Source impedance of a bifilar transducer

[Brinkman]

I've posted this question to another forum to no avail. Perhaps someone here can help me...

Ok. I've been working the following scenario over and over in my head and I need to be sure I have it figured right:

Let's suppose we use a magnetic pick-up (a rod magnet wound with N number of overlapping turns of magnet wire) near an oscillating metallic object to generate an AC voltage. When we measure the source impedance, we measure the DC resistance of the of the magnet wire, correct? For the sake of practicality, let's suppose the DC resistance of N number of turns is 1Kohms.

This can be modeled (within reason) as a voltage source in series with a 1Kohm resistor with a capacitor in parallel (capacitance of magnet wire winding). Simple enough.

Now let's suppose we require as high a signal-to-noise ratio (SNR) from the source as we can get. For this purpose, we desire our AC signal to operate as a balanced source which is then run into a Balanced-to-unbalanced converter of some sort (either passive UnBal transformer or active opamp). Still with me?

Here's where things get tricky:

So the magnetic pick-up is wound in a bifilar fashion: we take two parallel lengths of magnet wire (wires "A" and "B"), each length (naturally) having two ends, or "taps"; an inside winding tap and an outside winding tap.

Because two wires have twice the volume of one, we wind wires A & B in parallel N/2 number of times around the rod magnet. We then connect the inside tap of wire A to the outside tap of wire B (or vice versa). This connection is referenced to ground.

At this point, here are the facts as I understand them:

1) We are now left with two taps: an inside tap and an outside tap, the instantaneous induced voltage at each tap is 180 degrees out of phase respective to the other. Therefor, these voltages can be said to constitute a balanced AC signal.

2) Because we used two lengths of wire, each half the length of the example used up top, the DC resistance of each wire is 500 ohms (1/2 of 1Kohm).

Here are my questions:

1) In my mind, I see two 500 ohm lengths of wire in series, as the two coils of reversed direction are connected in series. Measured tap-to-tap, the resistance is still 1Kohm. However, if the ground reference for the coils is tied to the ground reference at the input of the BalUn, I see the source impedance as being two 500 ohm coils in parallel. Which would be a total source impedance of just 250 ohms. Or is the DC resistance of the windings just the real (non-reactive) component of the impedance?

2) What happens to the self-capacitance of the windings that are out-of-phase? Is it electrically canceled out? Cut in half?

3) The SNR is increased by a factor of 2, correct?



I think that's about it. Thanks to anyone who can help me out here.