What the 'crossover network' does...

One of the least understood aspects of a loudspeaker system is the function of the electrical circuit (the crossover network) and how it integrates the acoustic outputs of the drive units. This design task can only start after the cabinet dimensions are finalised, the prototype cabinet is assembled, internally lagged, the drive units designed and fitted, and measurements of the frequency response of the 'raw' drive units taken, without a crossover, in their final physical position on the speaker's front baffle. We will cover the subject of actually making the measurements in another chapter. Before we can turn to my Notebook, we need to step back a bit.

Let's assume that we've taken the acoustic measurements of the 'raw' drive units and we can now start to think about the crossover. Below, I've drawn what seems to be most people's general impression of the division activity inside a two-way (woofer + tweeter) crossover. The horizontal (or x) axis is marked in frequency, and the vertical (y) axis in decibels. This chart could be telling us something about how the electrical signal is divided in the crossover between reaching the voice coils of the woofer and tweeter, and/or it could be telling us about the sound pressures generated by the respective drivers, as we would measure with a Sound Level Meter held some way away.

In the crossover region where the woofer's output is forced to fade out with increasing frequency (by virtue of components in the crossover network) we need an increasing contribution from the tweeter with the result that what we will measure on our SLM - or indeed hear - will be a perfectly flat, smooth, seamless transition from bass unit to tweeter. If only it were that simple the crossover could be designed in an afternoon, not three to twelve months effort.
Graph 1:

Graph 2 below is the frequency response plot for an idealised woofer and perfect tweeter. These drivers do not exists! They never will. Note that in this theoretical situation the frequency responses are virtually flat in the operating band and well beyond it, except for a few insignificant squiggles here and there. Note also that at the bottom end of both driver's responses their acoustic output rolls off: it's hardly surprising that a tweeter can not reproduce low frequencies (otherwise a bass unit wouldn't be necessary) and that the woofer can not produce the sub-bass that a subwoofer can.

I've drawn the woofer as if its high frequency response continues smoothly well past the 'crossover frequency' but of course, this is not achievable with real-world bass/mid drivers.

Also note that the woofer and tweeter have a perfectly matched sensitivity - they both align along an imaginary 87dB line.
Graph 2:

The ghastly truth is that real world drive units are neither perfectly smooth, nor are they matched in output level. Tweeters are invariably much more sensitive than woofers (i.e. thy produce more decibels for the same power input, but only work at high frequencies). We'll look at these points on the next page.

Worse: take a nice smooth bass/midrange driver, mount it in a normal-size cabinet and something very strange happens: we call it "The Baffle Step". (Ignore the differences in small squiggles on the two curves).
Graph 3:

As you can see, at a special transition frequency - about 300Hz (but this depends upon the size of the cabinet face) what was a nice flat sound pressure response from our driver on a big baffle starts to rise, and continues until it reaches a peak of about +8dB at around 3kHz. This is, by any reckoning, a huge step-up in output, and left as it is, this would debar the speaker from any serious hi-fi use: the mid frequencies would sound extremely dominant and/or the bass subjectively very weak. However, that is not to say that the 'rising axial response' doesn't have its uses: the drive unit is certainly very efficient in those middle frequencies and would produce a crisp, attention-grabbing sound: ideal for PA perhaps?

What can we do to equalise the baffle-step above about 300Hz? Back to the crossover again, and a closer look at the measurements of real-world bass/mid drivers.
Graph 4:

As mentioned when we measure the frequency response of a bass/midrange drive unit on a very large smooth plate (baffle) we may well have a flat response. But take that same driver and mount it in a typical speaker cabinet and the sound pressure of medium-to-higher frequencies rises relative to the low frequencies.

This is due to that fact that as frequency increases (and wavelength shortens) those short-wavelength frequencies are 'trapped' on the baffle, not being of long enough wavelength to bleed away around the side as the long-wavelength low frequencies do. So the sound pressure level that we measure with our frequency-response measuring microphone progressively increases across the audio band.Now we can revert back to the Notebook to 1988 and to a measurement of two drive units, A and B as measured below.
Graph 5:

A and B are basically the same unit except for subtle differences in their frequency response. They both have the characteristic flat frequency response in the 100-200Hz region after the roll-up from the deep bass, marked [A1] and [B1], and they also both have a 'baffle step' transition at around 200Hz. Note that by about 3kHz (a normal crossover frequency for this sort of driver) the sound pressure level has risen by approx. 7 to 8dB. Also, just above the baffle step frequency, around 300-500Hz, unit A has an output plateau, tracking unit B's general shape from about 650Hz upwards. We know that unequalised, these drivers will sound terrible - all middle, no bass, so we have to address this situation. We have two conceivable strategies open to us:

Possible solution #1: Massively boost the bass frequencies below the baffle step frequencies by 8dB or so to bring the bass frequencies below 200Hz up to the peak output level at around 3kHz. The problem is that this amount of pre-emphasis would demand a much higher amplifier power, and would greatly erode the bass units power handling since even during quiet, bass-light music we'd be forcing the driver to flap about generating lots of distortion - and probably a burned-out voice coil too. Risky: this is a design dead-end. Let's think again.

Possible solution #2: We could throw away power in the crossover components. We could design a circuit design that kicked-in at the baffle-step frequency (but not before), which cut the electrical energy reaching the bass/mid driver by exactly the same 8dB amount that the drivers efficiency increases in our examples A and B. Downside: The crossover will generate a little heat as signal Watts are being converted to heat Watts; the marketing people will have to knock 8dB off their specification for maximum loudness and of course, crossover complexity increases. So we may well be able to equalise the sound-pressure response of our bass/mid driver back to flat again - even in our modestly proportioned cabinet. On the next page we'll look at the crossover itself.

By careful and time consuming manipulation of the components and topography of the crossover network, we are able to reduce the electrical energy reaching the bass/mid driver above the baffle-step frequency. What we want is a drive level that is the exact mirror-image of the bass/mid driver's increasing efficiency we noted on the previous page. Our solution is shown in Graph 6 below.

We can clearly see that there is a rolling-up of the electrical signal reaching the tweeter through the crossover region, and then a leveling out above about 6kHz. This implies that the tweeter does not suffer from the baffle-step problem: the tweeter's wavelengths are so short that it is always operating as if it were on a huge baffle. But do note that the tweeter's average drive level is about 4dB below that of the woofer at it's unequalised 'zero level'. This is because the tweeter is 4dB more sensitive than the woofer and to bring the overall system response down to flat, we don't need to drive it as hard as the bass/mid unit. Contrast these real-world curves with the very simple one on Page 1: there is no comparison between the 'theoretical' curves and the actual ones we use at Harbeth to get the sound we need.

So before we take a look at the final 'system response' for our prototype cabinet, here is a reminder of the three primary functions of a Harbeth speaker crossover network:

Function #1: Division of frequency so that only low/mid tones reach the bass/mid unit and only high frequencies are passed through to the tweeter.

Function #2: Equalisation of the baffle-step which occurs when bass/mid drive units are mounted on real-world speaker baffles as opposed to wall-sized sheets

Function #3: Adjustment of the relative drive level so that the tweeter generates a matching level of output to the equalised bass unit and that the system response is adequately flat.

Function #4: Time alignment. Another whole saga in itself!

Trace 7 is the curve of a prototype system's acoustic frequency response. Much more work was needed to get it into production, and you'll notice that I overdid the baffle-step correction so that the overall response is perhaps a little dished in the middle frequencies and possibly a little strong at the highest frequencies. Now the 6-9 month long listening and tweaking phase can begin.
Graph 7:

LS3/5a: I've added two curves from the LS3/5a archives with the same vertical scale as Graph 6. They illustrate how much mid-band energy is "thrown away" in the crossover as heat (about 10dB!) to bring the 3/5a's 500Hz-1kHz acoustic output level down to that of the 100Hz region so sound correctly balanced. For a small, 5" drive unit, to dispense with 10dB of its already small output capacity in the interests of high fidelity has two consequences: the overall system rated sensitivity drops (to about 82dB) and the maximum loudness is restricted by how far the tiny bass unit can move before clipping and/or voice coil burn-out. This is proof positive that a design like the LS3/5a walks a very fine line between adequate loudness and overdrive of the bass unit. The volts appearing across the drive units in the original BBC LS3/5a looks like this ...
Graph 8:

and in the later (Harbeth) licenced version like this ... None of these curves, tell the designer anything at all about how the system will sound. Pity.
Graph 9:

Hope this throws some light on the mysteries of crossover design. © AAS 7.2005