A Senior Project for Brigham Young University

Active Feedback Controlled Subwoofer System

The Audio N.E.R.D.S

 Negative Electronically Reduced Distortion Systems

 Daniel P. Marx

Latu Fifita

April 3, 2000

Table of Contents

Servo Controlled Subwoofer …………...……………………………………………1

Table of Contents…………………………………………………………………....2

Proposal of Project……………………………………………………………….…3

Description of Project……………………………………………………….…….…4

Background on Subwoofers………………………………………………..…….5 - 8

Project Plan Details……………………………………………………………..9 - 13

Flow Chart of Signal Paths……………………………………………………….…14

Schematic………………………………………………………………………......15

Test Procedures and Results…………………………………………………....16-19

Data Sheets on Components……………………………………………….….21 – 30

Pictures of Final Product………………………………………………...……….....31

Bibliography…………………………………………………………………………32

Proposal of Project

     Build a prototype of an actively controlled subwoofer using a feedback loop to correct unwanted distortion.  The unit must monitor the motion of the subwoofer’s cone and feed it back to a circuit which will compare the input signal with the signal coming from the cone.  Any differences will be cancelled out by our custom circuitry, thereby creating a modified signal which when sent back to the subwoofer, will have less distortion.  The entire set up must be a completely analog design.  The device we will use to monitor the cone’s motion will be an accelerometer made by Measurement Instruments model number ACH-01 and is capable of measuring up to 250 g-forces in each direction.  We will most likely only be using about 50% of this range.  It wasn’t until just a few weeks ago that Analog Devices came out with a smaller accelerometer capable of measuring 100 g-forces in each direction which would have been perfect for our application.  We hope to achieve a minimum of 10% reduction in distortion throughout the subwoofer’s range of 30 to 80 Hz.  We also hope to smooth out the response of the subwoofer by at least 1 or 2 dB.  If we do reach our goal, the result will be a sonically superior subwoofer which will sound better and perform more precisely to the way the original source material was meant to sound.  The subwoofer will be used mostly for home theater and home music purposes.  All that is required is an existing stereo system and a subwoofer.  All the added components we will design and build.  A person interested in turning their subwoofer into a feedback controlled subwoofer, may do so easily and with few expenses and by downloading the plans from a website such as this one.

      The Servo Controlled Subwoofer is a complete subwoofer system that consists of specially designed feedback loop circuitry and a high performance accelerometer.   The accelerometer connects to the feedback loop and will read and monitor the motion of the cone correcting any abnormalities that may be present.  This will reduce distortion and improve low-end response of our subwoofer.  The subwoofer being used is 10 inches in diameter and is capable of swallowing 0.5 liter of air.   The Thiele/Small details of the driver we will not be concerning ourselves with at the moment.   The enclosure is a 2^nd order sealed alignment, which has proven itself to be superior in reproducing bass over any other design.  It is also the least complicated of subwoofer designs and will be the most forgiving in the event of any kind of failure.  The sub box is made of ¾” MDF and covered in mahogany plywood and stained a beautiful light American Oak.  The driver can handle 100 watts RMS and 150 Watts peak and is rated at a nominal 4 ohm impedance. The finished servo controlling part of the project resembles a piece of stereo equipment and will sit near your existing power amplifier.   It has a power switch, filter cut switch, feedback cut switch, two analog meters, and a feedback volume control.  One meter monitors the input source signal and the other monitors the motion of the cone.  This new stereo component is connected between the subwoofer and the power amp with standard RCA connectors while the accelerometer within the subwoofer is wired via special connectors known as XLR’s.  This helps to shield the signal coming from the accelerometer as well as drive it with the necessary  +15 V that it needs in order to operate.  The exact set up for the Servo Controlled Sub is as follows:  The sub out jack from a stereo receiver is connected to the input jack on the Servo Sub Module.  The output jack from the Servo Sub Module is then connected to the input jack of a power amplifier.  The power amplifier should have a fixed volume knob and should not be adjusted after finalization of the Servo Sub into the system.    The volume being sent to the subwoofer is based upon the level set by the receiver.  This is to ensure that the input signal from the sub and the input signal from the receiver are always at the correct levels.  Otherwise oscillation will occur as the volume is turned up.   The main stereo receiver should always be controlling the total sound for all the speakers.  This is standard for most stereo and Home Theater set-ups.  The user is allowed to adjust the amount of feedback that is introduced to the system with a volume knob.  An analog meter will aid the user in determining a suitable amount of feedback for a desired level of listening.   If the right meter at anytime reaches the red, the volume on the power amp should be turned down.  This is calibrated to read the excursion limits of the driver.    The left meter indicates the volume of the signal coming from the receiver and into the amplifier.  This is an indication of how loud the stereo is.   When listening to music all you must do is turn on the Servo Sub Module and adjust the feedback level until the output from the subwoofer is just barely reduced by about 1 dB.  The system is now set and you can turn up and down your main volume as you like and the sub will stay in tune until you decided to change it. 

Background on Subwoofers

    Subwoofers are designed to produce only the very low end of the music spectrum.  Most subs perform between 20 and 80 Hz only.  Though the exact range varies depending on preference.  In order to filter the frequencies above 80 Hz, you need a high-order low-pass filter.  We chose to build a 24 dB/octave filter at 90 Hz by cascading two 2-pole Sallen-Key filters together.  This filter can be bypassed if an external crossover is to be used.  There are also many types of subwoofer enclosures ranging from 2^nd order IB, to 6^th order bandpass that we could choose from.  Each design is more complicated than the first and much more difficult to achieve predicted results.   In our case we chose to go with a 2^nd order sealed (or acoustic suspension) because of simplicity and accuracy in achieving predicted results.  Also sealed enclosures have a more linear phase response with relationship to frequency.   They have a naturally more shallow roll-off rate of 12 dB/octave. So it can be argued that in a sense they yield the most low frequency response.  Also a sealed enclosure has more control over the motion of the cone.  Since we are actively monitoring the motion of the cone, we wanted to make sure that it was tightly under control to begin with.  The driver has less of a tendency to bottom out in sealed enclosures.  Overall it was a much better design approach to go with that any of the others.

     A subwoofer must also have a really good flat response curve.  Below you will see the response curve of our subwoofer as it was after we built the enclosure and mounted the subwoofer.  An air tight seal is essential.  This can be checked by pressing in the cone and then watching how fast the cone moves back up to its rest position.  Our cone sure enough took about 3 seconds to return so we were definite we had a good sealed box. [It was pointed out to me recently that this is actually an indication of a small leak in the enclosure.  With a truly air-tight enclosure pushing in the cone will actually compress the air inside that when released will result in the cone springing back rapidly, not slowly, to its rest position.]

     The response was measured with an SPL meter and the input signal was from a function generator.  Starting at 20 Hz we plotted the SPL at 5 Hz increments up to 80 Hz.  As you can see the response is not very smooth at all.  There’s a large hump near 53 Hz, and then it drops some and there’s another hump near 35 Hz.  Although this isn’t a terrible response, it could be better.   Most subwoofer’s have a natural roll-off in the very low end, which can be seen here.  This is because in order to get a lot of SPL between 20 and 30 Hz, we need to have a driver that can move enormous amounts of air.  It would take a much larger driver in a much larger enclosure to produce a flat response curve down to 20 Hz.  So the low frequency roll off we aren’t going to worry so much about.  Just the small humps and dips that lie above 30 Hz.

    One other inherent property with subwoofers is distortion.  Due to the complex characteristics of a subwoofer, it takes some pretty hefty engineering to make a subwoofer with zero distortion.   The inside’s of a typical subwoofer are shown below.  There is a motor assembly which consists of a spider, voice coil and cone.  These are the moving parts of a speaker and they take the most abuse.  As the voice coil moves up and down within the magnetic gap, the non-linearity in the spider, surround and cone cause distortion.  The properties in which the voice coil will operate within the magnetic gap also change as the coil moves up and down.  This also causes distortion.  Below is a picture of a sine wave produced by a subwoofer.   The top sine wave is the signal that was sent to the subwoofer.  The mountainous looking signal below the sine wave is what the subwoofer produced as recorded with the ACH-01 accelerometer.

       Here is another type of distortion that we were able to record from our subwoofer.

     This distortion made an audible vibrating sound which can clearly be seen by the rough peaks in the signal shown above. The sine wave below was the original signal sent to the woofer and the signal above it was recorded from the ACH-01 accelerometer.  Now that we have presented the current problem and identified exactly what were are trying to achieve, we’ll explain exactly how we did it.

      There are various techniques for reducing distortion.  The one we chose to implement  into our system is what is called a negative feedback loop.  With a negative feedback loop, a signal from the output is fed back into the input where the signals can be compared.  In this comparison process, changes are made to the original signal that will in effect cancel out the differences between the two signals.  When the corrected signal is fed back into the output, a more exact signal is produced.  In order to get a signal off our subwoofer to see exactly how it was responding, we needed to use an accelerometer.  This accelerometer would show us how the cone moved in terms of voltage over time.  The accelerometer is calibrated to deliver 9.8 mV per g-force.  Since we’re not really concerned with exactly how many g’s the driver is pushing, the calibrated output is irrelevant.  We will be boosting the signal up to a couple of volts anyhow to sum with the source signal. In order to start designing a schematic, we had to first decide what we needed all these signals to do.  So we broke it up into various stages.  Starting at the source, the signal runs to a low pass filter, to a buffer, to an adjustable gain amp, to a summing amplifier, and out to the power amplifier.  From the accelerometer the signal runs to a buffer, then to an RC network which removes the DC bias voltage from the accelerometer, then to a phase adjust network which compensates for delay from the woofer, to an adjustable gain amplifier (which is user controlled) and finally to the other input on the summing amplifier.  This will make more sense in the block diagram. The source signal coming from a receiver will have no more than 2.0 Vpp.  It will be a full range signal so the first thing we must build is a low pass filter.  THX standard for home theater suggests a cutoff point of 80 Hz.  Music allows for a little bit more of the upper frequencies and would suggest a cutoff of 100 Hz.  Since our sub would be for both movies and music, we shot for a cutoff frequency of 90 Hz.  This was achieved by cascading 2 two-pole Sallen-Key Filters in a low pass butterworth orientation.  Below is a chart that shows how to design a filter of this type.  We used 0.1 uF caps and 15 K ohm resistors as calculated by the formulas.

     From the output of the filter we go into a buffering stage.  We found this necessary only because if we didn’t use it, the circuit wouldn’t work at all.   From the buffer stage the signal runs into a gain stage where we can adjust the gain from simple unity gain to a gain of 10.  This helps us be able to properly sum the source and accelerometer’s signals the achieve the proper cancellation factors without the system going into oscillation.  This is not a user control.  This is a control that is set once and left alone.  The summing amplifier is where all the fun happens.  But first let’s explain the signal path of the accelerometer.   The ACH-01’s signal comes off the cone and runs down a shielded 3-wire cable and into a buffer.  This buffer keeps the accelerometer from blowing up in the event of some catastrophe inside our circuit.  Since we already went through 3 accelerometers before this one, we didn’t want to take any chances.  The ACH-01 has a DC offset of 1 V which we needed to get rid of.  To do this we used a simple RC network set to filter everything below 5 Hz.  The formula for this is t = R x C  where time is 1 / 5 Hz and we chose C to be 0.1 uf.  R came out to be 200K ohms.  We went with 180K which set our filter at 5.5 Hz instead.  Still a very suitable cutoff frequency.  From the RC filter the signal runs into a user controllable gain stage.  This stage allows the user to determine how much feedback is introduced into the system.  After the level control, the signal runs into a phase adjust filter.  This can be seen to the left.  We found this filter necessary in order to help us align the source with the feedback so that they were exactly 180 degrees out of phase.  We were hoping to be able to have all frequencies sum exactly 180 degrees out of phase, but we were unable to find any circuitry available that would do the trick for us.  So we were left to only fix the phase at a single frequency and allow the others to fall as they would wherever they would.  From various plots we made, we were able to see that the sub had a phase change of about 40 degrees at 30 Hz and went up to 187 degrees at 80 Hz.  Since we could not correct this completely we were left to compensate for phase at a single frequency.  We chose around 50 Hz.    So we set the phase adjust to sum the two signals exactly 180 degrees out of phase at exactly 50 Hz and then above and below that the phase will change just as it did before, except now its centered at 50 Hz, instead of 80 Hz.  We found this to work very well.  Even though at most frequencies the signals are still not summing entirely out of phase, we were able to get acceptable results.  Some extra features we threw into the Servo Sub was the ability to bypass the filter.  This we did with a simple DPDT switch.    Also we made it possible to bypass the feedback loop enabling direct AB comparisons.  The meters on the front were more for aesthetics than anything else.  The meter on the left indicated input signal strength and the meter on the right allows the user to see the actual motion of the cone.  If the meter hits the red, the sub is being overdriven and is an indicator to turn down the volume before the subwoofer burns up or is damaged.  This is the basic outline of how all the circuitry works and why we chose to use it in this project.  On the next page you will see a simplified flow chart of our design.

    Once again a quick explanation:  the signal comes from the source at roughly 1.0 Vpp.  With a frequency response of 20-20,000 Hz.  The signal is amplified to about 5.0 Vpp.  It is then fed to a 24 dB/octave low pass filter (which is not shown) that has a cutoff frequency of 90 Hz.  The summing amplifier sums the source signal with the signal from the accelerometer, but because of time delay issues, the two signals do not sum exactly out of phase except at a single center frequency of 50 Hz.  The summed signal is sent to a 60 watt amplifier which drives the woofer.  The ACH-01 reacts to the movement of the woofer and its signal is amplified.  The user is allowed the ability to determine how much amplification is necessary to achieve desired listening environment.  The signal is then delayed using the Phase Adjust to set the 180 degree phase shift right at 50 Hz.  When the signals are summed together, the differences are canceled out and the result is less distortion.

 Test Procedures and Results

      In order to test our Servo Controlled Subwoofer, we needed some equipment.  Unfortunately the distortion analyzer we were planning on using was completely dysfunctional and gave us no useable data at all.  So we were left with using an oscilloscope and just comparing sine waves.  This proved to be an effective method in the end.  We also were able to use a program called JBL SmartPro which measures harmonics from any type of signal.  We were able to record before and after shots of the harmonic distortion of our subwoofer with and without the feedback circuitry.   The first picture you will see is a plot generated by JBL SmartPro showing us the harmonics present in our subwoofer.  These harmonics were recorded with a calibrated microphone and a test signal of 40 Hz.

     From this graph we are able to see a large harmonic peak centered at around 500 Hz.  This we could also hear with our ears.  It didn’t sound too good.  Then we turned on the Servo Sub Feed Back loop and plotted the same response.  The graph below shows the results.

     You’ll notice that the peak at 500 Hz is greatly reduced by about 9 dB.  This shows a vast improvement.  Not only with the computer were we able to see a change, but with the oscilloscope as well.  The next page will show a sine wave as generated with the subwoofer.  The first oscilloscope readout is without any active feedback.  The signal is distorted by the little notch that can be seen in the upper right hand of the waveform.  The second picture shows the waveform from the woofer after the Feedback Loop is employed.  You can see that the peak is removed and the signal is cleaner. 

   Although the improvement was minimal, we were able to see on the scopes and hear with our ears the slight change in subwoofer performance with and without the feedback loop.  Now to show what happened to the frequency response.  Below is a plot of the before and after response curves of the subwoofer with and without the Feedback Loop.  The top line (series 1) is without feedback while the bottom line (series 2) is with feedback.

    The green line shows how the response was smoothed across the 40 – 80 Hz region by at least 1 dB.  Since this was our goal, we can safely say that we achieved smoothing out the response of our subwoofer.  It would have been nice to improve the low end by a few dB but that would probably only have been achieved by using many more 10” woofers.

     In the end we proved it was possible to reduce the distortion and improve the frequency response of an ordinary subwoofer using a negative feedback loop.   Some major obstacles we encountered that prevented us from truly achieving our goal was lack of real measurement equipment to do some better tests.   Although we were able to see the improvement in the before and after plots, it would have been nice to get a true percentage of reduced distortion.  Also if we had more time we would have been able to implement a better circuit to correct the phase properly.  One such design we had thought of was to use a F/V converter and convert the frequency to voltage and then to light with an L.E.D.  This L.E.D. would couple to a photocell which would vary the resistance across our phase shift network.  Since we’d mentioned earlier that we were able to adjust the phase at a single frequency, this was via a variable resistor, we would connect in place of this variable resistor the photocell.  That way the phase would adjust according to the frequency of the signal.  As the signal dropped in frequency we could make the phase shift up.  Which theory goes contrary to all practical analog filters.  Even without having perfect correlation between input and output phase, we had very good results and are both very happy with how our project turned out.  The sub sounded clean and the bass was tight and deep and had overall less total distortion.  We learned a great deal about operational amplifiers and how to use them in various types of situations.  We also learned a lot about phase shift and how it can be dealt with.   All in all, this was a time extensive project but the final product was well worth the time put into to making it work.

Pictures of the Final DIY Sub with Active Feedback Loop Controller

Bibliography

Mimms, Forrest M the III.  IC Op Amp Projects, A Siliconcepts Book.  Engineer’s MiniNotebook from Radio Shack.  Copyright 1985

Smith, Steven W.  The Scientist and Engineer’s Guide to Digital Signal Processing.  Copyright 1997 by California Technical Publishing

Analog Devices Prototypes a Servo Controlled Subwoofer http://www.analog.com/

Dan Marx’s Gallery of Speakers and Designs

Speaker Builder Magazine January 1990 pp. 15-20.

Speaker Builder Magazine March 1989 pp. 24-27.