Electronics > Beginners

Plotting the upper bound of harmonic content - yes it's assignment time again.

**Simon**:

--- Quote ---1. 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.

--- End quote ---

So i am stumped on (a). the bandwidth of the signal is deemed to end at 1/(Tr*pi) which is just over 3GHz. what exactly do they want. if it's any help attached is the lesson that is supposed to tell me all. Cryptic at best as usual.

**dmills**:

A is figure 4 in your book scaled appropriately.....

Regards, Dan.

**Simon**:

OK so I copy the diagram and fill in the numbers, that simple? So where does the 10GHz come in? or is it that I need an end point to work back from as I have no way of knowing any amplitude coefficients (well I can actually but it feels like the explanation has been less than expansive and i suspect they want to make it easy). The last line should actually be a curve ?

**MrAl**:

Hi,

Looking at your first post only this looks like an exercise in Fourier analysis where you want to know the signal spectrum. The highest harmonic is due to the rise and fall times because that dictates the highest frequency that would be needed to reconstruct the original signal from the spectrum information. If the rise and fall times were instantaneous the highest frequency would be infinite, but because they are ramped that limits the upper bound in any practical analysis because a ramp has lower amplitude harmonics than a step wave.

After looking at your pdf briefly, it looks like they may have actually done the analysis for you and found the spectrum function and so you could use that to figure out your answers. I didnt read the whole thing though so there may be more info in there too you can use. Study that well.

**Simon**:

It's the 10GHz that is confusing me. Looking at figure 4 the graph is not that hard to work out as they give the values. So the first section is due to the fundamental, then you have the ever decreasing harmonics of the fundamental and then the fundamental of the rise time and the harmonics from that that will decrease exponentially. so the Rise time produces a frequency of just over 3GHz. If the rise time dictates the frequency at which the last segment of the graph starts and that line follow a 1/f^2 then how can they decide that I am to plot to 10GHz? the plot will end when it ends......

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