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//
// iirdes_pll_example.c
//
// This example demonstrates 2nd-order IIR phase-locked loop filter
// design with a practical simulation.
//
// SEE ALSO: nco_pll_example.c
// nco_pll_modem_example.c
//
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#include <math.h>
#include <getopt.h>
#include "liquid.h"
#define OUTPUT_FILENAME "iirdes_pll_example.m"
// print usage/help message
void usage()
{
printf("iirdes_pll_example [options]\n");
printf(" u/h : print usage\n");
printf(" b : pll bandwidth, default: 0.01\n");
printf(" z : zeta (damping factor), default 0.70711\n");
printf(" K : loop filter gain, default: 1000\n");
printf(" n : number of samples, default: 512\n");
printf(" p : phase offset (radians), default: pi/4\n");
printf(" f : frequency offset (radians), default: 0.3\n");
}
int main(int argc, char*argv[]) {
srand( time(NULL) );
// options
float phase_offset = M_PI / 4.0f; // phase offset
float frequency_offset = 0.3f; // frequency offset
float pll_bandwidth = 0.01f; // PLL bandwidth
float zeta = 1/sqrtf(2.0f); // PLL damping factor
float K = 1000.0f; // PLL loop gain
unsigned int n=512; // number of iterations
int dopt;
while ((dopt = getopt(argc,argv,"uhb:z:K:n:p:f:")) != EOF) {
switch (dopt) {
case 'u':
case 'h': usage(); return 0;
case 'b': pll_bandwidth = atof(optarg); break;
case 'z': zeta = atof(optarg); break;
case 'K': K = atof(optarg); break;
case 'n': n = atoi(optarg); break;
case 'p': phase_offset = atof(optarg); break;
case 'f': frequency_offset= atof(optarg); break;
default:
exit(1);
}
}
unsigned int d=n/32; // print every "d" lines
// validate input
if (pll_bandwidth <= 0.0f) {
fprintf(stderr,"error: bandwidth must be greater than 0\n");
exit(1);
} else if (zeta <= 0.0f) {
fprintf(stderr,"error: damping factor must be greater than 0\n");
exit(1);
} else if (K <= 0.0f) {
fprintf(stderr,"error: loop gain must be greater than 0\n");
exit(1);
}
// data arrays
float complex x[n]; // input complex sinusoid
float complex y[n]; // output complex sinusoid
float phase_error[n]; // output phase error
// generate PLL filter
float b[3];
float a[3];
iirdes_pll_active_lag(pll_bandwidth, zeta, K, b, a);
iirfilt_rrrf pll = iirfilt_rrrf_create(b,3,a,3);
iirfilt_rrrf_print(pll);
unsigned int i;
float phi;
for (i=0; i<n; i++) {
phi = phase_offset + i*frequency_offset;
x[i] = cexpf(_Complex_I*phi);
}
// run loop
float theta = 0.0f;
y[0] = 1.0f;
for (i=0; i<n; i++) {
// generate complex sinusoid
y[i] = cexpf(_Complex_I*theta);
// compute phase error
phase_error[i] = cargf(x[i]*conjf(y[i]));
// update pll
iirfilt_rrrf_execute(pll, phase_error[i], &theta);
// print phase error
if ((i)%d == 0 || i==n-1 || i==0)
printf("%4u : phase error = %12.8f\n", i, phase_error[i]);
}
// destroy filter object
iirfilt_rrrf_destroy(pll);
// write output file
FILE * fid = fopen(OUTPUT_FILENAME,"w");
fprintf(fid,"%% %s : auto-generated file\n", OUTPUT_FILENAME);
fprintf(fid,"clear all;\n");
fprintf(fid,"close all;\n");
fprintf(fid,"n = %u;\n", n);
fprintf(fid,"x = zeros(1,n);\n");
fprintf(fid,"y = zeros(1,n);\n");
for (i=0; i<n; i++) {
fprintf(fid,"x(%4u) = %12.4e + j*%12.4e;\n", i+1, crealf(x[i]), cimagf(x[i]));
fprintf(fid,"y(%4u) = %12.4e + j*%12.4e;\n", i+1, crealf(y[i]), cimagf(y[i]));
fprintf(fid,"e(%4u) = %12.4e;\n", i+1, phase_error[i]);
}
fprintf(fid,"t=0:(n-1);\n");
fprintf(fid,"figure;\n");
fprintf(fid,"subplot(2,1,1);\n");
fprintf(fid," plot(t,real(x),t,real(y));\n");
fprintf(fid," xlabel('time');\n");
fprintf(fid," ylabel('real');\n");
fprintf(fid,"subplot(2,1,2);\n");
fprintf(fid," plot(t,imag(x),t,imag(y));\n");
fprintf(fid," xlabel('time');\n");
fprintf(fid," ylabel('imag');\n");
fprintf(fid,"figure;\n");
fprintf(fid,"plot(t,e);\n");
fprintf(fid,"xlabel('time');\n");
fprintf(fid,"ylabel('phase error');\n");
fprintf(fid,"grid on;\n");
fclose(fid);
printf("results written to %s.\n",OUTPUT_FILENAME);
printf("done.\n");
return 0;
}
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