Home Theater Design and Criteria
This is a summary of criteria and design decisions leading to a home theater (HT) speaker system. It's meant to describe the things that one should consider and try to implement in an HT speaker system. The objective here then is to identify the aspects of the home theater envirionment which will drive speaker and system designs for a THX qualified system which performs properly with the currently available surround formats for a 5.1 or 7.1* system. The following includes an analysis of speaker designs for the left/right, center, and surround speakers. The surround analysis includes a look at lobing and null effects for a surround speaker located on a wall adjacent to the primary HT listening position. *6.1 systems employ a rear center channel. The critera for designing a rear center channel isn't discussed here.
Assumptions for the HT system being designed
A moderate size rectangular room approximately 12' by 18'.
An HT receiver with 5.1 or 6.1 surround, Dolby Pro Logic, Pro Logic II, Dolby Digital, Digital Theater Systems (DTS). For reasons to be explained later, the reciever should be rated to operate all channels into 4 ohms. Also assumed is a subwoofer output and operation with low frequency effects or "larger/small" settings.
Criteria
As a minimum, the center channel speaker must be fully shielded or shielded suffiently enough that it can be placed within 4" above or below a CRT (tube) type TV. I used the 4" distance in the realization that no speakers are completely free of stray magnetism even if they are shielded with bucking magnets and cans. Surround and left/right main speakers can also be shielded although not required.
Left, center, and right (LCR) and surround speakers should provide bass response below 100 Hz. In order to smoothly integrate with the subwoofer, the bass roll off should be 12 dB/octave.
Surround speakers must provide a diverse sound field. Depending on a movie's sound engineer's practice, the surround will receive a full range signal, particularly in DD/DTS surround mode. Therefore, the surround must operate over the same full bandwidth as the other speakers.
LR main speakers can be floor standing or sit on stands. The center channel will sit above or below the TV. It may also be used behind a perforated projection screen. The surround speakers will be wall mountable. They will be located above and to the side of the listening position.
The subwoofer should provide response down to 30 Hz and up to 200 Hz to enable smooth transition at the 100 Hz crossover point. The subwoofer will be powered by a subwoofer amplifier with volume control and be fed a line level signal from the HT receiver which is attenuated to a 100 Hz crossover frequency.
Drivers for all speakers should be identical for to provide identical tonality/voicing.
The LR main speakers will be a two woofer MTM configuration. This provides more dynamics, better bass headroom to correct for baffle diffraction loss, and closer match of level with the tweeter when compared to an MT speaker. And since the center channel speaker will work best as a horizontal modified MTM, the MTM configuration for the LR mains makes a good match.
Center channel will be a modified MTM on it's side. To provide reasonable horizontal dispersion the tweeter will be offset vertically. The center channel will receive a full range signal in most surround modes. Therefore, it must provide full range output equal to the LR main speakers.
Since the center channel will be heard directly on the horizontal axis by a center seated listener, the upper level frequency response of the center channel should be attenuated to match the off axis response of the LR mains.
Cost less than $100 per speaker except for the sub. The sub's cost should be expected to range from $200 to $500.
LR speaker design
The Dayton 5 1/4" shielded woofer and 1 1/8" shielded silk dome tweeter will be used. Both are good performers and have very few bad characteristics to deal with in crossover design. The woofer has a very good mid-range with fairly smooth response up to the cone breakup region and sufficient bass output. The tweeter can be crossed over as low as 2000 Hz using a second order filter. Its response is fairly smooth, characterized by two ripples above 5 kHz which are generally listenable.
Attention to the woofers' low impedance point with respect to minimizing phase angle at that point will make the 4 ohm impedance tolerable for most amplifiers, even those not "4 ohm rated".
The LR mains will be two-way MTMs with the drivers aligned vertically.
The drivers will be located as close together as allowed by the frame/faceplate dimensions. A crossover frequency well be below 2500 Hz which corresponds to a wavelength of about 5 3/8" and just exceeds the minimum center to center spacing for the Dayton 5 1/4" woofer and silk dome tweeter of 5 1/16".
A sealed enclosure of 0.45 cu. ft. provides a 12 dB/octave low frequency roll off with an F3 point of approximately 90 Hz.
Center channel design
Placing the tweeter above the horizontal line of the woofers such that an approximate 45 degree angle is formed should provide minimal horizontal lobing.
The crossover point will be the same 2500 Hz; tweeter attenuation will necessitate a somewhat lower woofer low pass frequency to maintain the 2500 Hz point.
The same enclosure volume as the LR speakers will be used however the front baffle dimensions will change to accomodate the tweeter vertical offset. F3 will be around 90 Hz.
Surround design
The surround will utilize two woofers operating in parallel. A design option is to locate one woofer on top of the enclosure facing upward and the other on the bottom, facing downward. This keeps the woofer output above the baffle loss frequency (~500 Hz) from beaming directly at the listener. One tweeter will face forward and the other toward the back of the room. In dipole operation, the rear tweeter is connected in reverse polarity while the front tweeter is connected with normal polarity. In bipole operation, both tweeters are in normal polarity. Woofers cannot be dipole connected since their output would totally cancel below 500 Hz. Thus, the speaker would operate with one driver (tweeter) in reverse polarity from two woofers and the other tweeter.
In order to visualize the drivers' interaction, I went to http://www.falstad.com/mathphysics.html. This site contains an amazing array of java applets which provide visual simulations of a variety of physical phenomenon. The 2-D sound wave applet allows boundries (speaker baffles) to be drawn. The frequency and phase can be changed and the resulting summation of the speakers' outputs are seen as red (+), green (-), or black (zero). I first did the tweeters as in the proposed surround speaker located on baffles which are 45 degrees angled back from the front, which places the tweeters at 90 degrees to each other (see drawing). Note that the drivers in the simulations don't exhibit normal off-axis roll off, rather they are point sources and ratiate in 360 degrees. Still, the visualizations give an idea of the radiation patterns.
Two speakers on 45 degree baffles, bipolar operation per the drawing above. Frequency is set at the highest the applet allows. (the applet doesn't provide the frequency, but judging by the the scale of the enclosure, the wavelength is about 2" or 6700 Hz. The view is looking down at the top of the speaker and taking the front of the speaker to be on the left. Lobing is evident across an approximate 45 degree arc on the left.
Same setup at 6" wavelength/2260 Hz.  In the crossover frequency range, a listener will experience two nulls in the bipolar tweeter output.
Dipolar operation.  Very similar except lobes are reversed. It's interesting to confirm as seen that two drivers a distance apart greater than the wavelength, operating at the same frequency, will produce lobing.
Same as above at 6" wavelength/2260 Hz.  In the crossover frequency range, a listener will experience three nulls along the horizontal in the bipolar tweeter output.
Including the wall, the applet response is very similar.
To see what it would look like if the tweeter baffles were at 90 degrees instead of 45 degrees, here is the applet, wall included, 2200 Hz, dipole. Almost all of the energy is along the walls.
Same thing at 6700 Hz. Lobing is present and is caused by interaction with the wall.
Here is bipolar operation. Very similar.
And bipolar at 2200 Hz.
View from front of speaker -- the listener is looking to his right directly at the speaker -- top and bottom sources are woofers, left and right are the tweeters (the tweeters in this case are located on baffles 90 degrees to the front of the speaker instead of on the 45 degree baffle, again, a limitation of the applet).  All drivers are in phase. With 45 degree tweeter baffles, we can imagine that the strength of the sound from the tweeters will exceed that of the woofers since the woofers' 90 degree off-axis output will be significantly lower while the tweeter will be only a few dB down on the 45 degree axis.
Same view dipole mode. Upper and lower woofers in phase, right tweeter out of phase. (The left tweeter is removed because the applet will only allow changing phase in pairs). Looking at the right side of the picture the nulls are reversed, but the pattern is similar. Most of the mid range energy from the woofers will be radiating vertically up and down along the wall. Alot of the tweeters' energy will also radiate along the wall, however, most of the energy will beam into the room.
One more option not considered to this point is a configuration with the tweeters firing along the wall and a woofer firing directly toward the listener. This is the configuration Vance Dickason uses in his home theater surrounds.
What we see here, in bipolar operation at 6700 Hz is lobing effects from the drivers summing as well as wall interaction. However, the lobing effect in the direction of the listener (to the left) is less prevalent.
At 2200 Hz, the lobing is much less prevalent.
Dipolar operation looks much the same.
Dipolar at 2200 Hz has one strong null toward the rear.
Another simulation -- bipolar at 2200 Hz with a narrower baffle. The dispersion pattern is relatively smooth with subtle lobing effects. This appears to be the smoothest configuration with a very diverse field.
One more. Two woofers placed horizontally on the front (toward the listener) on a wide baffle.
So, putting some of what we see in the ripple tank simulations together: 1. Tweeters placed on 45 degree baffles directs energy toward the listener, however lobing is significant. 2. Placing tweeters on 90 degree baffles directs most of the energy along the wall and there is lobing occuring due to interaction with the wall. 3. In the side view with woofers firing up/down and tweeters at 90 degrees along the wall, there is lobing above and below the horizontal axis. 4. The Vance Dickason configuration seems to provide the least amount of horizontal lobing aimed toward the listener. 5. A narrow baffle version of the Vance Dickason design provides a smooth and dispersed sound field. 6. A wide baffle with two horizontally aligned woofers seems to provide the most even distribution. Location of the woofers should be as close together as possible and also close to the ends.
Summary
A design for a HT system consisting of sealed LR and center speakers should work well for the assumed HT system. The center channel should have the tweeter and woofers arranged in an inverted "V" configuration. My initial design for a surround speaker with tweeters on 45 degree angled and up-down firing woofers isn't conducive to a smooth dispersive soundfield with lobing. It ends up working better with tweeters on 90 degree baffles and the woofers on the front toward the listening position. Remaining considerations for the surround speaker include the crossover and relative levels for the woofer and tweeters. This will need to be determined by measurments and listening.