Loubeeka Podcast #3: Basics – Frequency Crossovers and Correction Networks for Newbies

Loubeeka Podcast #3: Basics – Frequency Crossovers and Correction Networks for Newbies

Frequency crossover networks and full-range
correction networks – what are they? Why do we need them? How do they have to look like
and how should they not? Hi there, this is Marius Loubeeka from Hamburg,
Germany and welcome to the Loubeeka Podcast number 3! Our today’s topic is the theory
behind passive frequency crossover networks and full-range correction networks. This podcast
has become really good – and probably long. Active crossovers might be covered by a future
podcast. The slightly shorter German version and all other podcasts and videos I mention
here are linked in the description below. First question: what are crossover networks?
They split the audible frequency range in two or more smaller ranges which they pass
on to drivers specialised for that particular range. Those ranges are called “ways” and only
by looking at the crossover you can tell if your speaker with three drivers, like this
one, which has one tweeter and two presumably identical mid-woofers, is 2-way, 3-way (as
the manufacturer claims) or maybe 2½-way. The latter has two drivers overlapping at
the bass (everything else doesn’t make sense) and being high cut at different frequencies.
BTW, this speaker on the pictures is only 2-way in reality. – A low pass lets low frequencies pass to
the woofer. A first order low pass contains a coil in series with the woofer. A second
order low pass additionally contains a capacitor in parallel to the driver, connected to the
point between coil and driver. In a third order low pass a second coil is connected
in series with the other coil and the driver in between the capacitor and the driver.
– A high pass lets high frequencies pass to the tweeter. It looks similar to a low pass
but caps are exchanged with coils and vice versa.
– A band pass lets a limited bandwidth pass to a midrange driver. It consists of low and
high pass either connected in series or nested. (I’m not 100% sure if that’s the right word.)
All of them are called filters. The order of a filter determines the steepness of the
slope: 6 dB/octave for a first order filter, 12 dB/octave for second order, 18 dB/octave
for third and so forth. It further determines the phase shift at the cut-off frequency:
45 degrees at a first, 90 degrees at a second, 135 degrees at a third order filter etc.,
but a low pass has a negative, a high pass a positive shift.
– Special elements in crossovers are band stop filters, which are as well called notch
filters. They are the opposite of band pass filters and attenuate a limited bandwidth
to e.g. smooth out symmetric peaks or bumps either in the frequency response or in the
impedance response. They let all other frequencies pass. They consist of a coil, a cap and in
most cases a resistor which is called “RLC circuit”. I’ve never seen a second order band
pass in a crossover because the slopes of the first order ones are already defined by
their Q-factor. A high Q leads to a deep notch (then sometimes without a resistor), a low
Q to only a few decibels attenuation. There are two types, a series and a parallel RLC
circuit. One has R, L and C in series to each other, the other one has them in parallel.
A parallel RLC circuit only works as a band stop if it is connected in series with the
driver. A series RLC circuit only works if it is connected in parallel to the driver
and a part in series with the driver is already causing attenuation at centre frequency of
the band stop. Without an attenuating part in series it only has an effect on the impedance
response and can smooth out peaks or bumps there.
– Nearly every crossover contains an L pad as a voltage divider or a single resistors
to attenuate a driver. An L pad has the advantages that it linearises the impedance of the connected
driver and that the resulting impedance of L pad and driver can be adjusted within a
certain range. Together with a driver that is used at its resonant frequency, mainly
woofers, an L pad or a single resistor in series should not be used.
Note that passive crossovers can only attenuate not amplify. For amplification an active crossover
is needed. Second question: what is the difference to
a correction network? Full-range drivers are normally not cut off by low or high pass filters.
Commonly used filters in correction networks are band stops and high or low shelf filters.
Shelving filters can either be seen as a combination of e.g. a low pass with a bypassing resistor
(coil and resistor in parallel) or two third of a parallel RLC circuit. From a certain
frequency on it attenuates the rest of spectrum by the same level. They rarely occur in crossovers,
too. Third question: why do we need it? Easy answer!
All drivers have resonances. Some of those are good, e.g. the fundamental resonance,
i.e. the resonant frequency, but most others are bad. Having a fundamental resonance is
inevitable for an oscillating system but all other resonances are unwanted. The fundamental
resonance can be read from the impedance response. I already talked about that in my last podcast.
Only at tweeters which contain highly viscous ferrofluid inside their air gap, it cannot
be read from the impedance response. At least in most cases those are tweeters. Anyway,
in addition to the resonant frequency other resonances occur in nearly all drivers, in
some there are more, in some less. In better drivers there should be fewer resonances within
the usable range. Outside the usable range they do not necessarily need to be less strong.
Within the last several years some driver designers seem to use less damping in drivers,
as for example coatings, and instead try to shift resonances to higher frequencies by
adding rigidity – hard word. 😉 Seas for example use magnesium cones in their Excel product line which have
many strong cone break-up resonances but only above 5 kHz. Other designers add long fibres
as wood, cotton, banana or polymers to paper or create their design in a way that resonances
don’t even occur. There’s this trend to preserve more detail in music by lowering mechanical
losses. Of course every bit of damping adds mechanical loss because it not only suppresses
resonances but also the desired signal. Even if that means that e.g. the resonance of the
surround, which is usually somewhere around 1 kHz, is not fully suppressed as it can be
seen in mid-woofers by SB Acoustics. Because you use a crossover anyway resonances do no
harm outside the desired range. Another thing you need a crossover for is
shaping an adequate frequency response because the ideal frequency response of drivers is
rare. I already talked about that in my podcast about frequency responses which you find now
on the info icon. As I said, every driver has some resonances. Mid-woofers have them
in the highs, where the wave length is about as big as the cone and therefore standing
waves occur within the cone. The fundamental resonance is of course no standing wave but
a mechanical resonance. Also in tweeters standing waves do occur. In hard domes like aluminium
domes it’s worse than in soft domes. That depends on how much propagating waves are
attenuated inside the material which means how the internal damping of the used material
is. Maybe I should cover that in a podcast, too. Attenuation is very low in metals and
waves can propagate very fast in it. The speed of sound in metals is very high, about 6300
m/s inside aluminium. The harder the material the higher the frequencies shift where resonances
occur. In an aluminium dome the break-up resonances usually are at 20 kHz or higher. In beryllium
domes by Scan Speak, Seas or SB Acoustics these resonances are above 30 kHz, nearly
even outside the extended measurement range which goes up to 40 kHz. The third purpose of a crossover is to protect
midrange driver and tweeter against frequencies they’re not capable of. Because of small diaphragm
area it is not suitable for it to play bass notes. To be capable of doing that it would
have needed the capability of large excursions for which tweeters are not designed. So the
frequency ranges the driver can or shall not be used for are kept away from it. Also a
midrange driver needs a high pass because the sound quality improves if the bass is
cut away. Therefore it doesn’t have to produce large strokes for which it is mainly not designed
because it is usually smaller than the woofer. The need not to produce bass improves the
sound quality in the mids. Intermodulation distortion, to mention a key word, is avoided
and the harmonic distortion of low frequencies, which basically occurs in the mids, is reduced. Distortion is another topic
for an upcoming podcast. Even if you use a driver with an ideal frequency
response, which for some full-range drivers and several tweeters is at least partly true
within a specific range they cannot be used without a crossover because the baffle step
is still a problem. Okay, one mounting environment doesn’t have that. An infinite baffle or in-wall
mounting, which is a quasi-infinite baffle because it is large in relation to the drivers,
has no baffle step. To get well comparable results most frequency plots of drivers are
measured by manufacturers or the German DIY loudspeaker magazine Hobby HiFi in an infinite
baffle or an IEC standard baffle. The latter has the dimensions of 1.65 m by 1.35 m, which
is quite big in relation to most types of drivers. On such big baffles drivers are more
likely to behave ideally. Now you might think you wouldn’t need a crossover for in-wall
mounting but of course all other problems still occur as for example unwanted resonances
at the cone break-up. Normally we work with relatively small enclosures which don’t have
huge baffles. On those we have three influencing factors which change the radiation pattern
of a driver depending on the frequency. 1) Radiation is spherical if the emitted wavelength
is several times larger than the baffle. 2) To higher frequencies the pattern transforms
to a hemisphere where the wavelength is about as big as the baffle wide.
3) The pattern transforms to planar radiation from that frequency on where the wavelength
is as big as the driver. I hope everyone remembers the law of Conservation
of Energy from physics classes. At the spherical pattern the acoustical energy is spread upon
the surface of the sphere. The surface area of a sphere is A=4 π r² so the sound intensity
decreases to the power of two with distance. To look at it from the other direction: the
area on which the energy is spread increases with distance by the power of two. On a hemisphere
this looks quite similar but the area is only half as big. The energy spreads on half of
the area as on a sphere. So the energy at the same distance is twice as much as on the
sphere which means 6 dB more. The exact geometry of the baffle also plays a role, where the
driver is located, how far off it is from top and bottom etc. Therefore the baffle step
can be more than 6 dB high, in rare cases up to 9 dB. And this is located in a range
where the hearing is most sensitive in the mids. I recommend my podcast about frequency
response for details about hearing perception. Therefore in a small box which has the dimensions
of the emitted wave length the commonly feared baffle step occurs. I mentioned planar radiation
which has not so much relevance, except for full-range drivers. Normal mid-woofers are
not used in that range where they start focusing which is the effect that occurs at the transition
from hemispheric to planar radiation. Usually that is the range where mid-woofers emit less
sound due to the radiation resistance of the diaphragm. The fifth reason for the use of crossovers
is differences in volume, or to be more precise sensitivity, between mid-woofers and tweeters.
The woofer determines the maximum overall sensitivity of the whole speaker together
with the enclosure. Passive crossovers only allow attenuation not amplification. Amplification
is only possible in active crossovers. So the baffle step has to be compensated by the
crossover by attenuating down to the SPL of the bass. Usually tweeters have a higher sensitivity
than mid-woofers. Most dome tweeters produce about 90 dB/W/m which means 90 dB from 2.83
V at a distance of 1 m. An average 5 inch (13 cm) woofer only produces about 80 dB/W/m in the bass. A crossover can look as complicated as this
if you want to get the frequency response perfect. If you use expensive drivers it may
even be worth every penny you put into this much parts. I’m already preparing a podcast
about the different types of parts and their qualities and a video about what quality to
use at which position of the crossover. What you see on the screen at the moment is a short
glimpse of that. I want to mention that all of this about baffle
step correction is used for multi-way speakers. In 1-way or full-range speakers baffle step
is often corrected by mounting the driver in a horn enclosure which lifts the bass to
about the same level as the mids. Especially for 8 inch (20 cm) drivers it is very common to use a
horn which boosts up the volume up to the lower midrange instead of heavily attenuating
the mids to achieve a balanced response. Basically this all shows that a correction
of the frequency response by a crossover network is essential. Even those just mentioned horn
loaded full-range drivers still have a little emphasis in the mids because the boost of
the horn is not enough to balance the response. As I said, sometimes a difference of 9 dB
has to be flattened out and therefore a correction network even makes sense for full-rangers
in a horn. My next topic is “how to get it wrong” but
from there I give a positive outlook at the end. Often we see, mostly in cheap speakers,
only a high pass capacitor in series with the tweeter, for example in coaxial systems
for cars. This is of course done to prevent it getting damaged by low frequencies. Mid-woofers
in car hi-fi often use highly dampened cone materials to keep the cone break-up more or
less clear from resonances to get a smooth roll-off. I doubt that that is sufficient
in all cases and recommend measuring each individual subject. Presumably it’s not the
optimal solution to only use one capacitor because, as I will explain in a minute, both
slopes have to match each other and should be symmetrical. Otherwise the sum at the crossover
point is not ideal due to phase problems. If the slopes are not symmetrical cancellations
or suboptimal summations occur where both drivers emit sound. That leads to non-linear
responses. A mistake many people make, who did not yet
dive very deep into speaker building but like the idea of creating one of their own, is
using crossover calculators from the internet, which many speaker parts online shops offer,
or formulas from a book. Of course a calculation with a formula is possible which works very
well in active crossovers but due to all the reasons I mentioned before, resonances, absence
of ideal responses, baffle step and so on, these formulas don’t work for passive speakers.
Another very important reason why formulas don’t work is that impedance responses of
drivers are not linear. I already explained that in my podcast about impedance responses.
Basically these formulas aren’t wrong but you need to know the impedance plot to get
a reasonable result because the exact impedance at the crossover frequency counts. You need
to know the frequency response of the driver mounted on the enclosure and then you can
use these formulas to get a starting point for your model for example in BoxSim. I usually
go that way. I look at the frequency response of my mounted driver to see how the baffle
step looks like. You can see how I work that out in my tutorial “How to Design a Passive
Crossover Network for a 2-Way Speaker”. I tried to describe all steps vividly in it.
Here’s a short summary of the video. I normally use these formulas which are also incorporated
into a crossover calculator in BoxSim to attenuate the baffle step. I take the point where the
baffle step is 3 dB higher than the bass. That is the crossover point which has to be
put into the formula because the crossover frequency is defined as that point where the
amplitude is decreased by 3 dB. This is as well a bit problematic because this is not
the real crossover point in the end because if two drivers are in phase and have the same
SPL there their sum is 6 dB higher than each one of them and not 3 dB as the formula seems
to predict. As I said, I take it as a starting point for my simulation and adjust the values
from there to get a good-looking graph. I earlier mentioned that I start at the mid-woofer
because the bass determines the SPL of the whole box. I flatten out the baffle step then,
and look where resonances have to be suppressed, where some work has to be done. The best thing
would be a minimal phase shift with a first order crossover with a slope of 6 dB per octave.
If I can create a nice looking curve that way and if only few and small resonances are
present in the lower treble then a first order crossover might produce an adequate result.
It further depends on what I get when I flatten out the baffle step, where the falling slope
starts, where the -6 dB point is and if the tweeter is capable of taking over at that
point. More about that in the next podcast. If I don’t get a good result it perhaps helps
to try a higher crossover frequency and at first keep a little of the baffle step and
later flatten it out with a parallel RLC circuit in series or better a series RLC circuit in
parallel to the driver. The one in parallel is better because it doesn’t add lossy parts
in series with the driver. The less parts in series the less the probability to lose
sound quality. These circuits unfortunately cannot fully be calculated by hand. We get
their centre frequency with the following formula: f=5000 / sqrt(LC), with L in millihenry
and C in microfarad. I then try out the correct values in BoxSim. Here again I use the formula
for high or low pass as a starting point for either L or C. For a parallel RLC I calculate
L at the lowest frequency of the bump. For a series RLC I calculate L at the highest
frequency of the bump. At first I leave out the resistor to find the correct centre frequency.
Then I try different values for R until the bump has the correct level at the centre frequency.
Unfortunately the resistor changes the bandwidth of the RLC circuit so L and C have to be adjusted.
Parallel RLC: bigger coil and smaller cap means bigger bandwidth. Series RLC react the
opposite: bigger cap and smaller coil means bigger bandwidth. It works best to change
both by the same amount, e.g. +/-20%, +/-50% or increase and decrease tenfold until it
fits. Here the E series of preferred values comes handy, because for most electronic parts
E12 values are available. These values are 10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68,
82 and 100. Then it continues 120, 150, 180 etc. We can just go the same amount of steps
in both directions and the centre frequency remains roughly the same. Quick example:
L=1 mH, C=5.6 µF, then f=2113 Hz. We vary three E12 values:
L=1.8 mH, C=3.3 µF,
then f=2051 Hz, so only 3% deviation. If the first order filter doesn’t suppress
all higher resonances I add a capacitor in parallel to the driver to upgrade to a second
order filter. If that still isn’t enough I change it to a third order filter or I add
series RLC circuits in parallel to the driver. Only if cone break-up resonances are suppressed
by more than 20 dB in comparison to the final average SPL they aren’t audible any longer.
Aren’t they suppressed far enough you can find out by a listening test if they are audible
and / or bother. But that’s a later step in crossover development and not obvious that
early. The steepness of the slope is determined by the mid-woofer and the tweeter then needs
the same steepness. Due to the natural slope of most tweeters I only shape it a little
more with the high pass until it matches. The natural slope has to be taken into account
which is another reason why a single capacitor, a simple filter calculator or a formula don’t
fully work. Therefore I shape both slopes symmetrical to get a smooth transition and
a summation of 6 dB in an ideal case. That means both drivers are in phase at that point.
As I said have a look at my tutorial “How to Design a 2-Way Crossover”. A word about
series RLC circuits in parallel to the driver: many manufacturers of commercial speakers
in particular don’t take the effort to design this into their crossovers. They sacrifice
the best possible response for lower costs. Unfortunately many audio test magazines seem
to have abandoned printing frequency responses during the last years. Most times I saw diagrams
shown in magazines I noticed non-linear areas, small humps or such, mostly below the crossover
frequency. Where the crossover frequency lies I usually guess from the impedance plot as
I explained in my podcast about impedance responses. I don’t want to say that those
small humps are very bad, often they aren’t. Most of the time it’s quite okay, but I think
there sometimes is room for improvement. If you want to know more about how you can modify
your speakers to make them better than off-the-shelf ones please have a look at my video “Top 10
DIY Speaker Improvements”. As you can see now it is not an easy task
to design a really good crossover. You need some experience for that. You can train that
by using hardware. For that you need an adequate inventory of crossover parts. You can as well
train by using software as BoxSim. I did that, too. Until now I modelled hundreds of crossovers
by playing around with values and topologies. Further, I played around with BoxSim’s built-in
crossover optimizer and tried out how it works, what it does and what outcome it produces.
If you don’t have enough time or enthusiasm to get this experience you can on the other
hand build a well-designed kit developed by someone else, for example from the magazines
“Hobby HiFi” or “Klang + Ton”, manufacturer’s websites like Visaton.com or some distributors
who offer their own kits. Make sure that they have measured graphs available that allow
a prediction of the quality of the kit, or even better, if you know a reliable independent
source for measurements that verifies some of the other measurements. That’s all for today. Next planned topics
are distortion plot, waterfall spectrum, Thiele-Small parameters, all types of crossover parts and
various enclosure types. If you have other suggestions please write a comment below.
If you found a mistake please have a look at the comments to see if I already corrected
it. If I didn’t then leave a message! Thank you for listening and I’m happy if you listen
to my other podcasts or watch some of my videos. If you like what I do please subscribe. Until
next time! Bye!

2 thoughts on “Loubeeka Podcast #3: Basics – Frequency Crossovers and Correction Networks for Newbies

  1. My speakers were originally made in Germany (Braun) in the late 70's. They became ADS in the USA. The thing that made them exceptional (other than basically superb engineering) is the quality of parts. The dome mid and tweeter are very accurate and uncoloured sounding. The woofers have a light, rigid construction, which is better than the pure-polypropylene Watkins woofers that Infinity was using then. While companies in 1979 used high ESR electrolytic capacitors in the crossover, Braun/ADS used metallized polyester. In my experience, they are low ESR and much better than electrolytic. I restored a pair and installed metallized polypropylene of the same values. I'd have to say that polyester is vastly superior and more neutral than electrolytic, and polypropylene is a little better still. I have heard Kef, and a host of other speakers re-capped with metallized poly and the speakers were obviously improved over the cheap stock capacitors. I found that exotic caps (paper in oil, tantalum etc) are high esr and a waste of money. PIO was used to roll off the treble of harsh klipsch speakers in the past.

  2. how the impedance change when using an amplifier with dsp that has separate channel for tweet ,mid and sub. The passive crossover for component speaker should be removed from the network right.

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