Tech Blog

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:

From wiki…
http://en.wikipedia.org/wiki/Thiele/Small

“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. 

Bl Model 

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. 

Excursion Graph

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!  

P. Thump

As most of you know, Klipsch works very hard at insuring our speakers will be “LOUDspeaker.”  Some ignore this philosophy because it is difficult to achieve, but it is the first rule that PWK founded and the first rule for our designs engineers at Klipsch. 

High Efficiency…

What some of you may not know is that high efficiency speakers do not necessarily dictate wide bandwidth or full range.  In particular, bass extension is one of the biggest challenges for high efficiency loudspeaker.  Here is why…

You can generally treat the characteristics of a woofer to the gain curve of a transistor.  This may not help you if you are not an electronic engineer but the same characteristics apply.  To make drivers more efficient you can fool the laws of physics.  Typically the motor has to be much more powerful.  This means a bigger and badder magnet and thicker magnet steel to avoid saturation of the flux.  This also means the cone has to be structurally rigid yet be a very light mass.  All of our systems are horn loaded but this effect only goes down to a certain frequency unless it is a pro theater speaker.  As I had mentioned earlier a 30 Hz horn must be 11.5 meters in length to control properly to that frequency.  We do this buy folding horns in the cabinet on our pro models and some of our home models.  So if you have a normal speaker size in a living room and you want it louder you should get a more efficient speaker first but remember that the bass may suffer if it has not been thoroughly optimized by a Klipsch engineer.

Attached is a representative graph of four theoretical driver responses.

In the graph you can see that the bass cutoff frequency is higher as the SPL goes higher.  This can tend to be a general characteristic for a high efficiency loudspeaker.  The 100 dB reference SPL driver has a -10 dB response at 35 Hz; whereas an 88 dB driver shows 23 Hz.  This example is highly simplified but for the sake of understanding I thought I would start out with a simple set of trends.

To make up for this difference there is several things you can do in a 2 channel or home theater system.  The most common thing to do is add a powered subwoofer.  This is a very practical approach because it takes a lot of power stress off of the receiver for the main channel speakers and reduces the chance of IM Distortion by elimination of the cone modulations in the subwoofer band.  In other words the 30Hz is no longer going to the main speaker (HP) but to the subwoofer so the IMD can’t occur.  Another option would be to use a larger speaker enclosure.  Typically the bigger the better to some extent when it comes to increased box size.  This makes some incorrect assumptions that the Thiele Small parameters are still optimized in this larger box but if the engineer has done his homework he will have modified the driver to allow for the larger box.  This is generally referred to as the Cas or Compliance of Air Mass for the speaker.  

If anyone is interested I can get into the more intricate parts of a driver design where we look at Q of systems and drivers and box volume, etc.

The next time you think about how to improve your sound system you might want to start with the speakers.  Amplifiers can only do so much, but if you have an efficient speaker such as a Klipsch you will gain more in decibels.

Keep Thumpin!

Have you ever wondered why Klipsch is so horny?

From Wikipedia, the free encyclopedia…

“Horny is an adjective that can describe any one of the following conditions:

• An animal that possesses a horn
• A slang term for sexual arousal and/or desiring sexual gratification
• Having a rough, knobbly surface — e.g., a horny skin, found in some lizards“

Hmm… Well some of that may be true but it didn’t really help describe Klipsch as a whole.

Looking under the term acoustic horn…

“A horn is a tapered sound guide designed to provide an acoustic impedance match between a sound source and free air. This has the effect of maximizing the efficiency with which sound waves from the particular source are transferred to the air.”

Getting closer….Looking at Horn Loudspeaker…

“Acoustic horns convert large pressure variations with a small displacement into a low pressure variation with a large displacement and vice versa. It does this through the gradual, often exponential increase of the cross sectional area of the horn. The small cross-sectional area of the throat restricts the passage of air thus presenting a high impedance to the driver. This allows the driver to develop a high pressure for a given displacement. Therefore the sound waves at the throat are of high pressure and low displacement. The tapered shape of the horn allows the sound waves to gradually decompress and increase in displacement until they reach the mouth where they are of a low pressure but large displacement.

A modern electrically driven horn loudspeaker works the same way, replacing the mechanically excited diaphragm with a dynamic or piezoelectric loudspeaker.
Modern horn designs typically feature some form of conical, exponential or tractrix taper… “

Now we are getting some where.  At least the term tractrix is used.

“…Horn technology history
 
 Photograph of the original painting of Nipper looking into an Edison Bell cylinder phonograph with a horn loudspeaker.
The physics (and mathematics) of horn operation were developed for many years, reaching considerable sophistication before WWII. The most well known early horn loudspeakers were those on mechanical phonographs, where the record moved a heavy metal needle that excited vibrations in a small metal diaphragm that acted as the driver for a horn. A famous example was the horn through which Nipper the RCA dog heard "His Master's Voice". The horn improves the loading and thus gets a better "coupling" of energy from the diaphragm into the air, and the pressure variations therefore get smaller as the volume expands and the sound travels up the horn. This kind of mechanical amplification was absolutely necessary in the days of pre-electrical sound reproduction in order to achieve a usable sound level.[3]”

Ironically there is no mention of Klipsch in this entire article whatsoever.  That will have to be remedied later.  Klipsch didn’t invent the horned loudspeaker, but it has stuck true to its principles. What we can learn from this is that PWK was correct in pursuing high efficiency designs for his 10 watt amplifier. The laws of physics haven’t changed.

So lets understand a little more about why Klipsch is so horny and why you should be horny too.

Acoustics 101

To start off, we need to define general concepts about acoustics, starting with what an acoustic wave or waveform is. 
Sounds are waves of pressure variations moving through the air. These waves can be compared to waves moving in the ocean, although they move much more quickly and in three dimensions, unlike water waves, which are confined to a two-dimensional surface. When we hear sounds, what we are actually experiencing are minute vibrations of air. As waves of these small air currents pass through our inner ears, they stimulate the nerves in tiny hair-like projections. Our brain then translates this stimulation into the audible sound that we hear.

Since a sound wave consists of a repeating pattern of high pressure and low pressure regions moving through a medium, it is sometimes referred to as a pressure wave. If a detector, whether it is the human ear or a man-made instrument, is used to detect a sound wave, it would detect fluctuations in pressure as the sound wave impinges upon the detecting device. At one instant in time, the detector would detect a high pressure; this would correspond to the arrival of a compression at the detector site. At the next instant in time, the detector might detect normal pressure. And then finally a low pressure would be detected, corresponding to the arrival of a rarefaction at the detector site. Since the fluctuations in pressure as detected by the detector occur at periodic and regular time intervals, a plot of pressure vs. time would appear as a sine curve. The crests of the sine curve correspond to compressions; the troughs correspond to rarefactions; and the "zero point" corresponds to the pressure which the air would have if there were no disturbance moving through it. The diagram on the next page depicts the correspondence between the longitudinal nature of a sound wave and the pressure-time fluctuations which it creates.

A simple two-dimensional plot will partially describe the entire three-dimensional pattern. Sound travels in a spherical 3D pattern, but this is difficult to document on a piece of paper.  The waves depicted in this line of the plane wave tube are just that.  (Plane as in one geometric plane)  Imagine if you will that these are travelling to all areas of space as the sound moves away from the vibrating cone that originally created this wave.  This is where directivity is of concern for an design engineer at Klipsch.

Polar Directivity Introduction

Wavelength of Sound as a Function of Sound Speed and Frequency...
 
Now that we know a little more about sound waves lets discuss the why Klipsch uses horns to project sound wave patterns. 
When a sound wave is generated, it travels away from its source in a beam, in similar fashion to a beam of light emanating from a flashlight.  The angle of the wave propagation is determined by the ratio of its wavelength to the size of the opening through which the beam is projected. 
The acoustic radiation pattern is a function of the frequency of operation and the size, shape and acoustic phase characteristics of the vibrating surface of the diaphragm.

Transducer Radiation Patterns

The beam width is usually defined as the measurement of the total angle where the sound pressure level of the main beam has been reduced by 6 dB on both sides of the on-axis peak.
 
When describing the beam patterns of transducers, two-dimensional plots are most commonly used. They show the relative sensitivity of the transducer vs. angle in a single plane cut through the three-dimensional beam pattern. For a symmetrical conical pattern, such as that shown below.

At low frequencies (when ka is small) a loudspeaker radiates sound equally well in all directions (a boxed loudspeaker will even radiate low frequency sound into the region behind the box). As shown in the animation below, sound waves radiating from the speaker spread out evenly in all directions. This behavior is primarily why the location of a subwoofer doesn't really matter - you can place it pretty much anywhere and it will still fill the room with sound.

As the frequency gets higher, but assuming the speaker diameter does not change, the value of ka increases and the speaker becomes directional. That is, the sound energy produced by the speaker becomes channeled into a preferred direction and very little energy is radiated at other directions. In the animation below the radiated sound is pretty much contained within a cone of 55 degrees from the center axis.

As the frequency becomes even higher (and ka becomes much bigger than 1) the sound field radiated by the speaker becomes even narrower and side lobes appear. Now the main lobe of radiated sound is limited to about 20 degrees on either side of the central axis, and the pressure amplitude falls off rapidly as you move away from the central axis. Notice that the side lobes are much lower in amplitude than the main lobe. Also note that the sound waves in the side lobes have the opposite phase as the sound wave in the main lobe.If you were using the same speaker (a large woofer) to produce both low and high frequencies, you would definitely notice a severe drop-off in the loudness of the higher frequencies as you step away from in front of the speaker. Fortunately, well designed loudspeaker systems from Klipsch don't attempt to send all frequencies through the same speaker but instead use a waveguide or horn for high frequencies.  

3D Directivity Maps are Another way to view directivity in a 2D or 3D plot Amplitude (color), Angle vs. frequency.   

So the next time you are thinking about loudspeakers, and LOUD is one of those terms, think about Klipsch.  We are still sticking to horny!

A key factor in acoustics is the effect of the room environment on the loudspeaker.  This is actually half of what you are hearing.  The loudspeaker distributes the sound around the room, drastically, influencing what we hear.  Loudspeaker systems do not radiate uniformly at all frequencies due to the enclosure shape, diffraction, driver directing effects, and driver interference near the crossover points.  A uniform frequency response off-axis results in more uniform room reflections, which directly contribute to a stable virtual source that is not frequency dependent. 

If that is too complicated, just remember you are hearing the room as much as the speaker.  We call this effect Room Gain and Imaging.

When someone speaks to you, they usually face you.  It would be odd if the person holding a conversation had his back to you, but if he or she did you would expect their voice to sound different.  Why?  It has to do with where the sound is traveling and how high the pitch is for that tone.

In order to properly evaluate a loudspeaker on and off-axis, Klipsch developed a custom program for dispersion acquisition.  This program allows the design engineer to quickly analyze the level of sound in relationship to the vector angle of that sound wave.  The results show how the Klipsch horn technology helps to control the energy radiated by the loudspeaker. 

A typical speaker distributes energy unevenly throughout the room in an uncontrolled manner.  The energy reflecting around the room influences how we perceive the recorded sound.  Loudspeaker systems do not radiate uniformly at all frequencies, due to the enclosure shape, diffraction, driver directing effects, and poor summation between radiating sources at the crossover regions.  A uniform frequency response off-axis results in more uniform room reflections, thus directly contributing to a stable virtual source which is not frequency dependent. This effect, in turn, directly contributes to a stable depth of imaging or perceived reverb as intended by the recording engineer.

The graphs shown are directivity data in relationship to frequency.  We call this a directivity response or map.   The colors define 3 dB increments in Sound Pressure Level, (SPL).  5 straight bars would be considered a perfect system but merely impossible to design.  If it existed, it would surely be a single source in one VERY large horn.  The mouth on the horn would need to be about nearly 57 feet for a 20 Hz horn.  The angle of dispersion would define the mouth size.  57 foot horns are very acceptable to wives, so we typically make the horn shorter and sometime fold it, like a Klipschorn.

The graph below is a competitive loudspeaker whose name will be undisclosed, but safe to say it is a direct competitor of the Palladium P-39F and NOT horn loaded.  So now you can see that the back axis dispersion is much more excessive at some frequency than others.  This data alone supports the fact that the competitive speaker will be more dependant on the room for a reasonable frequency response.  There is no choice.  The room becomes a bigger part of the equation.  If you are listening to this speaker in a linear reflection room, the sound will still be nonlinear due to the erratic dispersion off axis.  Please don’t overlook this fact.  Not only is a Palladium speaker much lower distortion it is also a purer response off axis. 

Nothing sounds like a Klipsch… and nothing sounds like a Palladium.