
SeriesTuned 6th
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:
 Determine Fr, the desired resonance frequency for the rear chamber Vr, and Ff,
the desired resonance frequency for the front chamber Vfr.
 Determine Lr and Lf, the required vent lengths to tune Vr and Vf to the desired
resonance frequencies. Use identical vent diameters (D) for both calculations.
 The correct length for the inner vent, Lr', can be calculated as follows:
Lr'=LrLf.
 If you wish to use a different vent diameter for the inner vent, first work out
Ff': the resonance frequency of a volume equivalent to Vr that is tuned with a vent of
length Lr' and diameter D. You can then vary the diameter and length of the vent, once Ff'
is maintained.
Example:
A standard 6th order bandpass design calls for the following alignment
parameters:
Vf=0.75 cu.ft., Ff=80 Hz
Vr=2.25 cu.ft., Ff=30 Hz
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 13.764.11 = 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 seriestuned alignment are therefore
as follows:
Front Volume: 0.75 cu.ft.
Rear Volume: 2.25 cu.ft.
Outer Vent: 4" diameter vent, 4.11" long
Inner Vent: 3" diameter vent, 4.86" long
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. 
