Series-Tuned 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'=Lr-Lf.
- 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 13.76-4.11 = 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.
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. |