Hi there,
Here's something kind of interesting/strange we found with the Z-4000 transformers recently about the harmonic distortion in their power output...
Sampling method. Each time domain trace is taken 100ms apart (capture rate 10 Hz)
We put a small USB oscilloscope inside a stock car and had it perform a time domain capture of the 18-20V power on the center rail of the layout every 10th of a second (10Hz). Each trace captured was 12000 points at 20 MS/s sampling rate. The exact scope is this one: (www.bitscope.com). No I don't work for them, I just think it's a cool/cheap scope for train projects.
Fundamental AC RMS voltage (60Hz) around the track layout
Going around the layout takes about 5 min and 30 seconds so we end up with 5x60 + 30 or about 330 seconds worth of data. This is 330 X 10 Hz or 3300 total time domain traces. For each trace we then compute the rms AC voltage and plot that value all the way around the layout. The result is relatively boring (the voltage is roughly constant across the entire layout as you would expect).
Where the interesting thing comes is we computed the Fast Fourier Transform (FFT) for each of the 3300 time domain traces we collected around the layout and extracted their harmonics.
In case anyone isn't familiar with harmonic distortion...
Harmonic distortion measures the amplitude of the fundamental sine wave for a power (or other) signal and compares it to the harmonics it contains. Essentially a measure of how "pure" the sine wave is. There is selective harmonic distortion which picks out a specific harmonic and compares it to the fundamental:
HD2 = (harmonic 2 power)/(fundamental power)
HD3 = (harmonic 3 power)/(fundamental power)
HD4 = (harmonic 4 power)/(fundamental power)
... and so on...
As higher harmonics roll off in amplitude most power system designers don't look beyond harmonic 5, picky audio designers usually consider up to harmonic 9, and RFIC designers (like me) typically worry up to 13.
For completeness there is also a thing called Total Harmonic Distortion or THD which compares the normal of all the harmonic powers to the fundamental:
THD = (HD2^2 + HD3^2+HD4^2+HD5^2...)/(fundamental power)
Anyways, here's the interesting discovery today. While the fundamental 60 Hz power is fairly constant across the layout, the HD2,HD3 values are actually very different in the different Z4000 transformers. Our layout has 3 transformers powering 3 different sections, and when you plot the HD2 and HD3 power as a function of time (linearly related to train position in the layout)...
Very Interesting! You can actually see clear differences in harmonic distortion between the 3 transformer sections of the layout even though all 3 transformers are the same Z4000 model. I'm not sure what this tells you about the transformer itself, but you could easily build a sensor from this into a train that can figure out what part of the layout it's currently in from the transformer distortion.
Maybe overkill... but to a circuit designer... it's kinda interesting anyways.
Adrian J Tang
