Contents

RC oscilloscope data

vpp = 2.0;
t = time*1000; % convert to milliseconds

Find 90% crossings

v90 = vpp*0.9-vpp/2;
n = length(vcap);
fall = vcap(1:n-1)>=v90 & vcap(2:n)<=v90;
rise = vcap(1:n-1)<=v90 & vcap(2:n)>=v90;
ndx1 = find(rise|fall);
tc1 = t(ndx1) + (t(ndx1+1)-t(ndx1))./(vcap(ndx1+1)-vcap(ndx1)).*(v90-vcap(ndx1));

find 10% crossings

v10 = vpp*0.1-vpp/2;
fall = vcap(1:n-1)>=v10 & vcap(2:n)<=v10;
rise = vcap(1:n-1)<=v10 & vcap(2:n)>=v10;
ndx2 = find(rise|fall);
tc2 = t(ndx2) + (t(ndx2+1)-t(ndx2))./(vcap(ndx2+1)-vcap(ndx2)).*(v10-vcap(ndx2));

show plot and cursors

m = min([length(ndx1),length(ndx2)]);
plot(t,vcap);
%grid on;
xlabel('time (msec)');
ylabel('vcap (Volts)');
hold on
x = [t(1) t(n)];
y = [-vpp vpp]/2;
plot(x,[v90 v90],'k--');
plot(x,[v10 v10],'k--');
for k=1:m
    x = tc1(k);
    plot([x x],y,'k--');
    x = tc2(k);
    plot([x x],y,'k--');
    diff = (tc2(k)-tc1(k));
    if (diff>0.0)
        fprintf('fall %.4g msec\n',diff);
    else
        fprintf('rise %.4g msec\n',-diff);
    end
end
hold off

fall 2.495 msec
rise 2.343 msec

See how good the exponential decay is

ndx = [5:105];
ratio = (vcap(ndx)+1)/2;
p = polyfit(t(ndx),log(ratio),1);
plot(t(ndx),ratio);
yfit = polyval(p,t(ndx));
hold on
plot(t(ndx),exp(yfit),'k','LineWidth',2);
set(gca,'YScale','log');
hold off
tau = -1/p(1);
fprintf('time constant = %g msec\n',tau);
fprintf('predicted rise/fall time = 2.2*tc = %g msec\n',2.2*tau);
xlabel('time (msec)');
ylabel('scaled response');

time constant = 1.16715 msec
predicted rise/fall time = 2.2*tc = 2.56773 msec

Published with MATLAB® 7.4