Sensitivity Vs. Size, MTM Vs. TMM, and Bookshelf Vs. Tower

[Big Daddy]

HOFFMANN'S LAW AND SPEAKER SENSITIVITY

When designing a loudspeaker, it is not possible to combine high sensitivity with compact enclosure size and adequate low frequency response. You can only choose two of the three parameters. For example, if you decide to build a small speaker with extended low frequency response, you must accept low sensitivity. This rule is sometimes called Hoffman's Iron Law, named after J. Anthony Hoffman (the "H" in KLH). This rule is a mathematical formula and was originally formulated in early 1960's and later refined by Thiele & Small (TS parameters), whose work now forms the basis of loudspeaker/subwoofer design.

Hoffman's Law states that the efficiency of a loudspeaker (woofer system) is directly proportional to its cabinet volume and the cube of its low frequency cutoff. This implies that if you want to lower the low frequency extension of the speaker by a factor of 2 from 60Hz to 30Hz and keep the same cabinet size, you will have to accept much lower sensitivity. In order to maintain the same level of efficiency, you must increase the cabinet volume by 2^3 = 8 times. In other words, if you want to lower the cutoff frequency of a loudspeaker and maintain the same the level of output, you need an extremely larger cabinet.

To summarize, low-frequency extension, cabinet size, and efficiency form the three key factors in speaker design. To increase any of them, you have to give up something from the other two. Of the three parameters, cabinet size is the most sensitive. That is why it is always recommended that you select the largest cabinet that you can live with. Since most people may not have the room to accommodate large speakers or cannot afford powerful amplifiers to achieve the desired loudness with inefficient speakers, that is another reason why subwoofers are becoming so popular. They have their own dedicated amplifiers and you can hide them almost anywhere.

If you want low frequency extension and are not willing to live with a very large speaker cabinet, the only other option besides a subwoofer is to use multiple drivers within the same cabinet. If you connect two identical woofers in parallel, the impedance will drop by half and you gain about 6dB in output (sensitivity). If you connect the two woofers in series, the impedance will double and there will be no increase in sensitivity.

As an example, if you are dealing with an 8-ohm driver that has a low sensitivity of 85dB and you want a very efficient speaker with over 90dB of sensitivity and 8-ohm impedance, you will need four identical 8-ohm drivers. You will have to connect each pair of drivers in series (impedance will rise to 16 ohms) and then connect the two sets of drivers in parallel. The net impedance will drop to 8 ohms and the sensitivity will increase over 90dB.

The procedure described in the previous paragraph is a common approach in dealing with sensitivity, but as they say, there is no free lunch and there are trade-offs. When you feed identical signals to these drivers, the frequencies from these drivers will interact somewhere in front of the speaker, resulting in comb filtering. As a result, some frequencies will be reinforced while others are attenuated and you will end up with peaks and valleys and a jagged frequency response.

Subwoofer Sensitivity Versus Xmas:

A speaker’s sensitivity is a measure of its efficiency. It measures how loud a speaker can play with a given level of amplifier power. There is a lot more information on this topic in the Impedance and Sensitivity of a Speaker thread.

Xmax is one of the Thiele/Small parameters of a speaker. It measures the maximum linear peak (or sometimes peak-to-peak) excursion (measure in mm) of the speaker cone. Xmax is used to determine the maximum linear SPL capability of the driver.

Generally speaking, a subwoofer’s sensitivity and Xmax are inversely related. With all things equal, the subwoofer with the higher Xmax will have lower sensitivity. Some believe that the cone area of a subwoofer driver can be reduced if the Xmax is increased. While this can be done up to a point, it is only possible to increase Xmax up to a few millimeters without a significant reduction in its efficiency.

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MTM VERSUS TMM SPEAKER DESIGN

An important consideration when you design a speaker is the baffle diffraction step, commononly known as Baffle Step (BS). In a free space away from the walls, at high frequencies, a loudspeaker's tweeter tends to project sound only in the forward direction (i.e., it has a 2 pi hemispherical radiation). At low frequencies, a speaker undergoes a transition by which its woofer begins to radiate sound in all directions (i.e., a 4 pi spherical radiation). As a result, the density of the low frequency energy is reduced in the forward direction where the listener is normally located. The overall effect is that the bass will be about 6 dBs lower in level than the treble. See the following diagram for an arbitrary 18" wide baffle.

One solution is to push the speakers against the wall to increase the bass output. There is always the danger that the sound will become too muddy.

A better solution is to add another midbass driver to compensate for the loss in bass output. There are two common ways of designing these type of speakers: MTM or TMM.

MTM Design:

This design configuration was first introduced by Dr. Joseph D'Appolito and is commonly known as the D'Appolito design. This configuration has two midrange or woofer drivers arranged vertically above and below the tweeter and uses a 3rd order (18dB/octave) 2- way crossover with the drivers connected in parallel and in phase. This allows the drivers to have similar horizontal dispersion, resulting in absence of any sudden change in directivity with frequency.

With MTM design, you have a vertical a vertical separation of the two mid woofers. Depending upon the distance from the ground, you will get two nulls at certain frequencies, one above and one below the speaker. However, each null is filled in to some extent by the other mid woofer which leads to two shallow dips rather than a single much deeper null.

MTM speakers can have have problems with frequency cancellations and comb filtering between the drivers, if you are not listening precisely on the axis of the tweeter. Imaging of the speakers can be affected.

You can minimize these issues by spacing the drivers as close together as possible. Some designers even put the tweeter to the side so that the mid woofers are closer.

In addition to the spacing of the drivers, you also need to design the crossover of the MTM speakers very carfefully. At a high crossover frequency, you will run into problems with acoustic cancellation between the mid woofers. There are some rules of thumb, but as a general rule, the lower the crossover frequency the better. This means your tweeter should be a capabale one so that it can handle the lower frequencies.

Rule of Thumb: The distance between the center of the tweeter and center of the mid woofers should each be equal to one wavelength of the crossover frequency. For example, if the crossover frequency is 2,100 Hz, you divide it into the speed of sound (344 meters per second or 1,127 feet per second) to get 1127/2000 = 0.537 feet or 6.5 inches.


TMM Design:

In theory you could use a TMM layout and wire both woofers in parallel connection and use a 2-way crossover. However it will cause some problems with the acoustic cancellation between the drivers. Two-way crossovers will work with an MTM configuration, but not so well with a TMM configuration because there is no way to preserve the phase alignment with the tweeters since the second woofer is further away. TMM designs normally use a crossover circuit known as 2.5 way or even a 3-way crossover. With this type of design it can be difficult to get good results and requires the use acoustic measurement and design software.

The addition of a 0.5 driver in the bottom requires that you set a low pass filter for it to coincide with the spreading loss of the upper woofer, net result is constant power output through the bass to midrange frequencies. Normally, you run the upper woofer all the way down, while the lower woofer goes through a low pass filter.

Some designers place one driver at the bottom of the cabinet to take advantage of the proximity to the floor to boost the output of the woofer. However, there are mixed opinions about whether it improves the sound or not. This type of design would work best with a 3-way crossover, so there would be less acoustic cancellation between the widely spaced mid woofers.

There are perhaps more MTM speakers than TMM speakers. These are some examples.


Polk RT55:

Cadence F-19 Mini Tower:

Horizontal Placement:

The performance of both MTM and TMM are significantly affected when placed horizontally. Designers have used different techniques to deal with problems associated with horizontally placed MTM speakers.

Different Center Channel Designs:

The problems associated with horizontal center channel speakers are discussed in the following thread:

Horizontal Center Channel Speakers and Why They Should be Avoided.


Moral of the story: It is all about BS. I mean Baffle Step.

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BOOKSHELF SPEAKERS VERSUS FLOOR STANDING TOWER SPEAKERS

The Usual Suspects

• Some may argue that it depends on the size of the room. I have heard this argument many times. My response is that unless you have a room the size of a commercial movie theater or a large auditorium, all home theater rooms are small compared to the wavelengths of lower bass frequencies.
  
  
  
  
  
• Some may argue that it depends on the quality of the bookshelf speakers. My response is that we are not trying to compare an excellent bookshelf speaker to an inferior tower speaker. The assumption here is that the comparison is made between a bookshelf and a tower speaker from the same manufacturer that have the same type of drivers and design.
• Some may argue that it depends on your budget as bookshelf speakers are generally cheaper. Although this may be a valid argument, I will respond that if you want better frequency response in your room, you will have to buy one or two subwoofers and that may increase the cost. Bookshelf speakers also need stands and the price of those should always be added to the total cost. Furthermore, there are some bookshelf speakers that cost several times higher than many tower speakers.
• To summarize, you are wrong and I am right.

Advantages of Bookshelf Speakers

• Lower cost.
• Less complicated to build.
• Smaller number of drivers and easier to integrate.
• Less complicated crossovers.
• They have higher WAF appeal.
• Lighter.
• More maneuverable and easier to place.
• Take less space.

Disadvantages of Bookshelf Speakers

• Lower efficiency.
• Less power tolerance.
• Poorer bass extension as compared to same level floor-standing speakers from the same company.
• They require stands and some stands are expensive.

Advantages of Floor-Standing Speakers

• Better low frequency extension. They will always have deeper and greater bass output.
• More drivers and additional wow appeal (tower of power). More drivers means a woofer for deep bass, a midrange for the bulk of instrumental and vocal sounds, and a tweeter for high frequency nuances like cymbals and percussion instruments.
• Larger speakers may have better imaging.
• More power tolerance.
• Higher efficiency.
• Can play louder.

Disadvantages of Floor-Standing Speakers

• More expensive.
• Heavier.
• Difficult placement in the room.
• Lesser WAF appeal.
• More difficult to integrate multiple drivers.
• More complicated crossover networks.

Let us start out our discussion by making the assumption that we all desire that our perfect speakers will have a relatively flat frequency response in our less than perfect rooms. Having made this assumption, a good place to begin is by reviewing the summary and conclusions of Post #1 of A Guide to Bass Management (Part II).

1. In a small home theater room, it makes sense to separate the low frequency drivers (subwoofers) from the main speakers and place them in a more appropriate and optimal position. This has absolutely nothing to do with the quality, design, or low frequency extension of the main speakers. The main reason is because the room forces us to do this and not because the speakers are deficient.
2. The low frequency sound waves have very large wavelengths. These waves will interact with the room boundaries and create standing waves and room modes. As a result, bass will become very uneven across the room. These modes occur in all small rooms and for all speakers/subwoofers and depend on the dimensions of the room and not the quality or design of the speakers/subwoofers.
3. The location of the bass generator and the location of the listener determine whether certain low frequencies are energized or cancelled. If your chair or sofa happens to be located in one of the troughs of the standing waves, you are not going to hear much deep bass. But if you get up and walk a few feet back, or to the left, or to the right, chances are you will hit one of the peaks and the bass will be very strong, perhaps too much of a good thing.
4. Standing waves in small rooms is a problem associated with low frequency waves and not high frequencies. All small rooms are subject to standing waves. It is a well-known fact that cubic rooms are the worst as far as bass performance is concerned. First of all, such a room will have a very high ceiling and will be impractical. Secondly, even if we make the ceiling height half of the other two dimensions, the room resonant frequencies will all line up together like Pawns on a chessboard (Dr. Floyd Toole’s words) with big gaps between them. As a result, some frequencies will be overly accentuated, and others not adequately represented. A room is normally better if its resonant frequencies are more uniformly distributed.
5. Standing waves occur even in non-rectangular rooms. However, their location becomes unpredictable and difficult to calculate. The advantage of a rectangular room is that you can easily calculate the location of the room modes.
6. The most appropriate solution to even out the bass performance across the room is to place 2 or 4 subwoofers in the room and set the other speakers to small with appropriate crossover frequencies. Some bass equalization is generally required. However, remember that an equalizer will solve some problems, primarily those related to peaks. A null is an entirely different situation and no amount of boost can fill a room-induced null. Think of it as a water drain. No amount of water can fill a drain. If you own one or more capable subwoofers, all the other speakers in the room become small by default. Again, this is not because your main speakers are deficient. As I said before, the room is the real culprit.
7. Depending on the capabilities of your speakers and their location in the room, a crossover frequency between 60Hz to 120Hz is appropriate for the vast majority of people.
8. In large halls, such as movie theaters, large auditoriums, large indoor stadiums, or outdoors, we don’t generally worry about low frequency standing waves.
9. Room treatment is effective to control the higher frequencies. However, they are generally very ineffective for frequencies below 100Hz. Although an anechoic chamber has better acoustics than even a well-treated room, manufacturers and researchers tend to go outdoors to perform tests on very low and deep frequencies.
10. The laws of physics do not stop working in your room because you feel a certain way or believe your speakers/subwoofers are designed a certain way or they are too good and too expensive to be subject to the effects of room modes.
11. Tower speakers made sense in the past in the era of stereo. However, they have become almost obsolete because of three reasons:
    1. The availability of advanced receivers/processors and their sophisticated calibration programs and crossover settings.
    2. The availability of very good powered subwoofers with excellent low frequency extension at very reasonable prices.
    3. The increase in the level of knowledge and availability of information as far as wave interaction, room modes, and bass performance are concerned.
12. Instead of wasting too much money on big tower speakers, it makes more sense for the vast majority of home theater users to spend their money on mid-sized front speakers that have excellent mid-range and high frequency performance and spend the additional funds that they will save on 2 or 4 quality subwoofers. In the majority of cases, the bass will be more even across the room and superior to the bass generated by tower speakers only.

Having said all of that, it may be easier to integrate larger speakers with subwoofers. Even if you have large full-range speakers, it is beneficial to redirect the low bass frequencies from them and send them to the subwoofers. Always use two or four (even number) subwoofers.

Additional Information

• A Guide to Subwoofers (Part II): Standing Waves & Room Modes
• A Guide to Bass Management (Part I)
• A Guide to Bass Management (Part II)
• Why Do We Need Equalization and Room Correction?
• Miscellaneous Ramblings on Subwoofer Crossover Frequencies
• The Misunderstood 0.1 LFE Channel in 5.1 Digital Surround Sound

[Big Daddy]

I have been asked questions about the topics mentioned in post #1 quite a few times. For the benefit of the members and to avoid repeating myself, I decided to combine the edited version of the scattered responses in this sticky thread.

[WiWavelength]

Big Daddy, many of your well researched informational posts are great, but this one in particular is top notch (no pun intended). The more that readers understand the science of audio reproduction, the better...

AJ

[Big Daddy]

Originally Posted by WiWavelength

Big Daddy, many of your well researched informational posts are great, but this one in particular is top notch (no pun intended). The more that readers understand the science of audio reproduction, the better...

AJ

Thank you. If they had given me a penny for all the BS I wrote in the sticky threads, I would have been be a millionaire.

[Saril]

I also want to thank you for your very well written posts!
Although I struggle trying to understand them, I am very appreciative of the quality of your work and the time you take to help others.

[Big Daddy]

Originally Posted by Saril

I also want to thank you for your very well written posts!
Although I struggle trying to understand them, I am very appreciative of the quality of your work and the time you take to help others.

Thank you for your thoughtful compliments.

[Fidi]

Hi, i have a question.
My question is about placing a speaker horizontal.
What if for example you have to place standard vertical direct radiating speaker horizontal.
What i want to know, is;
Will it influence sound quality(timbre, image,dispersion of sound) by placing the speaker in a horizontal position?
What's the disvantage by placing a speaker horizontal?


And from wich frequency responce can we say that a speaker is a full range speaker.
Short: When can we say that a speaker is a full range speaker, wich minimum frequency response must such a speaker have?

Thank u.

[Big Daddy]

Originally Posted by Fidi

Hi, i have a question.
My question is about placing a speaker horizontal.
What if for example you have to place standard vertical direct radiating speaker horizontal.
What i want to know, is;
Will it influence sound quality(timbre, image,dispersion of sound) by placing the speaker in a horizontal position?
What's the disvantage by placing a speaker horizontal?


And from wich frequency responce can we say that a speaker is a full range speaker.
Short: When can we say that a speaker is a full range speaker, wich minimum frequency response must such a speaker have?

Thank u.

It is generally not a good idea to place a speaker (e.g., an MTM speaker) horizontally. This is discussed in the Horizontal Center Channel Speakers thread.

Different manufactures and different people have different definitions for Full-Range. It is all semantics and really mean nothing.

If you have a subwoofer or several subwoofers in the room, all your speakers become small by default. Depending on the low frequency extension of the speakers, you should set the crossovers of the speakers to around 80Hz. The frequencies below the crossovers will be redirected to the subwoofer(s).

If you don't have a subwoofer, then you should set your front speakers to large (full-range) and the other speakers to small. The frequencies below the crossovers will be redirected to the front speakers.

[HAMP]

[Show spoiler]

Originally Posted by Big Daddy

It is generally not a good idea to place a speaker (e.g., an MTM speaker) horizontally. This is discussed in the Horizontal Center Channel Speakers thread.

Different manufactures and different people have different definitions for Full-Range. It is all semantics and really mean nothing.

If you have a subwoofer or several subwoofers in the room, all your speakers become small by default. Depending on the low frequency extension of the speakers, you should set the crossovers of the speakers to around 80Hz. The frequencies below the crossovers will be redirected to the subwoofer(s).

Originally Posted by Big Daddy

If you don't have a subwoofer, then you should set your front speakers to large (full-range) and the other speakers to small. The frequencies below the crossovers will be redirected to the front speakers.

Humm!!! I did not realize this little detail of information. I understand this information if you have an subwoofer, but I did not know this would happen with just having towers set to full range without a sub.

It seems kinda odd that, if your surrounds crossovers are at 100hz, and if bass below are meant to come from the surrounds, that it would be redirected to the towers subs/woofers.

So, basically it has to go somewhere and not just drop off?

[Big Daddy]

Originally Posted by HAMP

[SPOILER]

Humm!!! I did not realize this little detail of information. I understand this information if you have an subwoofer, but I did not know this would happen with just having towers set to full range without a sub.

It seems kinda odd that, if your surrounds crossovers are at 100hz, and if bass below are meant to come from the surrounds, that it would be redirected to the towers subs/woofers.

So, basically it has to go somewhere and not just drop off?

On many newer receivers, the front speakers are automatically set to large if you say NO to the subwoofer option.