Mike Keith,

Your math is correct, but you're calculating the wrong thing.

Assume, as you did, that the mic preamp has 1.5k differential input impedance. Now let's add a phantom power circuit and calculate how this changes. By symmetry, no differential current flows into the phantom supply, so it is as if we put 2*6.8k=13.6k in parallel with 1.5k.

1.5k // 13.6k = 1.351 kohm

Let's use that as our baseline, and recalculate with ballast resistors which are 10% and 20% lower.

1.5k // 12.24k = 1.336 kohm

1.5k // 10.88k = 1.318 kohm

This will have a negligible effect at low frequencies. If the microphone has a 200 ohm differential output impedance, then the gain will change by less than 0.03 dB.

What about high frequencies? Your example of 6 nF cable capacitance (300 feet) in parallel with 1.351 kohm yields a pole at 19.63 kHz. Repeating the calculation for 1.318 kohm, the pole moves out to 20.13 kHz. I think we can agree that this is a good thing.

In summary, cable loading matters a lot, while loading by the phantom power resistors is not very important.

Have a great weekend,

David L. Rick

Seventh String Recording