Geek Speek on Boxes
Recently I discussed Bandwidth VS Sensitivity. This blog I will delve more into the fundamentals of driver and box alignment, or what we generally call "loudspeaker tuning." This is where the speaker engineers at Klipsch dissect all the electrical, mechanical and acoustical elements of a driver and how they relate to the air volume of the speaker enclosure.
Richard Small and A.N. Thiele developed math algorithms for loudspeaker elements which allow engineers to model the response of a design before they even start to build the physical products. We refer to these parameters as “Thiele – Small Parameters” (TSP). Here are the fundamental terms:
“Fundamental small signal mechanical parameters"
These are the physical parameters of a loudspeaker driver, as measured at small signal levels, 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 metres.
• Mms - Mass of the diaphragm, including acoustic load, in kilograms.
• Cms - Compliance of the driver's suspension, in metres per newton (the reciprocal of its 'stiffness').
• Rms - The mechanical resistance of a driver's suspension (ie, 'lossiness') in N•s/m
• Le - Voice coil inductance measured in millihenries (mH) (Frequency dependent, usually measured at 1 kHz).
• Re - DC resistance of the voice coil, measured 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-metres (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 (ie, proportional to its input). These values are more easily measured than the fundamental ones above.
• Fs – Resonance frequency of the driver
• 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:
where ρ is the density of air (1.184 kg/m3 at 25 °C), and c is the speed of sound (346.1 m/s at 25 °C). Using SI units, the result will be in cubic meters. To get Vas in litres, multiply by 1000.”
At Klipsch, we tend to model speaker analysis prior to producing a single driver, but once we have some general targets for the TSP we will build drivers and then measure them using Klippel or our proprietary measurement system. Many programs are used for TSP analysis but the program that is generally accepted by Klipsch is LEAP (Loudspeaker Enclosure Analysis Program) produced by Linear X. LEAP is quite diverse in its abilities to model in different conditions which we eventually calibrate against our lab measurements to make sure all tools are properly aligned.
In the first graph you can see LEAP in action with a generic 8 “ woofer driver. In this simulation I have manipulated the box volume Vab from 1 cubic foot to 10 cubic feet. What you can see is this result, which affects both the mid bass level and primarily the low frequency extension. What you may not be used to seeing is that the response above 200 Hz is elevated. This is what we call a "free-field response" with baffle effect from the box included. Essentially the baffle effect is a result of the width and height dimension that the driver is place upon. This is similar to a horn effect increasing the on axis sensitivity.
In the picture above, you can observe how the simulation of the response is taken. The cross hairs are where the microphone is pointed and the anechoic wedges are depicted around the walls of the measurement room with the speaker box under test in the middle. The term "free field" means that the sound can travel spherically in all directions, as in outer space with no boundaries to reflect off of, excluding the speaker enclosure. This is a pure condition unlike any application, but this empirical method allows for uncomplicated data to be manipulated easily.
In this next graph, the response is a bit closer to what you might see in real life conditions. What we call this response is an “Infinite Baffle” response. The speaker could be considered mounted flush with the floor. In this response the Low Frequency is elevated similar to what the baffle effect would be and there is no restriction on the floor length. This condition is still somewhat artificial but similar to a measurement in a parking lot with no cars. What you can see from this is the relationship of how the room starts to play an important role in our listening experience.
This is the pictorial equivalent for an infinite baffle with the speaker box flush with the plane of the baffle. You can think of digging a hole in the parking lot and burying the box flush to the baffle as the empirical response condition. There are no sound waves reflected in the back axis, so there is reflective energy at all frequencies from the plane. This means that the “baffle effect” becomes reflective all the way down to 20 Hz. It actually goes all the way to 0 Hz empirically but for the sake of practicality we are only modeling to 20 Hz. Good luck finding music or movies below 20 Hz.
Excursion Effect with a Box
Now here are some other things to think about… Mechanical and Electrical Linearity, Distortion, Air Spring Mass. These are more critical elements of speaker design and performance. You can think of them as the side effects of a particular design.
In the photo above you can see a cross-section view of a typical loudspeaker from Wiki. This speaker isn’t designed correctly but I won’t get into that. If you looked at my recent blog it shows a moving coil speaker animated.
Notice the voice coil moving up in down in the magnetic gap.
In the photo above you can observe the colors to the flux field. This is a magnetic model showing the levels of magnetic power in the various areas of the motor structure. As the color gets redder the magnetic flux is more dense or “hot.” This means that more mechanical force will be driven to the cone assembly which translates to more acoustic energy. This would be the definition of "peak efficiency." As you move the coil up and down the placement in the flux field changes. You can observe this by seeing that the color changes to yellow, green then blue as the density of flux lowers. This is an effect that happens with all loudspeakers in general. When the flux field is lower this translates to less force driving the moving assembly (cone) so the speaker becomes less efficient and the SPL goes down. This entire effect is considered "Electro-Mechanical nonlinearity." The primary effect of the magnetic change to the field is increase third harmonic distortion. What you can think of it is that the cone has become detached from the translation of sound and the effect is typically harshness to the sound or coloration.
Let’s look at the excursion differences from two sealed boxes from the previous model. The first one is green and indicates the 1 cubic foot box volume. As the frequency goes lower the excursion elevates slightly. Excursion is the distance of voice coil travel in the magnetic gap. Now let’s look at the 10 cubic foot box volume. This blue curve rises to 3.2 mm as the frequency approaches 20 Hz. The representative top plat thickness is 6 mm thus the coil is 50% out of the gap. You will experience extreme distortion at 20 Hz with the 10 cubic foot box but the output will be nearly 10 dB louder. What is different? Air Volume... Air Volume acts as a mechanical spring. When the cone move the air reacts in the sealed box. If the box is small the spring coefficient to the air is also small, so it cannot displace much energy before it starts to brake the cone from travel. A vacuum starts to form in the box eliminating much chance of travel. If the volume of air is very large, than the cone does not see the air mass very much. Displacing a small ratio of air affects the braking effect much less, so the coil tends to jump out of the magnetic gap. This is why the excursion is much higher for the 10 cubic foot box compared to the 1 cubic foot. These are some of the trade offs of loudspeaker designs. Nothing is free in the laws of physics.
There are no perfect speakers, but Klipsch gets you a little closer to perfection. Rock On!