  ### DRAWING THE NUMBERS

Now if you want to design a filter it won't be enough to know which components to use, you also need to know their values, won't you? Well, with the following formulas you'll be able to calculate them according to the desired cut frequency. But keep in mind that results are true only if the filter is closed on a resistive load, that's to say a resistor. A speaker, we'll have the opportunity to better explain it if you'll survive this lesson, is everything but resistive.

In the following formulas, and in those that will come further on, we'll use some symbols:

 C capacity of capacitor, in microfarads (μF) L inductance of inductor, millihenrys (mH) fc cut frequency, in hertz (Hz) Z speaker impedance by the cut frequency, in ohms (Ω) π pi = 3.141592654... √2 root of 2 = 1.41421356237... a √(4+2√2) = 2.61312592975... b 2+√2 = 3.41421356237... d b-1 = 2.41421356237... e a*(1-1/d) = 1.53073372946...

And now, without delaying over, out with the abacus (yeah, a pocket calculator is worth the same!):

 I order LP L = (1/2πfc)*Z*103 [mH] I order HP C = (1/2πfc)*(1/Z)*106 [μF] II order LP L = (1/2πfc)*(√2Z)*103 [mH] C = (1/2πfc)*(1/√2Z)*106 [μF] II order HP C = (1/2πfc)*(1/√2Z)*106 [μF] L = (1/2πfc)*(√2Z)*103 [mH] III order LP L = (1/2πfc)*(3Z/2)*103 [mH] C = (1/2πfc)*(4/3Z)*106 [μF] L2 = (1/2πfc)*(Z/2)*103 [mH] III order HP C = (1/2πfc)*(2/3Z)*106 [μF] L = (1/2πfc)*(3Z/4)*103 [mH] C2 = (1/2πfc)*(2/Z)*106 [μF] IV order LP L = (1/2πfc)*(eZ)*103 [mH] C = (1/2πfc)*(d/eZ)*106 [μF] L2 = (1/2πfc)*(aZ/d)*103 [mH] C2 = (1/2πfc)*(1/aZ)*106 [μF] IV order HP C = (1/2πfc)*(1/eZ)*106 [μF] L = (1/2πfc)*(eZ/d)*103 [mH] C2 = (1/2πfc)*(d/aZ)*106 [μF] L2 = (1/2πfc)*(aZ)*103 [mH]

You will notice as in second-order filters the values of C and L are the same for both rows.

As we've already said above, these formulas guarantee an absolute correspondence between the simulated model and the real model on condition that the filter is closed on a resistor. A speaker is really assimilable to anything but a resistor, unless you accept a considerable degrade in filter performances. You'll understand therefore the importance in giving a closer look to the impedance of speakers 