.Comparing Wave Reflection in Strings and Wires

[Jdo300]

Ahhh I see,

So if I know the impedance of the line I am playing with, is there any formula out there I can use to calculate the speed of the wave? Especially if I know other factors like the voltage, pulse width, and frequency (if that matters)?

Thanks,
Jason O

 

[NoTime]

Distributed capacitance and inductance are the key factors which define a transmission line (impedance).

Time to do a little more homework

 

[Jdo300]

No problem. Do you have any recomendations for a good online tutorial on transmission lines?

 

[Claude Bile]

Hi Claude,

Maybe I missed something here but in an electrical sense, what is the difference between an electrical soliton and a simple pulse? Could I still produce a soliton by using something like a square wave pulse or does this require something more advanced?

Thanks,
Jason O

A soliton is just another name for a pulse whose shape does not vary as it propagates. Pulses have a natural tendency to change their shape as they propagate due to the properties of the transmitting medium varying with frequency. Typically solitons counter this natural tendency through some non-linear effect.

The difficulty of producing a solition depends on how quickly the pulse shape changes as it propagates, which usually depends on the bandwidth of the pulse. Square waves would be a good choice in my opinion, as the behaviour of each harmonic will give you a good overall picture of how the pulse is behaving. It is also very easy to measure changes in pulse shape of a square pulse. Higher amplitudes will improve the chances of creating a soliton, as the nonlinear effects that keep the shape of the solition will be enhanced.

Claude.

 

[Claude Bile]

2. When the pulse wave attenuates, does the amplitude alone decrease or does the width of the wave increase also as the amplitude decreases? (I'm asking because I thought I saw an animation somewhere where a decaying wave got wider as it got shorter).

Pure attenuation will result in a decrease in amplitude only. The animation you saw was probably on dispersion (the spreading of the pulse in time).

Claude.

 

[Jdo300]

Hi Claude,

Thanks again for your help. I am an EE student but I haven't even had my first "formal" electronics class yet so all this stuff I am teaching myself for my personal experiments. Would you happen to know of any good sources I can check out to find out how to calculate the speed of a pulse through a transmission line with X amount of impedance? I'm not sure where to start looking but I need this information for some formulas I'm trying to develop.

I derived some formulas to calculate how long it would take a pulse to travel down a length of wire but at the moment, I’m assuming that all the pulses are traveling at the speed of light, c. So I need to revise this notion for my formulas to at least approximate the real deal more accurately. By the way, what is the formula to calculate the nth sub-harmonic frequency of a wave? The one I currently came up with is F(n) = c / (Pi * d * 2^n) where Pi*d is the distance the wave travels (around a loop in this case) and n is the sub-harmonic number. I want this function to calculate the 1/n^2 harmonic for whatever the fundamental one is. What do you think?

Thanks,
Jason O

 

[Claude Bile]

Most wires quote a velocity factor (or something of that nature, I can't exactly remember the name) in the manufacturer's specs, you can then find the velocity by multiplying the velocity factor by c. The speed of a pulse in a wire is one of those things more easily measured than calculated from first principles, the only adjustment you will need to do to your equations in any case is to multiply c by the velocity factor whenever it appears.

With regard to your equation about harmonics, it looks like you are using the time in takes for the pulse to traverse a single loop as the period of your fundamental frequency - keep in mind that this quantity is unrelated to the frequency components contained within the pulse itself. Other than that the formula looks okay except for the typo 2^n, which should read n^2.

Claude.

 

[Jdo300]

Hi Claude,

How would you measure the speed of the wave in the wire experimentally? I have a function generator and a two-channel scope to work with.

Thanks,
Jason O

 

[Claude Bile]

Connect the output of the pulse generator to one channel. This will be your reference channel. Connect the output of the pulse generator to the transmission line, and the output end of the transmission line to channel 2 of the oscilloscope. Use the cursors to measure the delay between the two. Try to make the cables from the pulse generator to the scope/transmission line as close in length as possible to reduce the effect of delays introduced by extra cables.

Once you know the delay, you can figure out the velocity once you know the length of the transmission line.

Claude.

 

[Jdo300]

Hi Claude,

Thanks again, Simple and effective .