Product Review - Subwoofers Under the Christmas Tree - December, 2001
As we once again we head indoors from our summer of fun, we look to home theater to satisfy that itch . . . and, there are two types of audiophiles:
A. You like the little explosions and smooth guitar riffs.
B. You like the walls and floors to shake violently, and feel the bass guitars rip through your body.
If you pledge to the second type, you've found the right article. If you pledge to the first, you don't know what you are missing! We rounded up some of the newest subs and some of the industry's reference subs (photo above), and played them back-to-back. Regardless of which sub you choose, all will give the desired perma-grin, and any would look nice under the tree this year. But, first let's cover the basics so that we are on the same page.
What is a subwoofer?
The definition has changed over the decades, but it's defined usually as:
Subwoofer: a mechanical sound implement capable of reproducing frequencies close to or below the lower limit of the human auditory spectrum. We as the human species vary from person to person but on average we cannot hear below 20 Hz. Now, that doesn't mean we can't FEEL below 20 Hz. Most of the SHAKE in home theater is at or below 20 Hz, with explosions and such reproduced between 20 Hz and 80 Hz. That is one of the best things about subwoofers. They make something you not only can hear, but feel in your skin and in your chest.
What is SPL?
SPL is a measurement of Sound Pressure Levels made in decibels that reflect how loud a sound is perceived to be compared to the threshold of hearing. The human ear is much less sensitive at frequencies below 500 Hz than anywhere else in the spectrum. This means that it takes more SPL at 20 Hz than at 500 Hz for the two sounds to have the same perceived "loudness."
Notes by Colin Miller: The generally accepted threshold of hearing for average humans (and we're pretty uniform across the board aside from old age or premature hearing loss brought on by heavy machinery or loud concerts, etc.), is 0 dB at 1 kHz. At 2 kHz, that drops to -1 or even -2 dB. At, say, 40 Hz, it's MUCH higher. It was cited in both my physics book, as well as my perception books, but I've been foolish in the past by selling my textbooks after the classes ended. I would venture to guess that in the range that subwoofers operate, the threshold ranges from about 30 dB - 40 dB, though before actually citing a number, I'd verify the stats. This vastly decreased sensitivity is represented through the Fletcher-Munson curve. It (or some other plot) also shows that differences in perceived loudness in relation to dB varies with frequency, which is why I continually repeat that the 10 dB rule of thumb for a perceived doubling of loudness is only a rough approximation. Even without variations in frequency, if you start to turn things up and asked 10 different people to stop you when they thought that it had reached twice as loud, you'd get a range of answers to choose from. The dropoff of SPL in distance from the speaker is an inverse square function, meaning that if the distance doubles, the SPL drops by a factor of 4. If the distance triples, the SPL drops off by a factor of 9.
Perhaps a good way to explain it is that sound radiates more or less spherically. As the wave propagates, a particular instant of that wave expands as if it were on the surface of an expanding sphere. That sphere, in terms of intensity, will most certainly not be uniform, but the spreading is. The surface of the sphere, or any geometric 3-D object, increases by the square of the difference in distance. The total energy of the wave doesn't change, but the surface area does. Since the SPL is a measurement of energy per area, specifically defined in a formula which I remember as 10 log((acoustic watts/cm2)/(10-14 acoustic watts/cm2)). If you look at the equation, you realize that as the energy intensity is an inverse function to surface area, the SPL declines as an inverse square function of distance.
The doubling of the sound pressure levels represents a 3 dB increase, but it takes an approximate 10 dB increase in SPL to perceive a doubling in loudness. If this seems odd, it's because SPL is on a logarithmic scale of base ten. The human ear can typically distinguish a 3 dB difference. A subwoofer playing a 30 Hz note at 110 dB is perceived as twice as loud as one playing at 100 dB. Generally if you double the power input or add an additional driver you will increase the output by 3 dB. But, It should be noted that an additional driver only doubles efficiency if it's within close proximity of the other, so that they can acoustically load each other. As you play down the frequency scale it takes more power to play at the same SPL. You must also quadruple the excursion of the woofer every time you half the frequency. This is why it's so important for a sub to have large excursions, or large diameter woofers, or in some cases both.
Sound pressure level is not a pressure wave, but a logarithmic measurement of actual acoustic energy intensity. More accurately stated, sound is a collection of pressure waves. Distance from the speaker to the listener is VERY important. Every manufacturer rates the SPL capabilities of their speakers from 1 meter (about 3 feet). So, if the speaker is rated to 120 dB, why do I only get 108 dB in my living room? Starting at the 1-meter mark, every time you double the distance you lose 6 dB. So, if you place you sub 2 meters away, you're at 114 dB, and at 4 meters, 108 dB.
Most manufacturers don't tell you at what frequency they measured their peak SPL, so take it with a grain of salt. Rooms, distances, and placement all make a difference. It's really hard to compare subs unless the comparison is performed in the same room, for all subs, with the same placement, and same distance.
Now that we understand the terms, let's talk about subwoofer design.
Small box, Big Box, Big Driver, Excursion, Power, Vented, Sealed . . . it's enough to drive a bass addict to drink. But, subwoofer design is easy. Large Driver, Large Box, Lots of Power, Multiple Drivers. It's pretty hard to get that design wrong. But, what if you actually want to put it in you living room, or even fit it through the front door? You must compromise, and you must have talent.
There is one main factor when it comes to making sound, and that is moving air. No matter what you do, the more air your subwoofer can move, the louder and lower it can go. To move air, there is a diaphragm (speaker cone) that is moved back and forth, and this motion is called the excursion. The area of the moving diaphragm (π r2), multiplied by the excursion, gives us the displacement. The higher the excursion, the harder it can be to control the driver, and the better the chances for non-linear sound (muddy, cluttered sound). This is why larger drivers are often used, because they require less excursion playing the same material, at the same SPL as a smaller driver. There are all kinds of tricks in the book to change the design parameters, and for each woofer here we will talk about what design the manufacturer used. For more on Box (enclosure) design see MTX's Audio Reference http://www.mtxaudio.com/caraudio/education/.
All this talk and no subs yet! Well, it's important to understand the basics before you can swim. Understand that when a speaker is measured that it will always reflect its surroundings. The only exception is an anechoic chamber where no sound is reflected. This is important to note because my measurements reflect the room that they were taken in. What's more important is that all the subs here were measured in the same room, so no one subwoofer had an advantage. The measurements were taken with a 1.5GHz PC running SpectraLab Pro. The samples were measured with a calibrated microphone using C weighting. Distance from the corner of the room to the listening position was roughly 12 feet, in a room a little under 3600 ft3. Frequency sweeps were run from 10 Hz to 100 Hz. The volume was raised little by little until the sonic quality started to change.
Shake Value: Rated at 20 Hz with 70 dB being a 1 and every 10 dB above that another point. It's subjective, but an easy gauge at how much this sub will rock your boat. The rating also means for every point, it's twice as loud as the previous point. You will notice that the graphs all seem to have similar contours, and this is caused by the specific listening environment. An external EQ can be very useful here to change some of those large dips and peaks. No EQs were used in the test though, because that was not the purpose of the review. This is also why the response isn't as flat as the manufacturer's measurements, but it's a typical HT room.
All the reference scenes were listened to at "Reference Volumes." I listened to each sub as they came in the door, and at the end I started over, noticing the differences between them. Common problems were high distortion, absence of the effects, sub sounding like it's playing under water [muddy]. Also, port noise can become a problem at these low frequencies. A few subs even will shut off.
Reference 1: U-571, "Depth Charges". During this passage, you had better batten down the hatches. With information extending down to 5 Hz, it's difficult for most subs to reproduce. The best subs will play it, while others simply ignore it (they don't respond that low). If you can feel the floor board ripping away from the joists, you have a good sub. Check the 3-D plot of part of this movie passage below. There are lots of sounds at 30 Hz with bits and pieces into 10 Hz.
Reference 2: The Matrix DVD, Chapter 15 49:00 ; "I know Kung Fu" During this fight sequence there are many sub items present. The drums should roll and sound clear. The fight sequence has many drops that contain sound at 20 Hz, some subtle. The music has synthesized bass all over. The large drums during the passage have a deep rumble that some subs will reproduce, others miss it entirely. When Neo falls to the floor, you should feel the impact in your chest. You will be wincing at this one. A 3-D plot is shown below.
Reference 3: Fantasia 2000 DVD, Chapter 2 "Symphony No. 5". As a classical piece, the low transients should be smooth and clear. The sub should show no signs of strain to reproduce the low notes. In this symphony, many of the bass notes are sharp and force full. It becomes VERY important for the sub to blend into the rest of the system, and keep up, as the music contains equal levels, and play instruments that will overlap from the sub range into the main speakers. With music it's very important to have listened to the sub, and adjusted the gain. Often you will prefer one gain setting for music and another for movies. With most new receivers you can change the sub levels for the stereo and 5.1 material independently, so double check your settings.
Reference 4: Sting: "A Thousand Years; Brand New Day CD": The intro itself is a difficult piece to reproduce. Throughout the song there are lots of transients, but there are a few that are under 20 Hz. If you can't feel this song in your chest, your sub isn't playing with a full deck. The sections under 20 Hz shouldn't be heard, but felt, so if a sub loses it's head, you may hear nothing but distortion (or nothing at all). Sections roll right form the transients into the sub-sonic rumble; this should be clear and precise. At high volumes you're looking for that definition and clarity. During the first 5 seconds of the song there is a lot going on, and you should be able to shake the rafters.
OK, so bring on the subs . . .
You may be asking why the KSW was included amongst these much more expensive and elaborate subs. First, you want to know what you are paying for right? Why buy a $2,000 sub vs. a <$1,000 one. The $500 KSW-15 (15" driver, 800 watt amplifier) is your "typical" sub that represents that price range well, so it represents the general market. This model is part of Klipsch's Synergy Series.
Performance: With a peak SPL of 106 dB at 64 Hz, it's a bargain. Notice how steep the sub rolls off from 30 Hz. When listening to the sub, it felt as though it was dying under 30 Hz at full volume, and at 106 dB, it was straining. At mid to low volumes the sub sounds punchy, and will play fairly low, but it lacks the impact of the other subs.
Shake Value: 1.7 (87 dB at 20 Hz).
That may sound like a harsh review, but compared to the other subs in this review it just couldn't keep up. I didn't expect it to either. This is what you are paying for. For the cost of this sub you should expect this performance. For the price, it performed very well. Listeners with small to medium systems, or listeners with smaller rooms would be happy with this sub.
Reference 1: While playing the scene, the sub wanted to shut off, and if played loud enough it would. It lacked the ability to play the rumble, and didn't pull it off. A few pops and snorts, the KSW just couldn't keep up with U-571.
Reference 2: During the drop sequences the sub neglected to play a few of them. The one or two played didn't have the impact the other subs did; in fact they were faint.
Reference 3: The sub simply didn't play some of the notes; higher material was reproduced with a good punch, but lacked the force and definition that the other subs displayed. The kettle drums sounded a little muddy at higher volumes.
Reference 4: The intro was missing most of the material under 30 Hz; during the song there was no rumble, just some distortion/port noise. The sub simply wouldn't reproduce the <30 Hz cleanly at moderate to high volumes.
Appearance: The Sub comes only in black veneer, well put together.
Methodology: Tuned port design, with 15" down-firing driver.
Features: Built-in Amp, Crossover, Phase Switch, Line-Level, and Speaker-Level inputs.
More Information: http://www.klipsch.com
The CS-Ultra can be ordered as one or as a pair, connected to a single amplifier (1,000 watt external amplifier supplied). This speaker is the old fashioned route to big-bass. With a large enclosure size, large driver, and MASSIVE power, it's hard to go wrong. By using a cylindrical design, SVS made the footprint fairly small, but by no means do they hide in the corner. A very well made package, and well shipped. This was the first sub to be tested, and it took my breath away. At 20 Hz, the sub felt like it was going to rip the floorboards up. During the entire test it never sounded muddy, just clean and violent (it's a guy thing).
Performance: With a peak SPL of 118 dB @ 30 Hz, this sub rocks. Pulling above 108 dB from 16 Hz, it's guaranteed to make the floor move. As you can see from the SPL graph, it's a huge step up from your average sub. At 20 Hz it was 23 dB louder than at 16 Hz, and at 30 Hz it was more than 15 dB louder. All with perfect clarity. I think they could have played even louder, but I stopped when the provided amp started clipping. No severe port noise was noticed during the test. Below 20 Hz, port noise became noticeable.
Shake Value: 3.9. (110 dB @ 20 Hz).
Reference 1: Can you say rumble? I was ready to call the fire department after this sub, and reproduction was loud and clear. All I could hear was the rafters in the room move. Not for the light hearted. Impacts were strong and deep.
Reference 2: Poor Neo, poor neighbors. Every drop was heard loud and clear. The rumble of the drums was perfect, and the synth bass was clear.
Reference 3: With some changing of the crossover points, the sub integrated and kept up with my Klipsch horns to ANY volume. All the material was reproduced faithfully and clear. The CS-Ultras do not sound as accurate as the HGS-18 during musical play. Perhaps they sounded too bassy during portions that weren't supposed to have that amount of material. Also, the HGS-18 uses servo-feedback to eliminate harmonics, while the CS-Ultra does not, so some of the CS-Ultra sound will be harmonics.
Reference 4: Good Lord. Listening to the song at full tilt, I could see things on the couch move. Every note was clear and defined. No mud here. The subs never felt like they were struggling to reproduce under 20 Hz. Call the doctor. These things rock.
Appearance: The Sub comes only in black velvet cloth, but soon to be release is wood veneer version that looks beautiful. The CS-Ultra is well built. The woofer driver is at the bottom, firing down, with three large vents at the top. A nice black grille covers the vents, making a very well though out package that is resistant to kids and animals. No hiding this weapon. Everyone who saw it stayed glued to the couch till they could hear it for themselves. Display them like a trophy.
Features: External Amp, No Phase Adjust, No Crossover, only Line level inputs. Lacks most features found on this level of sub, but better designs may negate the need for these features . . . although phase would be a welcome bonus. However, you can get a simple phase inversion just by switching the output wires from the amplifier to the drivers.
Methodology: Tuned Port (3), one downward-firing 12" woofer per tube.
Comments: What great subs. My main towers are loaded horns, very hard for a sub to keep pace with, but the CS-Ultra kept up and more. They lack some bells and whistles of the other subs, and the external amp can pick up stray noise in the house electrical system. The laptop that was used to take the measurements had to be unplugged, because the amp picked up horrible noise from the laptop AC adapter. Something else to consider is the company. It's a rare thing for consumers to be able to consult with the designers and engineers of the products; SVS offers the wonderful customer service and support bar none. Have a question? Talk to the people who designed the sub. Optional is a equalizer to fine tune your in-room response which would be handy to flatten out the response curves inherent from in-room modes. The provided amplifier pulled enough juice to dim the lights in my home theater room. Those who choose this setup should definitely have a dedicated 20 amp - 30 amp circuit for the entire home theater system.
More Information: http://www.svsubwoofers.com
Atlantic Technology 372-PBM
This is a THX-certified front firing woofer with a 275 watt amplifier. With a single 15" driver in a sealed box, it's a fairly conventional design. The sub came in a simulated wood veneer, with a gray colored woofer cone. The overall package is very nice with a black screen covering the woofer. It's also just about the same height as an end table and might make an easy integration with furniture. The sub was set up in a corner with the woofer facing the listener. It's a hefty piece of sub. Lets see what it can do . . .
Performance: With a peak SPL of 111 dB at 56 Hz, this sub can belt it out pretty good. Unfortunately the AT really hurts down low, and below 30 Hz things got pretty hairy for the sub. During the test, the sub audibly started distorting below 40 Hz early on. The sub was very strong above 40 Hz, pounding out about 10 dB more from 40-75 Hz than the average sub.
Shake Value: 2.0 (90 dB @ 20 Hz).
The PBM did manage to get 5 dB up on the KSW at 20 Hz, but it wasn't as clean. The sub never shut off during the tests.
Reference 1: During U-571 the sub did admirable with everything except the really loud low stuff. A few pops and I had to turn down the volume. The sub never shut off like the KSW did.
Reference 2: The sub did very well, and I was surprised at how well it reproduced the rumble and fight scene. It didn't sound near as clear or as strong as the SVS. The punches were delivered fast and accurate. At full tilt, the rumble sequences started distorting, and the punches got soft, but the transients were still strong.
Reference 3: The sub didn't reproduce the lowest of notes, but did excellent in the transient sections. The transients had the needed force the music demanded. They were clear, but when pushed, the sub rounded the notes. It performed much better than the KSW, but lacked the 20 Hz reinforcement of the SVS.
Reference 4: The low rumble that was apparent with the CS-Ultra was very low, but playing the song at reference levels wasn't possible without distortion on the rumble. The sub did very well with the kick drum and transients present in the song. The PBM has lots of punch, and a soft sound to the transients. The song was very enjoyable, but lacked that bottom end.
Appearance: Very well made, neat, and simple finish. Would look fine in a prominent visible position. It looks beautiful with the grille off. The large gray woofer compliments the rest of the sub nicely.
Features: Front mounted gain control is very handy, crossover selection, low and high inputs, phase selection, and high pass outputs. This sub has all the features we would expect on a reference sub.
Methodology: Sealed enclosure, front firing 15" woofer.
Comments: Great sub, but it's missing the very bottom end. Music and special effects over 40 Hz are played like they should be. It's not the loudest, or the lowest, but has great output between the 40-75 Hz range. It never shutoff during the testing, but had a tendency to sound muddy or rounded when pushed hard.
More Information: http://www.atlantictechnology.com
What would any sub comparison be without the Velodyne HGS-18? This is one of the highest regarded subs in the world. It arrived at my door by way of semi, where they unloaded it on a pallet. It's big, it's beautiful, and how could anyone not like it? The HGS-18 uses a massive 18" driver and a nice 1,350 watt digital switching amplifier. At 105 pounds, the HGS is the daddy of subwoofers. It's a legend.
Performance: With a peak SPL of 113 dB at 55 Hz and 101 dB at 20 Hz, this sub pounds away. Look at the graph. From 15 Hz to 40 Hz, it varied only about 6 dB. It didn't manage to beat the SVS in total loudness, but it still shook the floor with an intense force, and there were no harmonics.
Shake Value: 3.1 (101 dB @ 20 Hz).
The HGS is servo-controlled, meaning that it corrects its own distortion (that is part of the reason why the absolute SPL may not be as high as some non-servo subwoofers). No matter what was thrown at it, the HGS never distorted, never sounded slow. It didn't have the same gut wrenching sound the SVS threw out, but unlike the other subs, including the SVS, when it reached its limits, the sonics still didn't suffer.
Reference 1: The HGS did justice to U-571; the explosions sounded clean and awesome. Never did the HGS distort the sound. It's cleaner than the SVS, but not quite as fierce.
Reference 2: Clean and Clear. At no time did the HGS distort or sound muddy. It sounded clear through every section. Transients and drops all were performed as expected. Compared to the SVS, it sounded a little more accurate, but didn't have as much impact. Where the SVS felt like a kick to the head (slam), the HGS felt like a kick to the chest (depth).
Reference 3: What a joy to listen to. The HGS sounded so smooth and refined. The instruments so well defined. Every note was created just as it should be. The HGS kept up with the Klipsch horns very well, until the very end where the horns seemed to dominate a little. Again even at the limit it sounded good.
Reference 4: Again the HGS sounds so pure. Probably the best sounding sub I have ever heard. The music was so clean and the bass so . . . perfect. The HGS may not play as loud as the SVS, but it plays with a little more definition. The SVS has more snap, but the transients with the HGS are like butter.
Appearance: The gloss black exterior is beautiful, but the gloss can represent a glare problem for home theater. With the lights low for movies, you can see reflections in the perfect gloss surface. The finish does add more elegance with the lights up. The finish is exquisite, even down the glowing blue LED. All the controls are on the back, which could be a problem, due to the sub's size. Velodyne even thought of that with a remote control for the volume. Take the grille off and scare your friends. That 18" woofer in the front is something to behold, definite cool factor. This 18" driver is probably the most highly engineered in the world.
Features: Remote control, Low/High inputs, Internal Crossover, Phase switch, Subsonic filter. Everything and more from a reference level subwoofer.
Comments: How do you put this sub in words? It was clean and accurate everywhere. Quite possibly the best sounding sub I've heard to date. Its output was twice as loud as the KSW. I listened to a few more CDs with the sub hooked up and found more passages I had been missing and not enjoying. It was a true pleasure to listen to the HGS18.
More Information: http://www.velodyne.com
Just released is the new RSW-15. With a 2,400 watt BASH® amplifier along with a 15" woofer and 15" passive radiator, just from the specs this sub had promise. It is part of Klipsch's Reference Series. When I first started listening to the sub, it sounded very peaky with the 60 Hz+ material. I tried repositioning the sub several times, but couldn't get the sub to balance out. With the radiator aimed 1 ft into a corner, I got the best results.
Performance: As you can see from the chart above, this sub was very peaky in the 70-120 Hz range. I'm not sure if I couldn't get the sub positioned correctly, but I was shocked that the sub didn't play better than it did below 30 Hz. The sub also performed very respectably at 30 Hz. Unfortunately, it rolled off so sharply under 30 Hz, it only scored a Shake Value: 2.4. The sub did play all material that was thrown at it, but just didn't belt out the <30Hz stuff with authority. Everything over 30 Hz was played with authority and clarity. Klipsch did their homework, because the sub sounded as clean and precise as the HGS-18 on material over 30 Hz. Where the RSW really excelled was with music. The RSW brought a lively sound to rock material, Classical material was reproduced beautifully. If I had to pick a sub to play music, and just occasional home theater, it would be the RSW. You can begin to see now that for different purposes and preferences, any one of the subwoofers we review here might be the best choice for particular consumers.
Shake Value 2.4 (93 dB @ 20 Hz).
Reference 1: U-571 played clean, but didn't shake the walls. The sub never sounded distorted, but to get the rumble I wanted caused the 60-80 Hz range to be much too pronounced.
Reference 2: The drops and all effects were played well, but with no authority. This sub could really use a good kick in the 20 Hz - 30 Hz range. Clean, but not loud.
Reference 3: This passage sounded great. Although the lowest notes lacked authority, the rest of the transients were perfect, the RSW rivals the HGS when it comes to playing it clean. Again, notice that we are saying you can get certain - but not all - of the good characteristics of the big subs, in the less expensive products depending on their design.
Reference 4: All of the intro was played, but not to the ripping levels of the other subs. The rest of the song was very well played. The Klipsch has a lot of punch, which makes music very enjoyable to listen to.
Appearance: Probably the best looking sub here. The Copper color cones are to die for. The sub comes with a grille, but personally I left it off the entire time, as they are real pretty.
Features: Crossover, Line level, phase, 2,400 watt BASH amp.
Comments: With drop dead looks and awesome performance, I would love to have this under the tree this year. The sub didn't hammer out the 20 Hz notes with the SPL some of the other contenders had, but the rest it covered well. This sub handles music nicely, better than it does with home theater (action movies).
More Information: http://www.klipsch.com
Canton AS 300
Performance: Shake Value: 1 (80 dB @ 20 Hz).
Reference 1: During U-571, most of the effects under 30 Hz were absent. The sub played very well with higher mid-bass material, but didn't keep up with the KSW at 20 Hz.
Reference 2: During the fight sequence, the sub did hold it's own, but couldn't pull the SPL meters up high enough on the material.
Reference 3: The Canton proved to be a very musical sub, producing very nice transients and blending well with the rest of the system. At reference levels (100 dB), the sub couldn't keep up, but at low-to-moderate levels (80 dB), the sub performed beautifully.
Reference 4: Again the sub didn't play the intro with authority, but at low to moderate levels the sub performed very well. The sub played very clean and never distorted. The sub is also half the size of the other subs here, including the KSW-15.
Appearance: Very nice looking sub, controls on the back with one driver on each side. The sub comes with a base that the woofer sits on with isolated rubber feet.
Features: Crossover, Line level, Phase.
Comments: Great sub for smaller rooms , and it is beautiful (as in spouse acceptance factor).
More Information: http://www.cantonusa.com
So with so many subs, who's the winner? All of them. Any of these subs would do a home theater justice. Some perform at a higher level, but then again, some cost significantly more. If clarity and musical performance were you main goal, it would be hard to pick from the Klipsch RSW and Velodyne. If you're looking for a sub to rip the floor boards up, then the SVS may be the perfect fit. Keep in mind that if you have a smaller home theater room, it might not be the best idea to have one of the largest woofers in this test (where are you going to put it?), again priorities. The Canton and the Atlantic Technology both have smaller footprints and could easily integrate into a smaller room, without sounding overwhelming. Keep an eye out for sales on any of these subs, as they all would look real nice sitting next to the Christmas tree. OK, I guess they won't actually fit under the tree like it says in the review title.
- Brian Weatherhead -
© Copyright 2001 Secrets of Home Theater & High Fidelity
Return to Table of Contents for this Issue.