Subwoofer Lowpass Filter
you had the itch to build a subwoofer — scratched it, in fact...and now your
new subwoofer just isn't up to, er, Scratch, shall we say. Oh, you were ecstatic
for the first hour, yet only relatively happy the next day. But by the time your
best friend came over for a listening session Saturday afternoon, you had your
doubts, and after hearing your friend say, "Well, yeah, it is... uh... it's
pretty good. No, really, it sounds all right."
All right? Pretty good?
Oh, the pain, the ignominy of being damned with faint praise!
And it hurts even worse because you already had nagging doubts and, well, what
are you going to do?
Ah... I heard your cries of distress, and here I am, ready to
help. Just sign this contract and we'll be ready to... oh, that barb on the end
of my tail? Pay no attention. Nothing to concern yourself with. Just sign right
there next to the X. That's a good fellow.
There's a relatively simple way to boost the bass in a
controlled way, but you have to be wary of the cost. (Read the fine print on the
contract, lads and lasses, as the devil is in the details.) First off, woofer
excursion quadruples for every octave you drop, assuming constant SPL. That
means that if your woofers are moving 1cm peak-to-peak at 50Hz and you try to
push them to the same SPL at 25 Hz, they'll be moving 4cm peak-to-peak. That's
over 1.5 inches for those of you who prefer units in the American way. That's a
lot of excursion. In fact, that's enough excursion to cause most voicecoils to
slap the back plate of the magnet structure — a harsh and unpleasant noise
often followed by the self-destruction of the woofer.
And good luck having it covered under warranty.
And as you might expect, that extra cone excursion requires
more power from your amplifier, so that's hit number two.
The third penalty is that the driver may... okay, probably will be in a non-linear area of its excursion for at
least some of the time. In real-speak, that means that you'll have somewhat
higher distortion in the bass if you play at higher volumes.
You want rolling bass that rearranges your intestines. You
want to feel dinosaur footstomps through the soles of your feet. You want organ
pedal notes that crack the plaster in the walls. In short, you want bass. Not
80Hz boom-boom car stereo wanna-be
bass, you want the real thing. Here you go:
Now, as to application: Let's say that you've got a badly humped-up area around 70-80Hz, followed by a slow rolloff that approximates a 6dB/octave slope down to somewhere around 25-35Hz before the response rolls over and begins falling in earnest. (Hint: This is exactly what you've got if you've bought one of the "High output, long excursion" house brand woofers sold under melodramatic names such as Earthquake 9.0! or Lease Breaker III! Or a certain woofer named after a supposedly unsinkable ship.) If that's your situation, then start with the 6dB/octave resistor (R2) value at something like 68.1k and C1 = .1uF. This sets a 6 dB/octave low pass slope to begin at a little over 23 Hz. Calculate values using the formula F = 1/(2*PI*R*C), where F is the desired frequency, R is the value of the resistor you want to use, and C is the capacitance in Farads. The two halves of the circuit will influence each other, so the actual rolloff will vary, but it's a good starting point.
Now, why would you want to use a filter on it? The speaker is already rolling off down at 23Hz, so it sounds a little strange to hit it with a low pass filter. But, as with so many things, it's all a manner of perspective. Let's pretend for the moment that the subwoofer's falling response really is a perfect 6dB/octave high pass slope. It isn't of course, but let's pretend. If you take a 6dB/octave low pass filter and a 6dB/octave high pass filter and add their responses, what do you get? Well, if you set things so that the two slopes intersect, mid-way down their slopes, and call that your 0dB reference, then add the two slopes, you'll find that the high pass will add +1dB when the low pass is -1dB. Reaching back to basic algebra, you recall that +1 added to -1 equals zero. Hmmm...so what happens when the driver is -3dB? The circuit is adding +3dB. Again, they sum to zero. And so on. You have just forced the slower part of the driver's falling response much closer to something you might call flat.
So what happens to the frequencies below 23Hz? Below this frequency, the filter does nothing. You're into the filter's pass band, where the response is flat. That means that the filter circuit takes no corrective action and the woofer is allowed to rolloff on its own.
Low pass + flat response = Low pass
Low pass + high pass = Flat response (assuming that the slopes are equal)
High pass + flat response = High pass
Now, the second half of the slope (the 12dB/octave resistor) can be used to do a little more frequency tailoring, and then cleverly set the rolloff for your subwoofer. Remember that there was a broad hump in the response centered around the 70 to 80 Hz region. Above that hump, the driver's response begins to fall and worse yet, it's pretty ragged up there. So a good strategy would be to set the other resistor (the one labeled 12dB/octave) to rolloff at something like 60 or 70 Hz — something a little below the hump — so the falling response of this part of the filter begins to offset the still rising response of the driver. If you use a 47.5k resistor for R1 and a 47kpF capacitor for C2, that will set things for a little over 71Hz.
And once the 12dB part of the circuit gets going, it is additive with the first part (the one we set for 23 Hz) and we now have a tidy 12dB/octave lowpass with an effective crossover point at about 80Hz already in place, without having to put more circuitry in the signal path.
Let us say that you've got a subwoofer with a better behaved response curve. In fact, let's say it is much closer to what the textbooks say to expect. It's ruler-flat down to 50 Hz, then falls in a perfect 12dB/octave high pass function. This isn't all that unlikely a scenario, as you'll find that the majority of the drivers out there peter out somewhere between 40 and 100 Hz, no matter what sort of cabinet configuration you use.
In a case such as this you can use pretty much the same trick, just set both
halves of the circuit for the same frequency — something fairly low, like the
23 Hz example we used earlier. Now, you're matching a falling 12dB/octave slope
against a rising 12dB/octave slope, and again you'll find that the response
between 23 and 50 Hz is flat. Below 23 Hz, the circuit's response is flat and the
falling response of the driver takes over; your sub rolls off. Above 50 Hz, the
driver's response is flat, but the circuit's response is falling, so you've
created a 12dB/octave subwoofer crossover slope beginning at 50 Hz. (Note that in
this case your main speakers will need to be able to go a little lower than in
the first example.) \
And if that's not enough, you can play with the Q of the circuit. Setting the Q to 0.577 will cause the filter's response to go a little "soft" at the knee of the curve. This allows you to take out excess bass. Conversely, a higher Q will give a bit of a hump right before the rolloff. This comes in handy if you have a dip in the frequency response that you want to fill in. The schematic shows several resistors; just use jumpers to choose a value.
The main point is to play with the response of the circuit — frequency, slope, and Q — to optimize the frequency response of your subwoofer. Just remember not to exceed your driver's Xmax or the limits of your amplifier and you'll be fine.
The schematic is drawn using a standard OpAmps symbol, and many people will be perfectly happy to drop in a chip OpAmps and fire the thing up. However, it's quite easy to build a discrete OpAmps and use that instead. If nothing else, you have control over the parts quality and don't have to worry about such things as having your capacitors executed in silicon, instead of something reasonable like mica or polystyrene.
The circuit starts with a JFET differential biased by a current source. The signal is realized against a load resistor (R2), which gives PNP transistor Q4 something to do other than watch paint dry. Q4 is biased by another current source which is set by the same reference voltage as the first current source. This current source gives Q4 what amounts to an infinite load impedance, so its gain is high. This is where all the voltage gain comes from. That signal, in turn, feeds a follower circuit (Q6), again biased by a current source, which maintains the voltage swing produced by the second stage, and adds higher current capability and low output impedance.
Short, sweet, and to the point.
Yes, there are any number of other topologies you could use. If you want inspiration, a good place to start is any OpAmps datasheet that shows an "equivalent circuit" schematic. Beware...some of the folks who design OpAmps also have contracts wherein they signed away their firstborn child or some other trifle in order to optimize this or that parameter in their circuit. Nevertheless, there are some exceedingly nifty topologies out there and you're more than welcome to try to reproduce them using discrete parts.
The circuit I've shown will tolerate quite a bit of part swapping and general fiddling if you feel the desire to play around. One thing to remember is that this is a really low frequency circuit, so frequency response from DC to light is superfluous. You're already using a low pass filter, so bandwidth beyond, say, a kiloHertz or two is more than you'll need. On the other hand, if you're seeking a more general purpose circuit with wider bandwidth, you might want to cascode the differential and/or use a lower value of load resistor. Push-pull voltage gain and output stages will reduce 2nd harmonic distortion a bit. There are thousands of variations depending on parts choices and topologies. Whatever floats your boat.
Be aware that the discrete OpAmps shown prefers rail voltages at or below +20V or so. That's more than enough for a line level application like this, and in fact the circuit can handle more voltage and current than the majority of chip OpAmps out there. The limiting factor for the rail voltage is the input JFETs if you care to push the envelope a bit.
There are other ways to equalize your subwoofer. A high pass filter can do a pretty good job in certain situations, particularly if you're willing to play with the circuit Q. Another useful circuit to have in your toolbox is a notch filter. They're good for selectively taking out resonances, whether they arise from within the speaker cabinet or your listening room. We'll take a look at those circuits next time.
After all, you may have signed away your soul, but we can still negotiate for your firstborn...