6a2a07..6d3073d 100644
--- a/src/common/math.c
+++ b/src/common/math.c
@@ -2,41 +2,62 @@
 
 #include <math.h>
 
+// https://www.sciencedirect.com/science/article/abs/pii/S0263224111002594
 // https://en.wikipedia.org/wiki/Steinhart%E2%80%93Hart_equation
 // https://onlinelibrary.wiley.com/doi/abs/10.1002/andp.18280890511
 // https://onlinelibrary.wiley.com/doi/abs/10.1002/andp.18441370202
 // https://bmcnoldy.earth.miami.edu/Humidity.html
 
-// TODO: Is resistance function semantically correct?
-// TODO: Check results for humidity conversion functions.
-
 // Thermistor general constants
-#define R1    10000.0f  // Resistor ohm value
-#define VRES  0xFFFF    // 16-bit ADC resolution
+#define VIN   5.0f    // Source voltage (VCC)
+#define GAIN  6.144f  // PGA gain setting 0x00
+#define AMAX  0x7FFF  // 16-bit ADC resolution
+#define R1    10000   // 10k Ohm resistor
 
 // Thermistor coeficients
-#define SC1  1.009249522e-3f
-#define SC2  2.378405444e-4f
-#define SC3  2.019202697e-7f
+#define SC1   1.009249522e-3f
+#define SC2   2.378405444e-4f
+#define SC3   2.019202697e-7f
 
-// Humidity conversion constants
-#define TH1  100.0f
-#define TH2  243.04f
-#define TH3  17.625f
+// Conversion constants
+#define TH1   100.0f
+#define TH2   243.04f
+#define TH3   17.625f
 
 float Resistance(int adc_raw)
 {
-	float r2;
+	float av, r2;
 
-	// TODO: Improve readability.
-	// TODO: Make sure output is correct.
+	// [GND] - [10K R] - [ADC IN] - [THERMISTOR] - [VCC]
 
-	// [GND] - [10K RESISTOR] - [ADC INPUT] - [THERMISTOR] - [VCC]
+	// The ADC measurement is taken between a 10k Ohm
+	// resistor and the thermistor. This is also called
+	// a voltage divider circuit which has the following
+	// equation:
 
-	// return ((VRES - adc_raw) * R1) / adc_raw;
-	r2 = (float) adc_raw / 264.8f * 0.05f;
+	// Vout = Vin * (R2 / R1 + R2)
 
-	return R1 / (5.0f / r2 - 1.0f);
+	// We can solve for resistance R2 by rearranging and
+	// simplifying the equation:
+
+	// R2 = R1 / (Vin / Vout - 1)
+
+	// If the ADC reference voltage and voltage divider
+	// source voltage (Vin) are the same, then the
+	// following is true:
+
+	// Vin / Vout = AMAX / AV
+
+	// This means the ratio of voltage divider input
+	// voltage to output voltage is the same as the ratio
+	// of the ADC full range value (AMAX) to the value
+	// returned by the ADC (AV). For a 16 bit ADC like
+	// the ADS1115 the AMAX is 0x7FFF.
+
+	av = adc_raw * (GAIN / VIN);
+	r2 = R1 / (AMAX / av - 1.0f);
+
+	return r2;
 }
 
 float SteinhartHart(float res)
@@ -45,6 +66,9 @@ float SteinhartHart(float res)
 
 	// Convert resistance to temperature
 
+	// When the temperature increases, NTC thermistor
+	// resistance will decrease:
+
 	//  25C = 10000 Ohms
 	// 100C =  6744 Ohms