PIC32MX: Sinusoidal Analog Output

The PIC32 is actually incapable of directly creating an analog output. Instead, the PIC32 can perform pulse width modulation (PWM) to create an average analog output. At a given frequency, PWM varies the time that the output pin is on (output is 3.3V) to create the duty cycle which can simulate voltages between 0V and 3.3V. For example, if the duty cycle is 50%, the PIC32 holds the pin at 3.3V 50% of the time and 0V for the other 50%. The average output voltage is then 1.65V. If the pin is connected to an external RC circuit, the PWM can be integrated. By varying the duty cycle sinusoidally, the output with an RC circuit can resemble a sinusoid. Thus, to create the sinusoidal output, a sinusoidal wave must be divided into a discrete number of points. These points can then be converted to a list of duty cycles to represent the sinusoid. In essence, this method is similar to connecting the dots.

The three most important parameters in creating the sinusoidal analog output are the cutoff frequency, the number of points per period, and the RC time constant. The combination of the cutoff frequency and the points per period helps tell the PIC when to change the duty cycle. The RC constant of an external RC circuit is important in creating smooth and accurate curves and in improving the quality of the output signal.

The code for the analog output will first generate a lookup table. This table contains values for the specific duty cycles and will generate the number of duty cycles based on the number of points specified by the user. After generating the table, the code goes through a loop which tells the board to output the appropriate PWM corresponding to the duty cycle in the lookup table at each time step. By looping through the duty cycles at the same time intervals, the output voltage is varied to match that of a sine wave. The external RC circuit acts as a buffer to store these voltages to smooth the final output voltage to yield the sine wave. Without this external RC circuit, the output would only be a series of pulses matching the duty cycle at a given time.

The examples below have a PWM frequency of 20kHz.

Cutoff Frequency

To choose the cut-off frequency of the external RC circuit, you use the equation

$f_{c}={\frac {1}{2\pi RC}}{\text{ Hz}}$

where $f_{c}$ is the cut-off frequency (${\text{Hz}}$), $R$ is the resistance ($\Omega$'s) and $C$ is the capacitance (F).

If the chosen cut-off frequency is too high (RC constant is too low), then the output signal will be very noisy and not as clear. If the chosen frequency is too low (RC constant is too high), then the final output signal through the RC circuit will be more likely to have a decreased amplitude, thus you'll only get a limited range of voltages.

Whether or not the cut-off frequency is too high or too low depends on the frequency at which the board is outputting the PWM voltage. So as the output frequency of the board increases and approaches the cutoff frequency (thus the cutoff frequency would be too low), the amplitude of the final analog output voltage will be decreased.

The sine waves were generated at 25Hz with 100 points. The sine wave labeled 1 was generated with an RC constant of 4.7 x 10^-5, the sine wave labeled 2 was generated using an RC constant 2.2 x 10^-4 and the sine wave labeled 5 was generated using an RC constant 4.7 x 10^-3. Notice that sine waves 1 and 2 have close to the same amplitudes (around 3.3V) but sine wave 1 has a very messy signal, thus the cutoff frequency would be too high. Also notice that sine wave 5 only has a maximum amplitude of 3.0V, thus the cutoff frequency would be too low.

Number of Points Per Period

Selecting the number of points to use to generate the sine wave is important because choosing too few will result in a very rough sine wave. When the number of points is too low, you can actually see multiple RC charging graphs between each point. However, if we choose too many points, a peak appears at what should be 0V on the sine wave. To prevent this peek from occurring, one could insert an “if” statement in the lookup table generation loop that replaces all of the occurring 0’s into 1’s. Inclusion of the if statement would result in no true 0V output for that particular output. The ideal number of points for 25Hz is around 200 points.

This demonstrates what happens when you pick too many points. The output signal has a peak occurring at the 0V area. This output signal used 500 points at 10Hz.

This demonstrates what an ideal analog output should look like. This output was generated using 100 points at 25Hz.

This demonstrates what happens when you select too few points. The output signal shows the capacitor charging. In this case, 10 points at 25Hz are used in generating the analog output.

RC Time Constant

The RC time constant plays a big role in creating the sine wave. By increasing the RC constant, the quality of the output signal is increased, where "quality" refers to the width of the output signals. Despite having such advantages, a larger RC constant will result in a phase lag which causes a delay between the output of the PIC and the output from the whole circuit.

The sine waves were generated at 25Hz with 100 points. The sine wave labeled 1 was generated with an RC constant of 4.7 x 10^-5, the sine wave labeled 2 was generated using an RC constant 2.2 x 10^-4 and the sine wave labeled 5 was generated using an RC constant 4.7 x 10^-3. Notice that sine waves 1 and 2 are almost synchronized, but sine waves 1 and 5 have a time offset caused by the phase lag from the high RC constant.

Sample Code

This sample code creates an analog output on PINS D0 and D1 using 200 points at a sine frequency of 25Hz.

/******************************************************
Sinusoidal Output
*/

#include "HardwareProfile.h"
#include "math.h" 

#define DESIRED_BAUDRATE    	(9600)      // The desired BaudRate
#define NUM_POINTS_PER_PERIOD		200

int timeStep = 0;
int LookupTable[NUM_POINTS_PER_PERIOD];

int main(void)
{
	int sineFreq = 25;
	int interruptFreq = NUM_POINTS_PER_PERIOD * sineFreq;
	int periodValue = (SYS_FREQ / interruptFreq / 1) - 1;
	
	// Configure the proper PB frequency and the number of wait states
	SYSTEMConfigPerformance(SYS_FREQ);

	// Allow vector interrupts
	INTEnableSystemMultiVectoredInt();
	
	// init OC1 module, on pin D0
	OpenOC1( OC_ON | OC_TIMER2_SRC | OC_PWM_FAULT_PIN_DISABLE, 0, 0);
	// init OC1 module, on pin D1
	OpenOC2( OC_ON | OC_TIMER2_SRC | OC_PWM_FAULT_PIN_DISABLE, 0, 0);
	
	// init Timer2 mode and period (PR2) // produces 20kHz PWM
	OpenTimer2( T2_ON | T2_PS_1_1 | T2_SOURCE_INT, 3999);


	int i;
	for (i = 0; i < NUM_POINTS_PER_PERIOD; i++)
	{
		LookupTable[i] = (int)(3999/2 * sin(2*M_PI/NUM_POINTS_PER_PERIOD*i)+ 3999/2); 
	}
	

	// init Timer3 for Sinusoid Interrupt
	// Assume Prescalar is 2
	// Need to verify that SYS_FREQ / sineFreq / numPoints < 65534
	OpenTimer3( T3_ON | T3_PS_1_1 | T3_SOURCE_INT, periodValue); 
	
	mT3SetIntPriority( 7); 	// set Timer3 Interrupt Priority
	mT3ClearIntFlag(); 		// clear interrupt flag
	mT3IntEnable( 1);		// enable timer3 interrupts

	// this will store the string for the LCD
	char LCDbuffer[33]; 

	while(1)
	{
		// Timer 3 ISR takes care of the code
	}

	CloseOC1();
	
}//end main
 
// interrput code
void __ISR( _TIMER_3_VECTOR, ipl7) T3Interrupt( void)
{
	if (++timeStep >= NUM_POINTS_PER_PERIOD)
	{
		timeStep = 0;
	}
	
	SetDCOC1PWM(LookupTable[timeStep]);
	SetDCOC2PWM(LookupTable[timeStep]);
	
	// clear interrupt flag and exit
	mT3ClearIntFlag();
} // T3 Interrupt