Fading LEDs with sine wave
Hi everybody,
the purpose of this post is to explain a simple technique concerning LED fading.
One common issue in fading a LED is blocking the execution of the loop() in a for loop as long as it performs the fading.
void loop() { // fade in from min to max in increments of 5 points: for (int fadeValue = 0 ; fadeValue <= 255; fadeValue += 5) { // sets the value (range from 0 to 255): analogWrite(ledPin, fadeValue); // wait for 30 milliseconds to see the dimming effect delay(30); }This approach wastes a lot of resources since the microcontroller can only perform this action until the execution goes on after the for loop.
One possibile solution is to drive LED fading with a sin/cos wave.
This means that at each iteration a harmonic oscillator value is assigned to the LED.The simple harmonic oscillator equation is:
So, we basically need the amplitude A, ω the angular frequency
and finally the optional φ which determines the starting point on the sine wave.
Let’s take a common cos wave shown below.
Cosine wave
This function oscillates in range [-1;1]. To perform a complete LED fading we need to simply modify our cos wave to our purpose.
Arduino’s output is always between [0;255] (256 values); for this reason we need a cos wave that start at 128 and oscillates oscillates between 1 and 255 to get a reasonable range (128±127).
The picture below shows y=128+127cos(x), which is the starting point to create our harmonic oscillator.
The OFFSET 128 shifts my cos wave from 0 to 128 and the AMPLITUDE 127cos(..) tells me that we want to amplifier our wave by 127x.Cosine wave – fading LED
What happens if we modify the OFFSET or the AMPLITUDE?
Let’s say we assign OFFSET = 150. This means that our wave OFFSET is shifted from 128 to 150 and it will oscillate in range [23;277] (note! same AMPLITUDE=127, oscillation 150±127) exceeding the upper bound and having 23 as min value. This means our led will never assume 0 value.
The upper and lower bound issues are easily fixed with a check function which clips the current value to 0 or 255 when it exceeds the bounds.Modifying the AMPLITUDE, i.e. AMPLITUDE = 100, will cause a smaller oscillation around my OFFSET.
Play with these coefficients to get your best result!Here there’s a sample code.
/* FADING A LED WITH SINE WAVE Andrea Toscano 2016 */ // Arduino LED PIN #define LED_PIN 10 // Baudrate for Serial Communication #define SERIAL_BAUD 115200 // Time period of fading in millisecs #define PERIOD 2000 // Angular Frequency by definition #define OMEGA 2*PI/PERIOD // No Phase #define PHASE 0 // Offset of the sine wave #define OFFSET 128 // Amplitude of the sine wave #define AMPLITUDE 127 // Used to generate time for the cos wave unsigned long timer = 0; void setup() { // Uncomment for serial monitor Serial.begin(SERIAL_BAUD); } void loop() { timer = millis(); // updating time int ledValue = OFFSET + AMPLITUDE*(cos((OMEGA*timer)+PHASE)); analogWrite(LED_PIN, checkValue(ledValue)); } // Useful to avoid LED values outside the bounds [0;255] int checkValue(int val) { if (val > 255) val = 255; else if(val < 0) val = 0; return val; }
and finally the optional φ which determines the starting point on the sine wave.
July 2nd, 2017 at 05:54 by Results Point
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My blog is in the exact same area of interest as yours and my users would truly
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July 3rd, 2017 at 08:01 by AndrewTosky
Hi!
Sure,no problem.
Just provide credits and links to my website where needed, thank you!
May 3rd, 2019 at 11:17 by Mariano
Brilliant code!! How would you implement a “fade up – on for a period of time-fade down – off for a period” without delay()?
May 3rd, 2019 at 12:33 by Mariano
What is the PHASE variable for?
April 22nd, 2020 at 18:11 by I love waves
Thanks for this great code, but there is an error that prevents the phase variable from working properly. You are missing a set of parenthesis to include PHASE in the cosine calculation. The line should be:
int ledValue = ledValue = OFFSET + AMPLITUDE*(cos((OMEGA*timer)+PHASE));
May 5th, 2020 at 11:04 by AndrewTosky
Thanks for pointing out 🙂
May 6th, 2020 at 12:06 by Mariano
Can you please explain what is the error
May 6th, 2020 at 12:25 by Mariano
What is the PHASE variable for or do? I have tried different values and cannot see the difference