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In Reply to: I'm thinking I might need to rolll my own posted by Christopher Witmer on April 27, 2007 at 19:51:46:
A big transformer can provide the same ability to absorb RF noise as a choke, but the secondary winding(s) may resonate if not properly loaded.My approach is to determine the resistor that will be transformed to 120 ohms at the primary, then put it in series with a capacitor that will limit the power dissipation in the resistor. This is because the characteristic impedance of Romex-type plastic wire, as used in the US, is about 120 ohms.
Transformers have a turns ratio approximately equal to the ratio of output to input voltage. Thus, a transformer that has a 120-volt primary and a 12-volt secondary has a turns ratio approximately 10:1.
The impedance transforms as the square of the turns ratio, so in this case it will take a 1.2-ohm resistor on the secondary to look like 120 ohms at the primary.
Most of the secondary voltage will be dropped across the series capacitor, so a good approximation is to calculate the current in the resistor that will keep its power dissipation under 1/2 of its rated value: P = I*I*R, then calculate the capacitance needed to limit the secondary current to this value with all the secondary voltage across the capacitor.
Capacitor impedance is given by Z = 1/(j*omega*C), where C is in farads. The capacitor current with the secondary voltage across it is given by Ohm's Law, I = V/Z. You will need to do the math.
This works better with a higher secondary voltage, as the capacitor can be a lot smaller.
When shopping for used transformers, be careful of units that look like they have been out in the rain. Rusty frames or spotted insulation mean they are risky for line exposure. Even ones that look new may have a loud mechanical hum, so plug them in before buying if possible.
Finally, use a circuit breaker or fuse in series with the transformer filter, in case the capacitor fails.
Follow Ups:
Sorry, one more question. When properly implemented, are Hammond series 193 chokes paralleled on the AC line and "half transformers" paralleled on the AC line doing the same thing? Does one approach do a better job than the other? Thanks!
The choke tweak is elegant in its simplicity. The transformer tweak needs some additional work, the R-C network as described, to make it behave. Once loaded, it may be a little better than the choke tweak, depending on the properties of the individual choke and transformer being compared."Characteristic impedance" is the relationship of current to voltage of a traveling electrical wave. Electrical disturbances move at the speed of light, so they have very long wavelengths at audio frequencies. We can consider cables as having negligible length and lumped values of resistance, capacitance, and inductance as long as we limit ourselves to the audio band.
Unfortunately, audio systems produce audio-band artifacts when exposed to radio-frequency noise. The Hammond choke tweak and several other esoteric measures improve audio-band performance by reducing the magnitude of RF noise in the environment and on the AC line. The frequency range of noise that can affect the audio system extends to the UHF band and beyond. This is the range where noise wavelengths are comparable in size to the wires being used, and the concept of characteristic impedance becomes important in understanding the noise behavior. Simply put, a low-loss cable with C capacitance per unit length and L inductance per unit length has a characteristic impedance of Z = SQRT(L/C). This is not the same as the small amount of resistance in typical wires.
Cables, such as power cords, interconnect and speaker cables, and segments of AC power wiring within the walls of your dwelling, have resonant frequencies because the traveling noise waves are reflected from the ends. Engineers use the concept of "matched impedances" to calculate how much energy is passed along and how much is reflected. If a cable is terminated in a resistance exactly equal to its characteristic impedance, all of the energy is absorbed in the resistance and none is reflected. Such a cable will not resonate.
Most cables do resonate because they are not terminated in matched impedances. This resonance can create strong RF tones out of weak background noise, in the same way an organ pipe creates a defined tone that can be painfully loud from the soft white noise of the inlet air. Your audio system is made of cables that can resonate, and is bathed in the resonant RF tones of your AC wiring environment.
The R-C loading of the transformer secondary is there to keep the transformer winding from resonating due to its inductance and capacitance. Since it is necessary but not of a critical value, I reason that it might as well be designed to match the impedance of the AC power cable without drawing too much power. It will only actually load the power cable if the transformer core allows the cable resonances to get through. The core may not, in which case the design is superfluous. I made capacitance and inductance measurements on a piece of plastic wiring cable I have, and calculated the characteristic impedance to be 120 ohms.
Some damping is better than no damping, so an exact match is not required. I've found that it is also useful to employ resistors and capacitors that are not made with steel parts. Take a magnet along if you can browse through parts bins.
To do the varnish dipping properly, you would have to heat the varnish and deal with the flammable vapors. This sounds like another Darwin Award project.
"If a cable is terminated in a resistance exactly equal to its characteristic impedance, all of the energy is absorbed in the resistance and none is reflected. Such a cable will not resonate."The corrolary to that in my case is, if an explanation terminates at cerebral folds with a resistance exactly equal to the explanation's characteristic impedance, all of the knowledge is absorbed in the cerebral folds and none is reflected.
I'd say I absorbed about half of the explanation but I think that was sufficient to keep me from making the evening news.
Are there any good one-stop resources online, or printed books, that can be recommended for me to read and obtain a better grasp of the science involved?
Thanks!
ever since James Clerk Maxwell formulated the laws of electricity and magnetism in a way that let the authorities at Cambridge University pose questions for the Tripos exam. See the link.Sorry that I don't know of a convenient on-line text. Used book sales sometimes have old college texts, and you could find a relevant one for a few dollars. New texts are all hideously expensive.
I'll let Al answer the technical stuff. He guided me through making the transformer version with the R-Cs on the secondaries as a quickie alternative to the chokes. I have no experience with the chokes, but this tranny version DEFINITELY works! Works well. You can immediately hear the difference when you switch it in and out; even my kids can hear it easily.On the other hand, be aware that all these core/coil devices are subject to some level of vibrational buzz. You have to mechanically damp that in the trannies, that's for sure.
This is good news to me because I have access to scads of inexpensive surplus transformers used by Japan's "Pachinko" industry. These all go from 100VAC to 24VAC, in sizes ranging from 250VA up to 2kVA, and they are generally quiet. The larger sizes (over 1kVA), such as the one shown here, have bifilar wound secondaries, so they can also be connected as 48VAC if desired. Most of them lack electrostatic shields between the primary and secondary windings, but I assume that is a moot point for this kind of application.One thing I am confused about is the reference to "characteristic impedance of Romex-type plastic wire" -- I thought impedance would depend on the length of the wire. Are you simply saying that 120 ohms is about average or typical? If so, I guess it is probably about the same in Japan as well, but it would be nice to get a bit more clarification on this.
And speaking of hum, what do you think of dipping a humming transformer into a can of varnish and then letting it dry? Or is there a better way to combat mechanical self-noise in a transformer?
Thanks!
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