The Good Old Boys Apprentice
Part II - Bass
By Philip E. Abbate © 3/12/00
Part one of the Good Old Boys Apprentice (SB x/00) covered the design of the MTM that sits on top of a closed box subwoofer. Construction of the subwoofer was explained in part one. Part two explains some of the design principles involved in matching the box and the NHT 1259 subwoofer driver, integrating the subwoofer with the room and various crossovers to integrate the Apprentice subwoofer with the Apprentice MTM.
Introduction
My 20-year-old son and his hot-rod Camaro recently moved back home. Luckily I am not a car nut, but every time I drive the hot-rod Camaro the kid inside of me urges my adult psyche to stomp on the gas pedal and feel the surge of power. Experience has taught me that it is not good to jam on the accelerator at every opportunity. That same kid inside of me also entices me to crank up the volume on the subwoofer. I have to thank the Goob's for teaching me that music sounds much better when the bass is balanced with the rest of the system.
Goob Lesson Number Two
- Better to sacrifice bass extension for bass-midbass integration.
Like most things I learn I had to learn lesson number two the hard way. For those of you who remember my Aftershock Subwoofer article in SB-6/96 you may recall that I am a bass addict and that I spared no expense getting every last Hertz and dB out of that subwoofer. Following along with the design of the MTM I decided to use the NHT-1259 woofer in a closed box with a Qtc of .707. The measured subwoofer Qtc turned out to be closer to .8 than .707. The cure for to high of a Qtc is a bigger box.
Since the carpet foam, linoleum and "evil stuffing" shown in part 1 (Photo 2 Apprentice panel cross sections) takes up an extra1/2 to 3/4 inches of internal volume, removing it was my first line of attack. The evil stuffing was removed in two rounds. During the first round the subs shed stuffing from one sidewall and the bottom wall. That added roughly 10 liters to the internal volume of the cabinet, nearly a 10% increase. The absorption properties of the sculptured foam also changed the alignment somewhat, and its removal brought about subjective midbass and bass articulation improvements.
The Goobs confirmed my sound quality assessment with a hearty approval after a quick listen. Enthusiastically removing the foam, linoleum and carpet pad from the other two sidewalls I ran into a slight snag. All the kings horses and all the kings men could not get Phil far enough into that 10.5" hole to remove the evil stuffing on the back panel. This is one of those rare cases where the kid inside of me could not escape the man that imprisons him! Photo 1 shows the total quantity of foam and linoleum removed from both of the subwoofers. Yes that pile is almost as big as one of those subs! Table 1 shows how Fc and Qts changed, as the box was unstuffed.
Low Frequency Measurements
Part one showed how LspCAD used imported frequency response (FR) and impedance (Z) measurements to model the MTM's 2-way crossover. Measurements for part one were taken with the microphone one or more meters away from the speaker while it was located in position within the listening room. The maximum length sequence (MLS) measurement tool is anechoic for the period of time between the arrival of the direct signal from the speaker and the first room reflection. After the first reflection arrives at the microphone the results are much less reliable, adding the room effects to the woofers response.
Two benefits of the 1 meter distance are it's correlation with sensitivity measurements (1watt at 1 meter) and the ability to simultaneously capture the sound data from several drivers which are blending together in space. The limitation of the MLS system is that the period between direct and reflected arrivals determines the lowest frequency that can be captured. Simply put, the sample period must be longer than the lowest frequencies period. If the period is not long enough, there will not be enough data to calculate the response of the lower frequencies. The practical low frequency limit for in room 1 meter measurements is about 200 - 300 Hz.
To overcome the low frequency limit of in -room
measurements, the microphone can be moved very close to the driver (1/4 inch) where the
loudness level of the test signal is very high compared to the level of the room
reflections. With this measurement configuration room reflections are essentially swamped
by the sound coming from the driver and thus eliminated. The disadvantage of the nearfield
measurement configuration is the blending of drivers in space can no longer be directly
measured; however they can be blended mathematically in LspCAD. All MLS FR measurements
imported into LspCAD for part two are made in the nearfield. Figure 1 shows the final nearfield response of the
completed subwoofer without the crossover.
In search of Q
What exactly is Qtc? In the case of a closed box it is the relationship of the drivers resonance in free air (Fs) to its resonance when installed in the closed box (Fc). It is also related to the Q of the driver in free air (Qts) by the equation Fs/Fc=Qts/Qtc. More importantly is how it sounds and how it affects other aspects of the design.
What does Qtc sound like? The lower the closed box Qtc, the quicker the driver will settle when the input signal ceases or change direction when the signal demands. This results in improved transient response. In general the closed box settles after one cycle of ringing. This is good in comparison to a ported box, which settles after two cycles, or three cycles as in a 6th order alignment such as the original aftershock sub. The resultant sound is tighter bass. Along with the benefits of improved transient response come increased box size, higher F3 and reduced power handling due to increased excursion.
How exactly does one verify the Qtc of a box? The mathematical models assume the drivers and box have perfect behavior, but reality does not always cooperate with the models. Working with measured data helps alleviate this shortcoming. To complicate the matter some of the losses that plug into the models can not be directly measured individually and in the various models they are lumped together. For instance there is no way to directly measure: losses due to box leakage (Ql); losses due to vibration/damping of the boxes walls (Qb), or the losses due to the stuffing in the box (Qa). Furthermore, changing one often changes other box parameters as well. The effects of the above are typically empirically derived.
| Table 1- Measured Changes as Subwoofer Was Unstuffed | ||
| Stuffing / Damping | Fc | Qts |
| Full | 29.56 | .776 |
| Half Full | 29.63 | .745 |
| Little | 30.08 | .707? |
The data in Table 1, acquired with Laud indicates that Fc is increasing and Qtc is decreasing as the box volume is increased. Logic would lead us to believe that Fc and Qtc should be decreasing. Taking a closer look it is possible that several parameters, which affect the measurement, work together and against one another.
- Removing the linoleum sheathed carpet foam increases the box volume (Vb) since the linoleum resists free air flow it essentially created a smaller acoustical box in the wooden box. Increasing Vb should lower Qtc and Fc.
- Removing the carpet foam and linoleum that was glued to the walls should have probably raised Qb (box wall stiffness) and create less box wall loss. Qb changes usually affect the impedance peak at resonance. Better damping would reduce the peak. I suspect the removal of the carpet foam and linoleum raised the peak and raised Qtc.
- Removing the evil egg crate foam fill reduced Qa. This would decrease the virtual volume and raise Fc.
MLS based measurement tools can measure Qtc and Qts, but a little investigation into the technique used shows that it is not an exact science either. The MLS technique is based on the Fast Fourier Transform (FFT). At its highest resolution FFT analyzers like Laud provide frequency response data at approximately 2.93Hz intervals. This resolution is more than adequate in the upper octaves, but it is wanting in the lower ones. With low Fs and Fb numbers in the 19-30 Hz range, there is room for 10% error. Laud in particular, attempts to short cut this limitation by using a curve-fitting algorithm to match the data to a perfect-modeled curve. While not perfect, manual measurements using a sine wave generator and an analog voltage meter has its problems too. There is more than one way to generate an impedance curve - constant current, constant voltage - and the levels at which the curve is acquired will often change the result. In short, direct measurement of Q it is not an exact science.
The question remains what is the Qtc of the Apprentice subwoofer? Several indicators exist to help place the Qtc in a range. A common misconception with closed boxes is that increasing box size lowers the F3 of the woofer system. This is true, but only for closed boxes with a Qtc higher than .707. Boxes with a Qtc lower than .707 have an F3 higher than Fc and boxes with Qtc of .707 should in theory have and identical F3 and Fc.
But which data is best to use for this assessment? The measured data in Figure 1 contains two indicators. First is the measured F3. By using point · as the high point reference, the -3dB point ¶ (F3) is lower in frequency than Fc point ¸ . This condition indicates a Qtc greater than .707. Theoretically the phase at Fc in a .707 box is -90 degrees. Using this condition (curve ¹ ) indicates Qtc lower than .707. Both of these conditions indicate a Qtc of less than .707 so we can safely conclude that the .707 target has been reached.
Point º on figure 1 appeared after the stuffing was removed. The distance from the inside of the front baffle to the inside of the back wall is 32 inches. From the equation speed of sound divided by the distance from the baffle to the back panel and back again (1130fps x 12") / 64"=211.875Hz we can see this aberration is a backwave reflection. Obviously the stuffing absorbed it before it was removed. Although 211Hz is more than 20dB down with the crossover I will be adding some Dacron to the subwoofer to lower Fc a little and soak up that nasty backwave reflection. In hindsight I am glad that I could not fit into that hole and pull the damping material off the back wall, as it would only have made this reflection worse.
Predicting In Room Response with LspCAD
The response aberrations and Qtc of the subwoofer discussed above are miniscule by comparison to in room response variations caused by standing waves. The rather high F3 of 28Hz is substantially changed by room gain. These effects can be predicted with LspCAD. The "room and cabinet effects" dialog box shown in figure 2 is part of the LspCAD box modeling application. It allows you to enter information regarding: 1) the room dimensions, 2) driver placement within the cabinet, 3) cabinet baffle dimensions, 4) placement of one speaker within the room, 4) listener location within the room, and 5) absorption coefficients for the room boundaries. It displays the in room response at the listening position as shown in figure 3.
Figure 3 curve ¶ shows
the room response with the effects of all 6 surfaces of the room and the cabinet edge
effects modifying the nearfield response imported into LspCAD. The effect of each boundary
can be examined individually by checking only the box next to the boundary in the
"reflections from" portion of the dialog box. This feature may help you
understand which reflections are the major and minor contributors to the response
anomalies and give you something to go on when attempting to modify the response by
repositioning the speaker in the room and the listening position. Another use for this
feature is to assist in matching the left and right speakers so their in-room response is
more alike, which may improve bass imaging.
Active or Passive Crossover
The Apprentice subwoofer began service as subwoofers for the 7-inch
and 1-inch drivers that sit on top of the Seismic Stack system, which was featured in SB
5/98. During that stint the system used a passive crossover developed by ear. The response
for this crossover is shown in figure 4 curve ¶ . This crossover, made with a 15 mH
Madisound Sledgehammer laminated steel core inductor and 600uf non-polar electrolytic
capacitor, worked well with the Apprentice MTM audibly filling in the bottom end. At that
time the system used two amps without a low-level crossover. The bass amp had 2 dB more
gain than the MTM amp, which bolstered the bass level a little.
While preparing figure 4, I was underwhelmed with curve ¶ so I used LspCAD's optimizer on the passive crossover and discovered the 4.5 mH/1500uf crossover in figure 4 curve · . This is close to the response I suspect I was getting with the Paradigm x-30 active crossovers. If I was to sell the MTM and subwoofer with self contained crossovers suitable for use with one amp, I would give the crossover modeled in curve · a listen.
The Paradigm x-30 active crossovers were used with the Apprentice for over a year before I decided to scratch-build an active crossover specifically for the Apprentice. To simulate the paradigm x-30 crossover for figure 4 I measured its response with Laud and simulated a similar transfer function in LspCAD's active crossover utility. Figure 4 curve ¹ shows the resultant response of the subwoofer and midbass integration. Low frequency extension is not bad, but the midbass dip caused by the Paradigm's 3rd order crossover summing out of phase with the MTM's 2nd order natural box roll-off indicates 10dB of frequency response variation. The system actually sounded quite good with the x-30s and I do not hesitate to recommend them. What's more, the x-30 has three separate HP outputs that can be used to limit bass response to the MTM. I do not use these outputs because I want to keep the entire system as minimalist as possible.
LspCAD's Optimizer
The transfer function for the current Apprentice Crossover
was developed using LspCAD's active crossover optimizer. Construction of the crossover
follows along with the Apprentice concept of tweak as you go - and trust your ears to tell
you what is best for you. Any non-textbook LP transfer function can be implemented simply
by changing 4 resistors and 4 capacitors.
LspCAD's optimizer has undergone an upgrade (version 4.1) since part 1 was completed. I uploaded the latest version for free via the Internet. Figure 5 is the optimizer window. The optimize dialog box is accessed through the crossover network pull down. The components to be varied in the optimizer - shown in the window on the left center - are selected in the network dialog box. As with the passive optimizer, it is best to select the caps from both sections optimize, then select the caps from one section at a time and optimize again. If required (sometimes you do not have the exact cap values on hand) you can enter the values you have for the capacitors and optimize the resistors from one section at a time which may result in a similar summed response.
Avoid adding to many components for the optimizer to vary at
a time, as the results can be unpredictable. As the response in the summed frequency
response window get closer to your target, remove components from the optimizer and reduce
the step size until you are satisfied with what you see in the summed FR window (figure 6). If
you have a fast computer select live update in the optimizer window and you can view the
summed response changes as the optimizer modifies the selected components.
LspCAD V4.1's new network "store and recall" feature allows you to quickly select between several viable crossover configurations. The responses for these configurations can be viewed simultaneously in the snapshot window (see Figure 4 as an example). While optimizing, the primary focus should be the summed frequency response window (figure 6). The target SPL in the "optimize" dialog box should be set to get a good match for curve ¶ (black) figure 6. Curve · (blue) in figure 6 is the optimized crossover operating on the imported subwoofer FR file. Curve ¸ (red) is the imported data from the bottom of the MTM. Locking the level keeps the optimizer from reducing the level of the network being optimized below the target, which was a nuisance in LspCAD 4.0.
Three curves are shown in the optimizer window (fig 5). Curve · (red) is the unfiltered response of the driver in the selected network. It is shown only if the View unfiltered response box is checked. Curve ¶ (gray) is the target response the optimizer is attempting to reach. It is set in the lower left box (for low pass) in figure 5. Two types of targets are available. Linkwitz yields a -6db response at Fc and Butterworth yields a -3db response at the chosen Fc. The order controls the target pass band slope; higher orders equate to steeper band reject slopes. Curve ¸ (thick red) is the achieved cross over response with respect to the target in curve ¶ . The example in figure5 is set up to more clearly show the features of the dialog box and is not the same as was used to optimize.
There are two ranges that select where the optimizer will operate. The include range (green) allows you to set the lower and upper frequency range of the optimization target. Note that it brackets the target curve ¶ . A new feature of V4.1 is the exclude range (red). It is handy for drivers with severe peaks or dips within the "include range" especially those that can not be optimized without adversely affecting the rest of the curve. For instance if you wanted to bring Fc of this sub up to 500Hz, a better fit to the target could be achieved if the 211Hz aberration was excluded. Without excluding it, the optimizer would lower the level of the response at the peak of the aberration to fit it under the target curve.
The last new feature in the v4.1 optimizer is passband slope. Passband slope allows the target to be slightly modified to put a dip in the crossover region. The dip is similar to the dip I am so fond of in the MTM crossover region.
The resultant active crossover realization is shown in figure 7.
References to the filter and gain setting components in the schematic of figure 8 are shown in the left column of figure 7.
Building the Active Subwoofer Crossover
This crossover is similar to the crossover featured in
Afterburner for Aftershock (SB 3/99). All of the parts are available from radioshack.com
except the AD 713 op amp, which is available from Newark Electronics. I used a steel
enclosure that previously housed a radio controller, which I dug out of the trash from a
place I once worked. The fuse holder and transformer are epoxied to the chassis. The three
circuit boards are mounted on plastic stand offs for easy access to the backside of the
board. The chassis were originally punched out for DB25 connectors on the back and a row
of LED's on the front. The front and rear panels are made from a sheet of 1/8"
plexi-glass. The RCA connectors were mounted directly to the plexi-glass and positioned to
protrude through the DB25 holes. This was done to control the chassis grounding. The RCA
jacks connected to one input channel is also connected to the chassis. The two pots on the
front panel were fitted through holes drilled into the LED slots and a piece of plexi
glass was fitted over it. Photo 2 shows the completed crossover with the top removed.
Making professional looking legends has always been a difficult task for the amateur constructor. Once the plexi-glass panels were drilled, I scanned them into Picture Publisher to locate the holes and printed the legends over the scan. The reverse color white letters on black panel pictures were laser printed and placed between the chassis and the clear plexi glass.
The
power supply board is a full wave rectifier using using LM78xx and LM79xx 15-volt
regulators. Specs for these regulators are available on National Semiconductors web page.
Better regulation may improve the S/N ratio of the system however, for a subwoofer amp,
the achieved 80dB S/N ratio is more than adequate.
Figure 9 shows the measured phase and frequency response of the
filter without the phase control connected.
The two filter boards
were constructed using wire wrap standoffs for the filter and gain components to
facilitate rapid component changes without the need to solder from the bottom of the
boards. The filters use the venerable Sallen-Key topology. Components on standoffs are
indicated in the schematic with a circle. Assembly Photos 3
and 4 show the underside and topside of the filter boards. The topside photo shows
the filter setting components outlined in yellow. The black X's are where the standoffs
are located. The underside traces are outlined in lighter color. The underside photo
should help when soldering the components.
The AD-713 is a high performance, unity gain stable quad op-amp. Each board is supplied m 15 volts DC via wires from the power supply board. 100nf bypass capacitors are connected directly to the Vcc+ (pin 4) and Vcc- (pin 11) and ground where the power wires connect to the op-amp. These capacitors prevent the op-amp from oscillating. Potentiometer P1 is a ganged pot which attenuates the line level source signal fed to input buffer op-amp A. R2 and R1 set the gain of op-amp A. Gain is calculated from the ratio of R2/R1. For more gain reduce the resistance of R1 which is connected to the board via stand-offs.
| Table 2- Filter Stuffing Options | ||||
| Component | 4th | 3rd | 2nd | 1st |
| R6 | Stuff | Stuff | Stuff | Short |
| R7 | Stuff | Stuff | Stuff | Stuff |
| C2 | Stuff | Stuff | Stuff | Open |
| C3 | Stuff | Stuff | Stuff | Stuff |
| R8 | Stuff | Short | Short | Short |
| R9 | Stuff | Stuff | Short | Short |
| C5 | Stuff | Stuff | Open | Open |
| C6 | Stuff | Open | Open | Open |
Final Adjustments and Measurements
Examine the frequency response plot of the subwoofer and crossover in figure 11. It was measured in the nearfield. It shows a roll off of -8dB down at 20Hz with respect to 40Hz. Note that the response at 20Hz is close in level to the response at 100Hz.
Now look at Figure 12. It is the same signal used in figure 11 but the microphone
was placed in the sweet spot and it was measured with Laud's 1/3 octave real time
analyzer. This graph includes room gain. Notice that it is rather flat in the bottom
octave. The response in the 20Hz band is 8.5dB higher than it is in the 101Hz band. This
is room gain folks. It can be your enemy or your friend, depending on how you use it.
The last procedure for adjusting the subwoofer consists of setting the volume and phase pots, as well as adjusting the configuration of the listening room. In my room I can move the speakers, listening chair and open doors. Using the RTA and MLS tools in Laud I found that a peak at 50Hz and dip at 70Hz could be corrected by opening doors. I found that opening two doors behind the speakers in my 27x13'8" room lowers the 50Hz peak 5 db and raises the 70Hz dip 8db. Sometimes I have to close one door in order to respect my wife and son who may not be indulging in music. With the doors open and the speakers and listening positions optimized Figure 13 is indicative of the response in the sweet spot.
With the phase control full CCW I get a dip in the 50 to 101 Hz region prominently in the 63 and 80Hz bands. With it adjusted full CW I get a peak in the same region. Stirring the pot and seasoning to taste, the final in room response is better than m 1.5dB in the sweet spot from the 20 Hz band to the 6.5kHz band. Above the 6.5kHz band the system rolls of at approximately 6dB per octave. The HF roll of is because air attenuates these frequencies at a much higher rate than lower frequencies. It may also indicate that I have a lot more acoustical absorption in that area, probably the acoustic coating on the drywall ceiling. Not shabby, but still not close enough to get me into the flat line club. It took 2 years and I had a lot of help from my friends! If I can do this again with a 4 way, without any help, the Goob's will make me a Journeyman. I'm afraid to ask what it takes to become a Master Goob because if you have to ask, you prove that you are not ready.
About the author
Phil Abbate is a registered professional electrical engineer who has been building speakers for over 30 years. He started with musical instrument speakers, graduated to sound reinforcement and for the last 8 years has focused on stereo and home theater speakers. Phil is indebted to Harold Taylor, Sam Papadas and Ed Drake who have taught him more about making speakers sound good in 4 years than he was able to learn on his own.