It should also be noted that telecom engineers working with frequencies below about 300 kHz generally don't use reflection coefficient or SWR. They work with return loss and reflection loss, measures that are designed to handle complex characteristic impedances.
73,
Maynard
W6PAP
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On 10/8/23 13:13, Maynard Wright, P. E., W6PAP wrote:
Hi, Tom,
Yes!? I spent a good part of my career working with telephone cable pairs at voice frequencies where the characteristic impedance had a phase angle of almost 45 degrees.? Your calculation falls right in line with that.
Power engineers working with the wide spacing of aerial lines often neglect the capacitance of the lines and use the approximation Zo = sqrt((R + jwL) / G).
73,
Maynard
W6PAP
On 10/8/23 12:29, Thomas Bruhns wrote:
Oh, fun!? Maynard, you're close to pointing out a common misconception about transmission lines at low frequencies.? I'll use your Romex example, but the same applies to pretty much any power wiring...or wiring in your stereo system to your speakers.
Typical Romex:? 12AWG conductors diameter 2mm, spaced roughly 5mm apart, insulated with PVC+Nylon, dielectric constant assumed to be about 2.5 and essentially infinite resistance.? My back of the envelope calc suggests about 620nH/m inductance in the wire and 44pF/m capacitance between the wires.? The wire resistance at 60Hz is about 0.01 ohms/m. Plug those into the formula relating Zo to R, G, Xl and Xc, and you get, at 60Hz, Z0 about 550 -j540 , all assuming I didn't make some horrible mistake.
My point here is that the 'impedance' of wire-pairs we use at low frequencies is dominated by the resistance of the conductors, and assuming decent insulation, the impedance will be highly reactive and not anything like the RF impedance.? This goes along with Maynard's note hinting at the free-space wavelength of 60Hz waves being about 5000 kilometers.? IMHO, it's a waste of time to think in transmission line terms at audio frequencies if you're not dealing with things the size of Rhode Island.? My apologies to people involved with long distance power transmission, as they do need to consider the length of lines.
Cheers,
Tom
"Weird hou men maun aye be makin war insteid o
things they need." -- Tom Scott (1918-1995)
On 10/8/2023 6:41 AM, Maynard Wright, P. E., W6PAP wrote:
Hi, Jim,
Note that this is actually done for large industrial 60 Hz loads where capacitor banks are used to compensate for highly inductive motor loads. ?Although not generally called impedance matching by power engineers, that's what it is.
For your light bulb matching, you have to decide on the source impedance.? It will be pretty low, regardless.? Maybe using the voltage at the branch circuit breaker would be a good point.? The Romex or other facility between the source voltage and the load can be considered a simple resistance or a transmission line. Unless your house is the size of Rhode Island, the length of line is probably negligible in terms of wavelength.
An incandescent bulb will exhibit a low resistance on startup and then increase in resistance as it warms up.? This phenomenon has been the subject of numerous emails recently in the Hallicrafters io group with concern about what happens when you change to an LED that provides resistance in parallel with a tube filament in a series string of such filaments.
Since you have a fixed source voltage and impedance and you are trying to match the load to that fixed source, the conjugate matching theorem will apply.? I suspect, without calculation, that it would require an enormous matching network to make a tiny improvement in illumination by overcoming the losses in the network components.
73,
Maynard
W6PAP
On 10/7/23 20:46, Jim Allyn - N7JA wrote:
It is always fun to watch the experts go back and forth on this sort of thing, each explaining to the others how he is wrong.? Maynard, as usual, shows a good grasp of the subject.
I would like to thank Fran?ois for touching on a subject I have always wondered about, and would like to ask the experts here, with tongue firmly in cheek, what sort of impedance matching network should I use when connecting a 100 watt light bulb to the AC line? And I assume the impedance matching network would have to be different for a 60 watt bulb?? Shouldn't these impedance matching networks be readily available wherever light bulbs are sold?
