Order Bandpass Systems
Series tuned systems are similar to the 'normal' 6th order bandpass systems, with one major difference - one chamber is vented into another instead of to the outside, as indicated in the diagram below:
Calculation of the appropriate length for the inner port is somewhat complex, as both the inner and outer ports work together to tune the rear chamber to a particular frequency. You can simplify the calculations somewhat by using the following method:
First, let's choose to use a 4" diameter tube for both vents.
To tune a 0.75 cu.ft. enclosure to 100 Hz with a 4" vent, our calculations suggest that the vent will have to be 4.11" long.
To tune a 2.25 cu.ft. enclosure to 30 Hz with a 4" vent, our calculations suggest that the vent will have to be 13.76" long.
Therefore, if we were to use a 4" tube for the inner vent, it's length will have to be 13.76-4.11 = 9.65" long.
Let's say that 9.65" is a bit too long for our needs, so we'd like to use a 3" diameter internal vent instead.
First of all, we use the port calculation equations to determine that a 2.25 cu.ft. enclosure with a 4" diameter vent that's 9.65" long will be tuned to 34.6 Hz.
Then, using the port calculations, we determine that, to tune a 2.25 cu.ft. enclosure to 34.6 Hz with a 3" diameter vent, the vent will have to be 4.86" long.
The physical parameters for our 6th order series-tuned alignment are therefore as follows:
Front Volume: 0.75 cu.ft.
Note: Typically, to make construction easier, I'd probably want to shift the theoretical resonance frequencies of this alignment up and down just a little, to see if I can get away with 4" and 4.75" instead of 4.11" and 4.86" lengths. Also, the geometry of the front volume may impact Fr as well (pushing it a bit lower, which is usually a good thing!). As with most designs, measure the resonance frequencies after construction, to see how close you've come to the target alignment.