[ulysses]

Yes, it really is that simple. A capacitor in series with the hot leg and another capacitor in series with the cold leg. The shield (pin 1) gets connected straight through.

And yes, it's as simple as calculating f=1/2πRC.

The complication is this: You get to choose C, and you most likely have some preference with regard to f, but the R factor will vary depending on what pieces of equipment you connect to it. If you use it to feed a microphone into a mike preamp with a typical 1300-ohm input impedance and you get a corner frequency of 250Hz, for example, and then you try to use it with a line-level source feeding a line-level input with a 25k input impedance, you'll discover the corner frequency is now down around 13Hz. You may not find that to be useful. Furthermore, using it with an input of unknown impedance means you won't know where the corner will be.

One solution might be to install a shunt resistor to force the R value in the equation into a particular ballpark. This resistor would be connected between pins 2 and 3 of the output XLR connector (after the capacitors). Problem is, in order for this resistor to effectively swamp wide variations in input impedances, it would have to be about one tenth the value of the lowest expected input impedance. In our example above, that would be about 130 ohms. Two big problems arise. First of all, you're loading the source very heavily, which may increase distortion in active circuits, change the frequency response of dynamic mikes, and combine with the source impedance to create a voltage divider that attenuates a bunch of the source signal. Secondly, the capacitance required to build a useful HPF working against such a low impedance would mean using physically large electrolytic capacitors. They wouldn't fit inside your XLR barrel connector, and their loose tolerances would cause an impedance mismatch between pins 2 and 3, which would destroy the common-mode rejection of the balanced circuit.

So the first thing we can do to save ourselves some headaches is to build two separate HPF gadgets. The first one will be specifically for use with mike preamps that have relatively low input impedances. The second will be built to work with the load impedances typically seen in line-level inputs and certain transformerless mike preamps.

Our "mike level" HPF might expect to see impedances ranging from 1000 to 10000 ohms. By using a shunt resistor of maybe 3000 ohms, we can be sure the impedance seen by the source will always be somewhere between 750 ohms and 2500 ohms. This means the corner frequency could vary over a factor of 3, but it's better than a kick in the pants. Going back to our 250Hz desired corner frequency and a 1300 typical load impedance (which will combine with our 3000 ohm shunt resistor to give 907 ohms), we find that we need 0.0000007 Farads of capacitance. That's 0.7µF (microfarads). But we actually have two capacitors in series in our circuit (one on pin 2, and one on pin 3). The signal current makes a round trip, passing through both of these capacitors. So we have to think about what happens when you combine two capacitors.

Capacitors are different from resistors. You put two resistors in series, and they add together and behave like one resistor whose value is the sum of the two. When you put two resistors in parallel, they sort of "divide". They behave like a single resistor whose value is the reciprocal of the sum of the reciprocals of the two resistor values. If they both happen to have the same value, we're in luck because this works out to being the single resistor value divided by two. (For seventeen identical resistors in parallel, it works out to the single resistor value divided by seventeen).
Capacitors are just the opposite. Put two capacitors in parallel, and they behave like a single capacitor whose value is the sum of the two. Put two capacitors in series, and they "divide" in the same way as parallel resistors. That is to say, the effective value of two capacitors in series is the reciprocal of the sum of the reciprocals of the two capacitors. Once again, if the two are of equal value this works out to the single-capacitor value divided by two. (For seventeen identical capacitors in series, it works out to the single capacitor value divided by seventeen).

Okay, so we have two capacitors in series and we want them to behave like a 0.7µF capacitor. Each capacitor will need to be 1.4µF. The nearest standard value is 1.5µF, and since we're using first-order approximations for the R value, we can settle for that here as well. Now we've got effectively 0.75µF working against a resistance that varies from 750 ohms to 2500 ohms, giving us a possible corner frequency ranging from 283Hz down to 85Hz. You'll have to look around and spend some money to find good, compact 1.5µF capacitors that are small enough to fit in a barrel connector, of high audio quality, and with a tight enough tolerance to preserve your common-mode rejection.

I'll let you do the arithmetic for our other example, in which we're expecting a line-level load impedance ranging between 10k and 50k ohms. I'll suggest a shunt resistor of 30000 ohms, which will mean the capacitors see an impedance ranging from 7500 ohms to 18750 ohms. Let's assume you're still looking for a 250Hz corner when used with your typical input impedance of 20000 ohms.

Here are the formulas you need:

f=1/2πRC

(Frequency equals the reciprocal of the product 2 time pi times resistance times capacitance)

Cp = 1/[(1/Ca)+(1/Cb)]

(The Capacitance Cp (formed by parallel capacitors Ca and Cb) is equal to the reciprocal of the sum of the reciprocals of capacitors Ca and Cb).

Let's see what you come up with for capacitor values! (Hint: They'll be a lot smaller than the ones in our mike-level HPF).

Two things I should mention about the above discussion. First of all, I have used the terms "impedance" and "resistance" almost interchangeably here. Impedance is a combination of resistance, capacitive reactance, and inductive reactance. We talk about the input impedance of a circuit because it may be a load resistance reflected through an inductance such as an input transformer. The effect is the same, as pertains to these calculations.

Also, I've completely ignored the source impedance of the microphone or circuit feeding the High-pass filter you're building. That's because it's usually rather small in relation to the load impedance, and disappears in a first-order approximation like we're doing here. If you wanted to consider source impedance, you would simply add it to the net load impedance (parallel combination of load impedance and shunt resistor) when calculating the corner frequency. Adding a typical 100-ohm source impedance to your 7500-ohm worst-case impedance will have a negligible impact on the corner frequency of your filter.