Question

A low voltage digital device has a low state of 0 V and a high state of
1.8 V. It generates a signal train of high pulses at a rate of 1 MHz, these
pulses having a 10 ns width and transition times of 100 ps.
(a) Plot the upper bound of its harmonic components up to 10 GHz.
(b) Determine the amplitudes of the third and 101st harmonics.
(c) Determine the signal bandwidth.

Answer 1

MATLAB code for plotting spectrum is shown below:

tres = 1e-12;
Tp = 1e-6;
t = (0:tres:Tp-tres);
n = t/tres;
Trise = 100*1e-12;
V(1:Trise/tres) = t(1:Trise/tres)/Trise;
Ton = 10*1e-9;
V(Trise/tres + 1:Ton/tres) = 1;
V(Ton/tres+1:(Ton+Trise)/tres) = 1-(t(Ton/tres+1:(Ton+Trise)/tres) - t(Ton/tres))/Trise;
V((Ton+Trise)/tres+1:length(t)) = 0;
frequency = 1/tres/npoint*(0:1:length(VFFT)/2);
index_10G = find(frequency==1e10)
semilogx(frequency(1:index_10G)/1e6,20*log10(abs(VFFT(1:index_10G)))-20*log10(npoint/2))
grid on
xlabel('frequency(MHz)')

ylabel('magnitude of FFT(dB)')

V_3rd = 20*log10(abs(VFFT(3))) - 20*log10(npoint/2)
V_101st = 20*log10(abs(VFFT(101))) - 20*log10(npoint/2)

index_bw = find(abs(abs(VFFT)-abs(VFFT(1)/(2^0.5)))==min(abs(abs(VFFT)-abs(VFFT(1)/(2^0.5)))));

fbw = frequency(index_bw);

Magnitude plot of spectrum till 10GHz is shown below

(b) 3rd harmonics magnitude = -33.98dB and 101st harmonic magnitude = -113.98 dB

(c) -3dB bandwidth of the signal = 44MHz