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November 2011
Subwoofer Lowpass Filter
II
Using OpAmps and other parts for
best results.
Article By Grey Rollins
Difficulty Level
Whew!
Halloween's past. Hopefully we can put Ol' Scratch behind us and get back to
more innocent pursuits. As promised, there are more ways than one to skin the
proverbial cat. Last time I described how to use a low pass filter to extend the
bass response of a speaker or subwoofer (see
previous article here). You can accomplish the same thing with
a high pass filter, although as you might imagine, the details differ. Using a
low pass filter with a subwoofer doesn't seem all that outlandish — after all,
you need one to divide the frequencies between the main speakers and the
subwoofer. But a high pass...? From reading posts here and there around the web
and from conversations with people, it seems that it's a bit of a conceptual
hurdle. After all, a high pass, by design, rolls off the low end. Isn't that the
opposite of what you want?
Well, yes... and no...
If the filter was a standard Butterworth maximally flat
design, then there would be no benefit to placing a high pass in the signal
path. But the words 'maximally flat' constitute a loophole of sufficient size to
coax an elephant through. The trick is that there's a parameter called Q, short
for quality factor, which describes how peaky the response is right before the
rolloff point. Honestly, I've never been all that fond of calling it peaky,
because half the curves out there are anything but. I defy anyone to look at a
curve with Q = 0.4 and point to a 'peak' anywhere in the thing, but that's the
term you see when you read about filters so we're stuck with it.
Mathematically, Q is the ratio between the width of a peak and
its amplitude. The higher the Q, the more peaked it is. A Butterworth filter —
that is the ordinary sort of filter that you're used to seeing — has a Q of
0.707, which means that as you approach the the rolloff point, the response
stays flat up until the last possible instant before beginning the slope; hence
“maximally flat.” But Q can be anything. It's not all that remarkable to
have filters with really sharp peaks that measure in tens or hundreds when
you're dealing with things like tuned radio frequency circuits. Fortunately for
us, audio circuits deal with much milder figures, as that sort of behavior can
lead to instability if you're not careful.
While we're at it, yes, there are Qs lower than 0.707, but
they go soft as they approach the rolloff point, melting slowly away even before
they get to the official rolloff. Indeed, it is not always apparent to the eye
exactly where the rolloff is (hint: it's still the -3dB level). For present
purposes however, we need to look at Qs greater than 0.707, so I am forced to
admit that the term peaky turns out to be useful after all — at least for this
circuit. A filter with a Q greater than 0.707 actually exhibits a rising
response as it approaches the rolloff point. How much rise? Depends on the Q, of
course, but a Q of 2.0 gives you a peak about 6dB or so above the pass band
response (the term pass band refers to the flat part of the filter's response
curve, where the filter has no effect) and that's a pretty good place to start
in our quest to enhance bass response.
So what will a 6dB boost in the low end get you? Let's say
that you've got a speaker that's -3dB at 40Hz. Assuming that the speaker is a
textbook maximally flat sort of speaker, then you would expect the response to
be down 6dB in the mid to low-30Hz range. So for starters set the 6dB peak in
the response curve for the point where the speaker is down 6dB, thus boosting
the speaker back to flat response. By the time the speaker and boost circuit are
down 3dB again, you're in the mid-20Hz region, so in practical terms you've
gained nearly an octave of low end extension.
If you're willing to accept a little wobble in your response
curve, you can set the circuit for even lower frequencies. There will be a
slight dip — how much depends on exactly where you set the filter — as the
speaker begins to rolloff, followed by recovery to nearly flat response, then
the final slope downwards. It is easy to devise a circuit that will boost
response by ten or twenty dB, but the aforementioned stability problems tend to
make life difficult so it's best to stay below Q = 2, or perhaps 3 at most. An
extra octave of low end is nothing to sneer at. If you feel that you need more
boost over a wider frequency range, then you might want to consider the low pass
circuit I outlined last time. This circuit gives you finer control over a
somewhat narrower range. It's all about having options and the more circuits you
have in your toolbox, the more things you can try when faced with wimpy bass.
This circuit is a mirror image of the low pass filter we used
last time. The resistors and capacitors have swapped places. I've included more
frequency options so you can try a variety of corner frequencies quickly and
easily. Simply jumper between the dots to select the frequency that you want.
The Q settings in the lower right corner are the star of the show, however. The
Q = 1 and Q = 2 settings will be the most useful. Feel free to experiment with
intermediate values between 10k and 25.5k, as there's no magic to whole numbers.
There's no reason not to use a 20k pot in series with a 10k fixed resistor. The
resistor will keep you from going below 10k and the pot will give you infinite
variability from Q = 2 down to a little over 0.707. Going much lower than 10k in
this circuit can be risky. Besides, going much over 2 will tend to give you
“one note bass” due to having a pronounced frequency peak over a very narrow
frequency range. Real world speakers will rarely, if ever, have such a narrow,
deep suckout that a really narrow, sharp boost is called for.
For this application, setting the Q to 0.707 defeats the
purpose of the circuit in that there will be no bass boost. I included the
resistor so you could switch the boost in and out for A-B comparison.
Alternatively, you could adjust the values of the crossover resistors and use
the circuit as a normal high pass Butterworth crossover. The Q = 0.577 resistor
allows you to take a bit of bass out of the frequency response. Many speakers
— the Rogers LS 3/5a being a famous example — use a slightly elevated Q to
give the subjective impression of more bass. In this case the slightly depressed
Q of the circuit, balanced against the elevated Q of the speaker, can be used to
restore flat response. You have more latitude in terms of resistor values when
working with Qs below 0.707 so tweak to your heart's content. Again, a pot in
series with a fixed resistor might be more convenient.
Whatever you do, do not switch the resistance with the circuit
live. This will effectively set the resistance to infinity and lose your ground
reference. If you want to play with the values while listening, a pot is your
safest bet. Otherwise turn the circuit off, select a resistor value, then turn
it back on. If you want to spend a few minutes with a calculator you can use a
default resistor value that's always in the circuit, in parallel with higher,
selectable resistor values. That way the default resistor will maintain ground
reference.
Like last time, you have the option of setting the two banks
of frequency selection resistors separately if you like. Some really interesting
EQ slopes can be achieved this way, but for most people, most of the time, the
ticket will be to choose like resistor values. This will give you textbook
slopes with easily predictable responses. All the disclaimers from last time
still apply. The devil is still in the details. If you're not careful, you can
exceed the excursion capabilities of your woofers. This is not going to make
your woofer manufacturer happy and they will not cover the damage under
warranty. Yes, they will know. Burned voice coils and crushed coil formers are
pretty distinctive failure modes. This will make you unhappy. In addition,
boosting the bass will require more power from your amplifier. You have been
warned.
Naturally, if you're bi-amping you'll need a low pass filter
to complete the crossover. See the low pass circuit from last time. You'll find
that it's better to place the low pass first, followed by the high pass. That
way the low pass limits the amplitude of the signal going into the boost part of
the circuit. It also reduces the chance of overloading the low pass by feeding
it a boosted signal.
Yet another take on the bass boost circuit is available on Siegfried
Linkwitz's website. If you scroll down nearly to the bottom of his
homepage, he offers a reprint of an article he published back in 1978 using
active crossovers to drive a three way system. The woofer section includes a
boost circuit. He follows a similar philosophy today. He employs a bit more
electronics in the signal path than I'm comfortable with, but it's a tried and
true solution and he's spent years fine tuning it. You can also — assuming
that you've built your own speakers — change the Q of the (sub)woofers
themselves by varying the size of the cabinet. Reducing the cabinet volume
increases the Q; increasing it lowers the Q. Ideally, there's a happy medium
somewhere in the middle where you can achieve a maximally flat tuning. You will
not always be able to find that perfect spot. The driver itself may not be flat,
your significant other may object to a cabinet that's large enough to do the
job, there may be resonances in the speaker cabinet or room.
Wait a minute...
There's a circuit for that.
Next time we'll address ways to tame resonances.
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