First, lets talk about imaging. Imaging is generally at its best when
the drivers are radiating in the most omnidirectional regime possible.
As the wavelength of the sound the driver is producing begins to approach
the diameter of the driver, the driver begins to start "beaming", i.e., it
starts radiating in a smaller and smaller horizontal window in front of the
speaker. Stated another way, imaging, quite simply, is the ability of the speakers,
when operated in stereo, to accurately place the instruments
and voices horizontally within the soundfield. When you
listen to speakers, listen for the "focus" -- how
precisely are sonic images created? Can you place from left
to right the voices and images? Or does everything appear to
emanate from a particular location? One thing I do is
visualize the drummer. Most drummers place the hi-hat to the
left of the snare drum, the tom toms to the right, and have
an array of cymbals from left to right. I listen for the
exact placement of the drums in the recording. The good part
about listening for drums is that they also can span the
crossover frequency, so I can learn something if, for
example, the cymbals and bass drum image well, but the tom
toms don't (that tells me that the imaging through the
crossover frequency is not good -- there is likely to be a
measurable off-axis null somewhere around the crossover
frequency).
So what causes this and what can you do about it? Well, as
you might have gathered from the title of this article is
that it could be due to a poorly selected crossover
frequency. What can you do about it? If the drivers will
permit, you can adjust the crossover frequency, but in some
cases the driver selection will not allow it, so avoiding the
problem early in the design phase is critical. Since I
recently read an exchange on a message board by some
experienced listeners/DIYers as to driver selection that my
own experience tells me will lead to poor off-axis
performance, I decided to measure some drivers to illustrate
the phenomena.
First, lets look at the basic design criteria for driver
selection in a two-way loudspeaker. The "textbook"
drivers will have a woofer with extension at least one octave
above the crossover frequency and a tweeter with at least one
octave below (assuming we're using relatively high-order
acoustic rolloff slopes for each driver.) More importantly, the 30 degree
off-axis response of the woofer will be down no more than
about 3-4 db at the crossover frequency. Figure 1 shows the
on-axis and off-axis performance of a typical 6.5" midwoofer for illustration.
What we notice about this woofer is that, aside from the
somewhat nasty peaks and dips, is that the response looks
like it's down about 3-4 db at 3khz. Although this looks like
a half decent crossover frequency for this woofer (and many
people write to me noting that they're crossing over this
woofer at this frequency) when we look very closely at the
relative response curves for this woofer, we find that the
optimum crossover frequency is a bit lower.
Here I've taken the 30-degree off-axis response for the
woofer and charted it relative to the on-axis response.
Further, to get a clear picture of what the woofer is doing,
I've used 1/3rd octave smoothing. This gives us a good look
at how quickly this woofer is rolling-off off-axis. Closer
inspection shows that the optimum crossover frequency for
this woofer is in the range of about 2300-2700hz before the
off-axis performance is likely to result in poor imaging.
Accordingly, our web pundits have done their job and the
off-the-shelf 2khz crossover frequency recommendation is
quite acceptable.
But is 2khz a magic number for all 6.5" woofers? No.
What we really want to do is to extend that crossover
frequency up as high as possible to move the crossover region
as far away from the portion of the audible spectrum that our
ears are most sensitive to. Moreover, I've heard very, very
few tweeters that didn't sound better crossed over at a
higher frequency -- although some tweeters sound equally good
at very low crossover frequencys, these tweeters tend toward
the top-end of the price spectrum. Being a bit more
technical, we ideally want a crossover frequency for the
tweeter that is at least 2-3 octaves above the resonance
frequency. For our expensive tweeters with a 500hz resonance,
this does not present a problem. Less expensive tweeters,
however, can sound as good as their more expensive
counterparts, however, if used within their optimal range
(which occurs at a higher frequency -- it makes sense if you
think about it, with some tweeters you're paying more
solely to be able to cross them over at a lower frequency
without a loss in performance.) If we have a tweeter
with a resonance frequency of around 900hz, things change
considerably and we would like a crossover frequency of
around 2700hz -- just at about the bare edge of this woofer's
performance. This is where extensive listening tests will
come into play after crossover modelling. What sounds better?
Should we crossover higher to accomodate the tweeter or lower
for the improvement in imaging? It's the speakers where the
designer has made this choice well that tend to sound very
good.
Going a bit further, what about the classic two-way with
an 8" woofer? Some of the best two-way designs use an
8" woofer with a 1" tweeter; and there's no reason
to succumb to popular trends and conclude that the 6.5"
woofer is the only choice for a two-way design. In fact, with
proper driver selection, I'll wager that a good 8"
woofer two-way will sound better than its' 6.5"
counterpart.
What we see in Fig. 3 are the response curves for an
8" woofer. It certainly rolls off earlier than the
6.5", but lets look at the relative response curve...
In the 30 degree relative response curve, we see that the
off-axis response starts dropping rapidly after about 2500hz.
For this woofer, we would want to use a crossover frequency
of no more than about 2000-2300hz. The good news is, though,
that we can use a crossover frequency of
2000hz-2300hz! This means that we want to look for a tweeter
with a Fs (resonance frequency) of less than about 750hz.
There are quite a few reasonably priced, high performance
tweeters that meet this criterion.
Now lets look at the "big boy" -- a 10"
woofer. Successful two-way designs with 10" woofers have
been few, historically. It was a message asking why a
10" woofer would be unsuitable for a two-way design
that, in fact, prompted this analysis. The question is
well-founded, too, when we look at the on-axis response of
the 10" driver.
I've seen it written that this 10" woofer might be
more suitable for a two-way design than the 8" woofer
previously discussed, due to the somewhat smoother on-axis
performance this driver exhibits. Clearly, the 10"
woofer has higher sensitivity, does not show the dip in
response at about 1500hz that the 8" shows, and the
10" extends out to about 2500hz. Good choice for a 2-way
design? No. Not, at least, in my estimation. Why? Lets go to
the video-tape...
In the relative response curve for this 10" woofer,
we see the off-axis performance starting to decline at about
800hz and dropping steadily thereafter. In fact, this driver
is down 3-4db in the range of 1200-1550hz. Although some
extremely high-performance tweeters may provide acceptable
performance with this low crossover frequency, the woofer
would have to have extremely good midrange performance to
make the effort worthwhile. An impossible effort? Certainly
not, but the average DIY'er is not going to obtain acceptable
imaging with this woofer in a two-way design. However, let me
raise one caveat that I alluded to earlier. The use of a
series crossover or low-order parallel crossover that
requires a large overlap in driver response through an
extended crossover region may provide suitable results while
still permitting the use of a tweeter with an Fs in the
500-800hz range while still exhibiting minimal distortion.
Personally, I have concerns about using a woofer in a region
where the geometric diameter of the driver is approaching a
wavelength that the driver is reproducing for many other
reasons (like having an unacceptably large interdriver
spacing). Nevertheless, although this particular 10"
woofer does not appear to be ideal for a two-way design,
there is considerable variation among drivers.
A particularly highly-regarded 6.5" woofer, for
example, is often recommended for use at crossover
frequencies of 3000hz - 3500hz. When we look at the response
curves for this woofer, we see why.
In these curves we see that this woofer has excellent
extension and does not start to rolloff appreciably until
above 5khz. Further, the response is quite smooth both on and
off-axis. Looking at the relative response curve only further
emphasizes the excellent performance of this driver.
In this relative response curve, we see that this
6.5" woofer has very good off-axis performance and is
quite easily capable of being crossed over as high as
3400-4000hz! Since many fine tweeters are available at very
low prices that have an Fs under about 1500hz, there is a
wide variety of great units to match up with this woofer to
achieve an excellent sound. But is there a free-lunch here?
No. Unlike the Dayton 6.5" woofer shown in the first
example (that has very powerful and articulate bass
reproduction at a very low price), the Vifa woofer shown in
these graphs has very little low-end bass performance and
most two-way designs using this woofer require a subwoofer
for optimum full-range performance.
In summary, choosing your crossover frequency is not all
that hard. It's simply matter of understanding why a certain
crossover frequency is preferable over another. Once the
crossover frequency is selected, a good determination can be
made as to the tweeter's performance parameters that are
necessary. In many cases, understanding these things and
applying them to your design process at the outset will
improve your success dramatically, i.e., select the woofer
first, determine the maximum crossover frequency of the
woofer, and then choose your tweeter accordingly to avoid
"overbuying" a tweeter with capabilities that you
will pay for but don't need, but making sure that you are not
buying an expensive tweeter that can't do what will be
required to work in conjunction with your chosen woofer.
Alternatively, you may find yourself choosing between two
equally priced tweeter and wondering which is better for your
application. Chances are, the one that tries to do less for
the same money, but still does what you need it to
do, might perform better for you. But that's another story.
