Small TL's

Small TL's 01/20/03

Small and TL is a relative thing. A TL enclosure will almost always be the largest option for a given driver. The criterion here is whether the pipe resonant frequency, f_p, is higher or lower than the driver resonant frequency,f_s. Using an arbitrary but realistic design criterion of f₃ = 30Hz, smaller drivers (5 1/4", 6 1/2") will have f_p < f_s, while larger drivers (10", 12", etc) will have f_p > f_s. Hence the term "small TL". The driver used in this discussion is the Peerless 850108, a 5 1/2" driver.

The first decision to make is the taper of the pipe. There are three basic tapers:

Narrow at the top, wide at the bottom (TQWT)
Straight
Wide at the top, narrow at the bottom (Conventional TL).

I find no reason to use the TQWT taper unless a customer demands it. The straight and conventional taper always give better results. Also, drivers with a Qts < 0.35 tend to work best in a straight TL, while drivers with Qts > .040 work best in a tapered TL. Here is a table of first guess measurements. Choose the taper and cut-off frequency:

Taper	f₃	Length	Top Area	Bottom Area	Driver Position Ratio	Port Size	Port Lentgh
TQWT	40HZ	72"	1*S_d	4*S_d	0.5	0.5*S_d	2"
TQWT	35HZ	84"	1*S_d	4*S_d	0.5	0.5*S_d	2"
Straight	40HZ	48"	4*S_d	4*S_d	0.25	0.5*S_d	2"
Straight	35HZ	60"	4*S_d	4*S_d	0.25	0.5*S_d	2"
Conventional	40HZ	48"	4*S_d	0.5*S_d	0.20	--	--
Conventional	35HZ	60"	4*S_d	0.5*S_d	0.20	--	--

Remember that these are starting values. The actual values you arrive at will depend upon the driver you choose.

OK, it's time to fire up Martin King's MathCAD worksheets. The one we will use is "ML TQWT". This is from the latest set and is dated 7/07/02. I use this one for rough design work because it is the easiest of the set and general enough to investigate simple configurations. Once I arrive at a proposed geometry, I draw up the plans, then put the actual configuration into the "Sections" worksheet. This is the most general worksheet and the most tedious to set up. It is worthwile, though, to assure that there are no surprizes once the design is committed to wood.

Let's go to the chart and pick parameters for a 35Hz conventional taper pipe. Putting the numbers into the worksheet, setting the driver prameters, and setting the stuffing to 0 lb/ft³ gives us:

Red = Summed Frequency Response, Blue = Infinite Baffle Frequence Response

Red = Driver Frequency Response, Blue = Port Frequence Response

There are two important things to note here. It was wildly optomistic to expect a 5 1/2" driver to perform down to 35Hz. This is demonstrated by the sag in the summed FR curve between 50-60Hz. Also, the bottom of that sag will be the maximum SPL possible from this pipe. Note that the high side of the pipe rolls off much faster than the driver rolls in. Let's shorten the pipe to 48":

Red = Summed Frequency Response, Blue = Infinite Baffle Frequence Response

Red = Driver Frequency Response, Blue = Port Frequence Response

The saddle in now only a dB or so less than the 1000Hz value. You could continue to shorten the pipe to bring the saddle up to the 100Hz value, but the cut-off becomes unrasonably high.

The next item to be handled is the driver position. Note the small spike in the summed FR curve at the arrow (it is much more obvious in the port FR). Actually the first guess is pretty good, but by adjusting eta to three decimal places, better than 1/4" in wood, the spike goes away almost completely. A value of 0.203 gives:

Red = Summed Frequency Response, Blue = Infinite Baffle Frequence Response

Red = Driver Frequency Response, Blue = Port Frequence Response

What we have just done is damp out the 4/5 harmonic. The practical value of doing this is to minimize the dip the the summed FR curve once the pipe is stuffed. From a practical point of view, it may be more important to place the driver slightly off of this position because of baffle geometry considerations. Next we put some stuffing in the pipe. Set "Density" to 1 lb/ft³ and Do₁ to 0.3 lb/ft³:

Red = Summed Frequency Response, Blue = Infinite Baffle Frequence Response

Red = Driver Frequency Response, Blue = Port Frequence Response

There it is. f₃ ~40Hz, +/- 2dB 40Hz up. The ripple above 400Hz will be less than modeled, particularly if the port is in the rear. The model begins to break down above 500Hz because some of the simplifying assumptions no longer hold.

Using the same procedures, a quasi-optimized 48" straight TL looks like this:

Red = Summed Frequency Response, Blue = Infinite Baffle Frequence Response

Red = Driver Frequency Response, Blue = Port Frequence Response

A quasi-optimized 60" TQWT looks like this:

Red = Summed Frequency Response, Blue = Infinite Baffle Frequence Response

Red = Driver Frequency Response, Blue = Port Frequence Response

I did not demonstrate changing the pipe volume or port dimensions. Adjusting these will change the inductive loading of the pipe. Both the pipe Q and the pipe fundimental resonance will change. The concept is important enough to demonstrate two cases here.

The first pair of graphs is for the conventional TL used in the primary example above, except the closed end area is reduced to 2*Sd. The second set of graphs is with the closed end area at 4*Sd, a repeat of the graphs above:

Closed End Area = 2*S_d

Red = Summed Frequency Response, Blue = Infinite Baffle Frequence Response

Red = Driver Frequency Response, Blue = Port Frequence Response

Closed End Area = 4*S_d

Red = Summed Frequency Response, Blue = Infinite Baffle Frequence Response

Red = Driver Frequency Response, Blue = Port Frequence Response

Notice that when the area is increased:

The pipe resonance sharpens
The SPL of the pipe increases 1dB at resonance
The Spl of the pipe decreases 3dB at 150Hz
A peak appears in the Summed FR
A saddle develops above pipe resonance
The fundimental frequency drops for 50Hz to 50Hz
The higher harmonics are unchanged
The driver position must be adjusted slightly

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