On The Linearity Of A Loudspeaker Suspension
The speaker used here is a 12" bass guitar speaker with a neodymium magnet. A pair were purchased a few months ago to try as bass units in a pair of two-way systems. The bass unit was mounted into a 2.5 ft^3 vented enclosure with an F3 of 49hz. With a power handling capacity of 300 watts, compensation of the bass roll-off was easily done without risk.
Table 1 tells the whole story. It has been said that a picture is worth a thousand words and this has to be one.
dB(V or I) = 20Log(V1/V2) = 20Log(I1/I2) dB(P) = 10Log(P1/P2)
where V and I are voltage and current, resp., P is power and Log is base 10 logarithm.
The apparatus. The copper strip atop the dust cap is to measure continuity at start-up after which is serves mainly as source of clicks when the dust cap touches the micrometer. Without it, the softer dust cap gives too much error as the sound is not immediately noticeable. With the copper foil, the point at which contact is made can be determined within a few mA of current. A digital meter isn't fast enough to catch that point. If DC were being used to energize the voice coil, that method would work. The caveat with using DC is that the voice coil heats up faster, resulting in the current reading to continuously drop, making it difficult to determine the exact current drawn at the time of contact. This current drop is slower using AC.
A 15hz signal was used. This was somewhat arbitrarily chosen and also because it can't be heard. When the signal generator stabilized, the frequency measured was noted at 14.7hz
A 14.7hz tone is 0.068 seconds in duration. The dust cap will touch the micrometer once during each positive half cycle, every 68mS. The actual duration of that point is probably less than one tenth that, less than 7mS. A scope would respond but this method was more than adequate with less cables.
Just a close-up.
|Line Ref||Excursion||Current||D current ref 0 amp||Power I2R||D power ref 0 dB||Radiation into 2p
steradian (hemisphere) at 1 meter
First, the column titled Radiation into 2p steradian may need explanation as some may have no clue as to what a steradian is. To be brief, 2p steradian is radiation into a hemisphere. For example, a speaker mounted on a flat circular panel of at least 57 feet in diameter will keep the back wave of the speaker from interfering with the front wave down to 20hz, causing cancellation or doublet action, as coined by Abraham Cohen of University Speakers sometime shortly after 1946.
The SPL figures in that column are derived from an equation I found many years ago which calculated the SPL of a diaphragm of given area, excursion and frequency. Here, that frequency is 15hz (14.7) Writing a simple computer program or using a programmable calculator made those calculations very easy.
The excursion column increases by 0.025 inch from A thru H. The reason was to facilitate adjusting the micrometer which wasn't easy to read. By placing the reference line of the mic in view, one rotation was 0.025 inch. This also made the increments linear.
That aforementioned SPL equation shows that as the excursion doubles, the SPL increases by 6dB. Here, A is the starting (reference) point. The equation states that for this speaker, an excursion of 0.025 inch will create an SPL of 60dB, measured at a distance of 1 meter. In this experiment, 15hz was used as it allowed a sizeable excursion while maintaining a relatively inaudible sound. A higher frequency would have forced making smaller measurements than 0.025 inch to keep the SPL down. Smaller measurements would have been awkward to note.
Increasing the excursion to 0.050 inch, thus doubling the excursion would produce 66dB. If the suspension is linear, the current should double also and it did to 0.321A At point D, the excursion doubled again as did the current for an extra 6dB. 0.654A is very close to twice 0.321A which is 6dB. This can be seen from C to F and from D to H. The slight error is blamed on voice coil temperature which will affect impedance and current. Attempts to circumvent this by letting the coil cool prior to the next measurement proved futile. The temperature rise, slight as it was, was enough to see the current rapidly begin to drop. These older Fluke meters, accurate as they are, don't have a peak hold function. The relationships among the currents, power and the change in power show that the speaker suspension is quite linear within it's specified Xmax, which is 5.2mm. Double half roll surrounds are usually found on bass guitar speakers. The single half roll surround is typical of speakers used in home systems.
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