Back in good ol’ 2012 (the year the world was supposed to end), I posted some code for a simple Arduino controlled low-frequency oscillator (LFO). It has made its way into some very interesting projects over the years, but recently I was asked in the comments if the code could be modified to have a wider frequency output up into the kHz range. I thought it was a good question, so I made the effort to see what the limitations could be.
How It Works
So, the original LFO employs timers on an ATMega328 (or ATTiny85 depending on which version of the code) to generate the audio output. By using a wave table of a basic sine wave stored in an array, one timer (TIMER0) winds up setting the sample rate by grabbing each sample from the array at a configured interval, and the other timer (TIMER2) creates a PWM output on the selected pin (pin 3 in the code). So by setting an 8-bit value on OCR0A, the sample rate can be adjusted which adjusts the frequency on the output of TIMER2. The datasheet for the ATMega328 gives the following formula for the frequency of the output compare register.
If we take this formula and divide it by the number of samples, we get the output frequency. That means that the output frequency can also be scaled by reducing the number of samples available. So, I made a big output table in LibreOffice and saw that an OCR0A value of 128 was twice the frequency from 255. At 255, I could reduce the number of output samples by half and sweep over the same sample rates but get an increase in output frequency. This introduced a method of frequency scaling. The trade-off, however, is that the sine wave on the output is much less sinusoidal being that it has lower resolution, and that introduces higher order harmonics thus changing the timbre of the sine wave.
Another thing to keep in mind is that the sample rate from the output PWM gets very low and even into the audio range itself. This means that some kind of audio filter is needed on the output. I put a first order low-pass filter using a 2.2k series resistor and a 10 uF capacitor to ground. This worked surprisingly well, though some of the sampling noise shows up on the output at very low frequencies. Being an 8-bit audio signal, this isn’t much to worry about in the grand scheme of things since. I also found that the noise on the output could be lowered by implementing a simple moving average filter in the code on the 10-bit ADC input of the rate control if using a potentiometer to set the frequency. With the timer prescalar set to 64, we should get 64 clock ticks before the next sample is grabbed, so this left some room for some calculations to happen in between sample changes.
It’s all pretty experimental, but it seems to work alright. The frequency range is from around 1 Hz up to 14 kHz (more or less). If you’re using a pot to control the rate, use a linear one as the frequency output gets very logarithmic towards the top of the range.
The Code
// Project: Arduino Audio Frequency Signal Generator
// Version: 1.0
// Author: Abram Morphew
// Date: 2021.10.12
#define cbi(sfr, bit) (_SFR_BYTE(sfr) &= ~_BV(bit))
#define sbi(sfr, bit) (_SFR_BYTE(sfr) |= _BV(bit))
uint8_t sineTable256[] = {
128,131,134,137,140,143,146,149,152,155,158,162,165,167,170,173,
176,179,182,185,188,190,193,196,198,201,203,206,208,211,213,215,
218,220,222,224,226,228,230,232,234,235,237,238,240,241,243,244,
245,246,248,249,250,250,251,252,253,253,254,254,254,255,255,255,
255,255,255,255,254,254,254,253,253,252,251,250,250,249,248,246,
245,244,243,241,240,238,237,235,234,232,230,228,226,224,222,220,
218,215,213,211,208,206,203,201,198,196,193,190,188,185,182,179,
176,173,170,167,165,162,158,155,152,149,146,143,140,137,134,131,
128,124,121,118,115,112,109,106,103,100,97,93,90,88,85,82,
79,76,73,70,67,65,62,59,57,54,52,49,47,44,42,40,
37,35,33,31,29,27,25,23,21,20,18,17,15,14,12,11,
10,9,7,6,5,5,4,3,2,2,1,1,1,0,0,0,
0,0,0,0,1,1,1,2,2,3,4,5,5,6,7,9,
10,11,12,14,15,17,18,20,21,23,25,27,29,31,33,35,
37,40,42,44,47,49,52,54,57,59,62,65,67,70,73,76,
79,82,85,88,90,93,97,100,103,106,109,112,115,118,121,124
};
uint8_t sineTable128[] = {
128,134,140,146,152,158,165,170,176,182,188,193,198,203,208,213,
218,222,226,230,234,237,240,243,245,248,250,251,253,254,254,255,
255,255,254,254,253,251,250,248,245,243,240,237,234,230,226,222,
218,213,208,203,198,193,188,182,176,170,165,158,152,146,140,134,
128,121,115,109,103,97,90,85,79,73,67,62,57,52,47,42,
37,33,29,25,21,18,15,12,10,7,5,4,2,1,1,0,
0,0,1,1,2,4,5,7,10,12,15,18,21,25,29,33,
37,42,47,52,57,62,67,73,79,85,90,97,103,109,115,121 };
uint8_t sineTable64[] = {
128,140,152,165,176,188,198,208,218,226,234,240,245,250,253,254,
255,254,253,250,245,240,234,226,218,208,198,188,176,165,152,140,
128,115,103,90,79,67,57,47,37,29,21,15,10,5,2,1,
0,1,2,5,10,15,21,29,37,47,57,67,79,90,103,115
};
uint8_t sineTable32[] = {
128,152,176,198,218,234,245,253,255,253,245,234,218,198,176,152,
128,103,79,57,37,21,10,2,0,2,10,21,37,57,79,103,
};
uint8_t sineTable16[] = {
128,176,218,245,255,245,218,176,128,79,37,10,0,10,37,79
};
uint8_t sineTable8[] = {
128,218,255,218,128,37,0,37,128
};
uint8_t sineTable4[] = {
128,255,128,0,128
};
uint8_t sineTable2[] = {
255,0
};
uint8_t tWave = 128;
uint8_t sWave = 255;
uint8_t ruWave = 128;
uint8_t rdWave = 128;
uint8_t rWave = 128;
uint8_t inc = 1;
uint8_t r = 0;
int n = 32; // number of averages for ADC input (should be a power of 2: 32 max)
int ocr[32] = {};
int i = 0;
int t = 0; // time delay index for rate sweep
int sweep = 1023; // sweep
int rate = 0;
int waveform;
byte d = HIGH;
byte down = LOW; // increase freq if LOW, decrease freq if HIGH
byte rateSelectPin = 1;
byte waveSelectPin = 0;
void setup() {
pinMode(waveSelectPin, INPUT);
pinMode(rateSelectPin, INPUT);
pinMode(3, OUTPUT);
setupTimer();
OCR0A = 128;
}
void loop() {
// -- Waveform Selection
waveform = map(analogRead(waveSelectPin),0,1023,1,7);
//waveform = 1;
// -- Frequency Selection with ADC pin 1
if (r >= n) r = 0;
ocr[r] = map(analogRead(rateSelectPin),0,1023,1015,3);
r++;
// -- ADC input averaging
for(uint8_t c = 0; c < n; c++) { rate += ocr[c]; }
rate = floor(rate / n);
// Uncomment for frequency sweep
/*--------------------
if (t >= 2048) {
sweep--;
t = 0;
}
if (sweep <= 4) {
sweep = 1023;
}
t++;
rate = sweep;
//----------------------- */
// rate scaling with increasing frequency
if (rate < 128) {
inc = 128;
rate = rate * 2;
} else if ((128 <= rate) && (rate < 256)) {
inc = 64;
rate = rate;
} else if ((256 <= rate) && (rate < 384)) {
inc = 32;
rate = rate - 128;
} else if ((384 <= rate) && (rate < 512)) {
inc = 16;
rate = rate - 256;
} else if ((512 <= rate) && (rate < 640)) {
inc = 8;
rate = rate - 384;
} else if ((640 <= rate) && (rate < 768)) {
inc = 4;
rate = rate - 512;
} else if ((768 <= rate) && (rate < 896)) {
inc = 2;
rate = rate - 640;
} else if ((896 <= rate) && (rate < 1024)) {
inc = 1;
rate = rate - 768;
}
OCR0A = rate;
}
ISR(TIMER0_COMPA_vect) {
if(i >= (256 / inc)) i = 0;
switch(waveform) {
case 1:
OCR2B = sine(i, inc);
break;
case 2:
OCR2B = triangle(i);
break;
case 3:
OCR2B = square(i);
break;
case 4:
OCR2B = rampUp(i);
break;
case 5:
OCR2B = rampDown(i);
break;
case 6:
OCR2B = rand(i);
break;
case 7:
OCR2B = white(i);
break;
}
i++;
}
void setupTimer() {
cli();
/*--- TIMER2 CONFIG ---*/
sbi(TCCR2A,WGM20);
sbi(TCCR2A,WGM21);
cbi(TCCR2A,WGM22);
sbi(TCCR2A,COM2B1);
cbi(TCCR2A,COM2B0);
sbi(TCCR2B, CS20);
cbi(TCCR2B, CS21);
cbi(TCCR2B, CS22);
/*--- TIMER0 CONFIG ---*/
sbi(TCCR0B,CS00);
sbi(TCCR0B,CS01);
cbi(TCCR0B,CS02);
sbi(TCCR0A, COM0A1);
cbi(TCCR0A, COM0A0);
cbi(TCCR0A, WGM00);
sbi(TCCR0A, WGM01);
cbi(TCCR0A, WGM02);
cbi(TIFR0,OCF0A);
sbi(TIMSK0,OCIE0A);
sei();
}
int sine(int i, int inc) {
if (inc == 1) {
return sineTable256[i];
} else if (inc == 2) {
return sineTable128[i];
} else if (inc == 4) {
return sineTable64[i];
} else if (inc == 8) {
return sineTable32[i];
} else if (inc == 16) {
return sineTable16[i];
} else if (inc == 32) {
return sineTable8[i];
} else if (inc == 64) {
return sineTable4[i];
} else if (inc == 128) {
return sineTable2[i];
}
}
int triangle(int i) {
if(tWave >= 255) d = LOW;
if(tWave <= 0) d = HIGH;
if(d == HIGH) tWave = tWave + inc;
if(d == LOW) tWave = tWave + inc;
return tWave;
}
int rampUp(int i) {
ruWave = ruWave + inc;
if(ruWave > 255) ruWave = 0;
return ruWave;
}
int rampDown(int i) {
rdWave = rdWave + inc;
if(rdWave < 0) rdWave = 255;
return rdWave;
}
int square(int i) {
if(i >= (128 / inc)) sWave = 255;
if(i < (128/inc)) sWave = 0;
return sWave;
}
int rand(int i) {
if(i == (rWave / inc)) rWave = random(255);
return rWave;
}
int white(int i) {
return random(255);
}
