Excellent job, Paul, on the descriptions and formulas!!!
Also would like to thank Joe for your interesting input, regarding UHF!
Being a "Low Frequency" guy myself, the first time I cracked open an Impedance Matching Transformer for a Television's RF input (300 Ohm twinlead to 75 Ohm Coax, 54-890 MHz), it caught me off guard to see the distinct separations between the Primary and Secondary windings!
A few days with my nose "buried in the books" explained that whole thing!
Anyhow, as said before, my dealings with AC items is of the Low Frequency areas. The highest Frequency I have dealt with (as far as Engineering goes), is the upper limit of the Audio Frequency Spectrum - basically around 20 kHz (or 32 kHz for ultrasonic filtering limits) - but for the most part, 20 kHz is the highest end, with Frequencies of 8 to 12 kHz being the norm.
In the designing of Passive Crossover Networks
for Audio Systems' Loudspeakers - most of which are a combination of Series LC and Parallel RLC Networks, the design will reflect the AC Audio output from the Power Amplifier, along with whatever Coupled DC component will be available from the Power Amplifier.
Frequency range is around 20 Hz through 20 kHz, separated into 10 Octaves.
The Low Pass Filters - for the range of 20 Hz through 500 Hz, for driving the large Woofer/Subwoofer Voice Coil of a 3 way speaker, will consist from a single Air-Core Inductor (for a 1st order Network), to an array of 2 Inductors in Series, and 2 Capacitors, in Parallel (for a 4th order Network).
The Band Pass Filters - for the range of 250 Hz through 4000 Hz, for driving the Medium sized Mid-Range Voice Coil of a 3 way speaker, will consist from a single Air-Core Inductor + Capacitor in Series (for a 1st order Network), to an array of 2 Inductors + 2 Capacitors, in Series with the Voice Coil, + 2 sets of LC Series, in Parallel of the Voice Coil (for a 4th order Network).
The High Pass Filters - for the range of 2000 Hz through 20,000 Hz, for driving the small tweeter Voice coil of a 3 way speaker, will consist from a single Polypropylene Capacitor in Series with the Voice Coil (for a 1st order Network), to an array of 2 Capacitors in Series, and 2 Inductors, in Parallel (for a 4th order Network).
Additional Filters have been used with these Passive designs, most of which are for "Taming Peaks" (Notch Filters), and for Impedance Equalization.
These take the form of Series and Parallel RLC, RL, RC and LC Filters.
Another "Tweek" was used to "Boost" Frequency Response of a Driver, due to reductions from "Step Response".
To "Boost" the higher Frequency Response on Tweeters, a Parallel RC Filter is placed in line with the Tweeter.
An additional Mylar Capacitor was placed in Series with the Voice Coil, with a Shunt Resistor around it (the Resistor is Parallel to the Capacitor).
Capacitor value - in microfarads, is based on the figure for a 1st order Crossover's Capacitor.
The Resistor is equal to the rated Impedance of the Tweeter's Voice Coil.
To "Boost" the lower Frequency Response on Woofers, a Parallel RL Filter is placed in line with the Woofer.
An additional Inductor was placed in Series with the Voice Coil, with a Shunt Resistor around it (the Resistor is Parallel to the Inductor).
Inductor value - in millihenrys, is based on the figure for a 1st order Crossover's Inductor.
Similarly, the Resistor is equal to the rated Impedance of the Woofer's Voice Coil.
None of this stuff takes place in the Speaker Circuits for Active Crossover Networks
, as all the Frequency Tweeking takes place on the Line-Level inputs of an Amplifier - similar to the Active Filtering done on each Octave of a Graphic Equalizer.
An example of the Filter for a single Octave of a "Tunable" multi-band Graphic Equalizer, consists of fixed RLC components, and an "adjustable R Component", which is a "Slide Pot" (Sliding type of Potentiometer, as opposed to a dial type of Pot).
These Elements work in conjunction with an Op-Amp (Operational Amplifier), most commonly and currently used would be something in a DIP type of an IC.
Just wanted to add a little more to the thread.