PLL.rar_PLL_Sin Pll

% Simulation of First order Pll with Additive noise % Written by: R. Thamvichai (copyright 2010 by R. Thamvichai) % Date of latest revision: March 21, 2010 clc; clear; close all npts = 4000; % default npts fs = 2000; % default fs twopi=2*pi; %define constants used below twofs=2*fs; G = 200; %loop gain %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%% Adding equivalent NOISE, n' %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %with an assumptions that Ac (input signal amplitude) = 1 %Specify sigma of n to add noise n' SNRi_dB = -5; %input SNR = (Ac^2/2)/sigma_n^2 SNRi = 10^(SNRi_dB/10); sigma = 1/sqrt(2*SNRi); % sigma_n/^2 = sigma_n^2/(Ac^2) % = sigma_n^2 if Ac = 1 nd=sigma*randn(1,npts); nq=sigma*randn(1,npts); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%% LINEAR %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% w2c=0; phivco=0; %in radians % beginning of simulation loop LINEAR for i=1:npts s1 = -phivco; s2 = s1; %LINEAR n_hat = -nd(i)*sin(phivco)+nq(i)*cos(phivco); %add noise s2a = s2 + n_hat; s3 = G*s2a; w1c=s3+w2c; %trapezoidal integration w2c=s3+w1c; phivco=w1c/twofs; phierror(i)= s1; phivco_vec(i) = phivco; end %end of simulation loop %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%% NON_LINEAR %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% w2c=0; phivco=0; %in radians % beginning of simulation loop NON_LINEAR for i=1:npts s1 = -phivco; s2 = sin(s1); %NON_LINEAR n_hat = -nd(i)*sin(phivco)+nq(i)*cos(phivco); %add noise s2a = s2 + n_hat; s3=G*s2a; w1c=s3+w2c; %trapezoidal integration w2c=s3+w1c; phivco=w1c/twofs; nphierror(i)= s1; %fvco1(i)= s3/twopi; nphivco_vec(i) = phivco; end %end of simulation loop %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%Finding Parameters (from Linear analysis) %%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %find it from the steady-state part of data Ns = 500; %sigma2_psi (phase_error) = sigma2_theta %since input = 0 sigma2_theta = std(phierror(Ns:end))^2; %Finding SNRL SNRL = 1/(2*sigma2_theta); disp(['SNRL = ', num2str(SNRL)]) disp(' ') %SNR_ratio = BW/BL since fs = 2000 = 2*BW (Sampling Theorem) SNR_ratio = SNRL/SNRi; %Loop Bandwidth (BL) disp('Loop Bandwidth (BL) from') disp([' Simulation = ', num2str((fs/2)/SNR_ratio)]) disp([' Theory = ', num2str(G/4)]) disp(' ') %Find variance disp('Variance from') disp([' Linear = ', num2str(sigma2_theta)]) disp([' Nonlinear = ', num2str(std(nphierror(Ns:end))^2)]) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%% PLOT (steady-state) %%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%% from LINEAR %%%%%%%%%%%%%%%%%%% [Ni, xi] = hist(phierror(Ns:end),20); W = xi(2)-xi(1); N=sum(Ni); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%% from NONLINEAR %%%%%%%%%%%%%%%% [nNi, nxi] = hist(nphierror(Ns:end),20); nW = nxi(2)-nxi(1); nN=sum(nNi); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%% from Theoretical Analysis%%%%%% psi = xi; rho = 1/sigma2_theta; p_psi = exp(rho*cos(psi))/(2*pi*besseli(0,rho)); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% figure(1) bar(nxi/pi, nNi/(nW*N),'g');hold on; %first graph %plot(xi/pi, Ni/(W*N),'k*-');hold on; %second graph %plot(nxi/pi, nNi/(nW*nN),'b*-');hold on; %third graph plot(psi/pi, p_psi,'ro-') %fourth graph xlabel('Phase error/ Pi') ylabel('Prob. of Phase Error') title('Probability Density Function') legend('Histogram', 'Th. PDF') %legend('Histogram', 'Linear','Nonlinear','Th. PDF') hold off; %end of script file