Driver Specifications and Enclosure Tradeoffs
Last month (FRONT of HOUSE, Jan. 2022, page 15), we answered some FAQs relating to subwoofer drivers and the most popular bass/sub enclosures that are well suited to the requirements of concert sound production/applications. We covered: vented (bass-reflex or ported) boxes, band-pass subs, bass horns, tapped horns and transmission line bass enclosures. We also touched on a few of the most important woofer Thiele/Small parameters, introduced Hofmann’s Iron Law and reviewed cardioid subwoofer arrays.
The downside of most classic/standard live-sound woofers? While they are typically designed for very-high sensitivity/output at mid-bass frequencies (80-800 Hz), most don’t have the long excursion nor low-resonate frequencies needed for true subwoofer use, so multiple (lower-sensitivity) true subwoofer drivers would be needed as well, to cover the lower <40-80 Hz range. Heavy low-end equalization can be used to extend the lower range, but doing so reduces the maximum sound level, due to excessive excursion and/or power. Premium live-sound subwoofer drivers from the leading brands do have the long excursion, high-power-handling (1,500-2,000 W RMS) and low-resonate frequencies needed for effective concert subwoofer and dance music applications, but some are more for use in smaller enclosures than higher output.
Hofmann’s Iron Law
Josef Anton Hofmann was a physicist, audio expert and entrepreneur. In addition to earning a Ph.D. in physics from Harvard and working on the Manhattan Project, he was a co-founder or partner in three groundbreaking audio companies including KLH (the H was for Hofmann), Advent and Acoustic Research. These companies are no longer the giants in hi-fidelity home audio that they were in their heyday. Acoustic Research was the first company to produce an acoustic suspension (sealed box) loudspeaker. A simple sealed speaker enclosure was not invented until the 1950’s by Edgar Villchur (the founder and president of Acoustic Research), and the vented enclosure was patented by Albert Thuras of Bell Labs in 1930.
We would not have the market for high-end audio equipment as we know it today without Dr. Hofmann. His work inspired Neville Thiele and Richard Small to create what are now known as the Thiele/Small parameters (more on Thiele/Small latter). He was an intellectual giant and focused on complex design issues like semiconductors, solid-state devices and the development of audiophile quality sound equipment.
Efficiency is a way of quantifying loudness relative to power level. A more efficient speaker can play louder with the same amount of amplifier power as a less efficient speaker. With today’s modern Class-D designs, amplifier power has become cheap. Low-end extension is the ability to play low bass frequencies. With the massive subwoofers available today, this is trivial. But this was new decades ago when Cerwin-Vega started producing special Stroker subs for movie theaters (for 1974’s film, Earthquake) and before WW2, even the best hi-fidelity sound systems could not play 20 Hz at a realistic level.
Dr. Hofmann was asked by his boss to develop a hi-fi loudspeaker that could reproduce quality music, covering wide band of frequencies, as had never before been done. This is where enclosure size and Hofmann’s iron law comes into play. He determined that if you wanted a bass enclosure that was efficient and had good low-end extension, the key was a large enclosure. Especially at a time in history when adding more power was not feasible. Hofmann’s Iron Law has been summarized like this:
With a given amount of power, you can go low (freq.), you can go loud, or you can have a small enclosure — pick any two.
This means that a small sub can either be efficient — it can have low-end extension — but not both. An efficient enclosure can either be small or have low-end extension — but not both.
Thiele/Small Parameters
Thiele/Small parameters (commonly abbreviated T/S parameters) are electromechanical parameters that define a loudspeaker driver’s low-frequency performance. Driver manufacturers publish these parameters in specification sheets so designers can compare off-the-shelf drivers for loudspeaker designs. Using these parameters, a loudspeaker designer can use software to simulate the position, velocity and acceleration of a woofer diaphragm, the input impedance, and the sound output of a woofer and enclosure design. Many of the parameters are strictly defined only at the resonant frequency, but the approach is generally applicable in the frequency range where the cone motion moves in and out as a rigid unit, without cone breakup.
Some loudspeaker design engineers define desired performance and work backwards to a set of parameters and manufacture a driver with these characteristics, or order it from a driver manufacturer. Thiele/Small Parameters are named after A. Neville Thiele of the Australian Broadcasting Commission and Richard H. Small of the University of Sydney, who pioneered this line of analysis for loudspeakers. Thiele/Small Parameters are used in designing loudspeaker enclosures for many markets, including P.A. systems. TSP calculations indicate how large a speaker cabinet will need to be and how large and long the bass reflex port should be, along with how loud it will play.
Fundamental Parameters
These are the physical parameters of a loudspeaker driver, measured at small signal levels and used in the equivalent electrical circuit models. Some of these values are neither easy nor convenient to measure in a finished loudspeaker driver, so when designing speakers using existing drive units (which is almost always the case), the more easily measured parameters listed under Small Signal Parameters are more practical.
Sd — Projected area of the driver diaphragm, in square meters.
Mms — Mass of the diaphragm/coil, including acoustic load, in kilograms.
Cms — Compliance of the driver’s suspension, in meters per Newton
Rms — The mechanical resistance of a driver’s suspension, in N·s/m
Le — Voice coil inductance, in milliHenries (mH), measured at 1 kHz.
Re — DC resistance of the voice coil, in ohms.
Bl — The product of magnet field strength in the voice coil gap and the length of wire in the magnetic field, in Tesla-meters (T·m).
Small Signal Parameters
These values can be determined by measuring the input impedance of the driver, near the resonance frequency, at small input levels for which the mechanical behavior of the driver is effectively linear (i.e., proportional to its input). These values are more easily measured than the fundamental values above.
Fs — Resonance frequency of the driver (low Fs is important for true subwoofers).
Qes — Electrical Q of the driver at Fs
Qms — Mechanical Q of the driver at Fs
Qts — Total Q of the driver at Fs
Vas — Equivalent Compliance Volume — i.e., the volume of air, which, when acted upon by a piston of area Sd, has the same compliance as the driver’s suspension.
Large Signal Parameters
These parameters are useful for predicting the approximate output of a driver at high input levels, though they are harder to accurately measure. In addition, power compression, thermal, and mechanical effects due to high signal levels (e.g., high electric current and voltage, extended mechanical motion) all change driver behavior, often increasing distortion.
Xmax — Maximum linear peak (or sometimes peak-to-peak) excursion (in mm) of the cone. Note that, due to mechanical issues, the motion of a driver cone becomes non-linear with large excursions, especially those in excess of this parameter.
Xmech — Maximum physical excursion of the driver before physical damage. With too much power input, over-excursion will cause damage to the voice coil or other moving parts of the driver.
Pe — Thermal power handling capacity of the driver, in Watts. This value is difficult to characterize and is often overestimated by manufacturers. As the voice coil heats, it changes dimension, and changes impedance considerably, changing the electrical interaction between the voice coil and passive crossover components, changing the slope and crossover points designed for the loudspeaker system.
Vd — Peak displacement volume, specified in liters (L). The volume displaced by the cone, equal to the cone area (Sd) multiplied by Xmax (important for true subwoofers).
Other/Output Parameters
EBP — The efficiency bandwidth product, a rough indicator measure. A common rule of thumb indicates that for EBP>100, a driver is perhaps best used in a vented enclosure, while EBP<50 indicates a sealed enclosure. For 50<EBP<100, either enclosure may be used effectively.
η0 — Reference Efficiency, specified in percent. Comparing drivers by their calculated reference efficiency is often more useful than using “sensitivity,” as manufacturer sensitivity figures are too often optimistic and the given frequency is well above subwoofer pass-band.
Sensitivity — The sound pressure, in dB SPL, on-axis, produced by a speaker in response to a specified stimulus. Usually this is specified at an input of 1 watt or 2.83 volts (2.83 volts = 1 watt into an 8-ohm load) at a distance of one meter, at a given frequency, or an average level.
There is much more T/S history and are secondary T/S Parameters that we will not attempt to cover here. Note, that while basic software to simulate bass box performance is very useful, building, measuring and listing to a new loudspeaker is much more revealing, as to its actual sound quality while at high power.
Stay tuned for some concert woofer manufacture tips on bass box vent size trade-offs and more on the difference between woofer sensitivity and efficiency.
For help with live-sound design in large spaces see David’s consulting sound design web site at www.D-K-A.com.
