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Real Vs False Claims?

 

The "Joe Rasmussen Approach to Crossover"

(as some have called)

A HOLISTIC APPROACH TO LOUDSPEAKER CROSSOVER DESIGN

(Holistic: The system as a whole determines in an important way how the parts behave.)

April 2011 - Elsinore Mk5 - some details below are obsolete.

Every designer hones over a time a certain methodology and years of refinement is the norm. The Crossover used in the Elsinore Project is likewise a result of more than ten years of what might loosely be called research (that seems to be a favourite term). But it basically comes down to how you deal with a number of issues that are of primary and secondary importance. To me the following are primary:

  • Summing 100% at All Frequencies - 100% Driver Integration

  • An Alternative to Butterworth and Avoiding its Failings

  • Butterworth and "Audio Interruptus"

  • Analysing Mechanic & Acoustic Limits Above Piston Range

  • Using The MidBass Driver's Natural Roll-Off

  • Contour and Equalisation at the Edges of Passband

  • Tweeter Hi-Pass - Single to Multi-Order Transition

  • Tweeter - Maximising Voice Coil Damping & Lower Distortion

  • Tweeter - Maximising Low Order Power Handling

  • Impulse Response and Electrical Phase Questions

  • Step Response & Time Coherence Issues

Looking at the crossover of the Elsinore Project, it seems quite simple. Yet that simplicity is quite deceiving. It deals with some significant problems as used in multi-driver speaker designs. Behind the Ellsinore's crossover is a highly defined methodology, one that needs further explanation.

The following is not designed to be the final word in crossover design but rather trying to explain an overall concept and a workable set of solutions, and put them into a single package. There are arguably multiple approaches to crossover design but just like all beers are either fundamentally ales or lagers; there are single-order and multi-order crossovers.

As I am in the former camp I need to be more critical of driver selection as they must behave more predictably at the edges of their passband. That term needs explanation. All drivers are bandpass devices and their useable range is the passband (or bandpass). Single (low) order requires drivers with wider passbands as their behaviour above and below the crossover point (Hz) is still contributing significantly to the summed response. The summed response is when two or more drivers contribute to a flat response.

Next, our phase at the crossover must have complimentary phase throughout the summed range, which means both below and above the crossover. This does not happen by chance. What concerned Linkwitz and Riley in their 2nd and 4th order crossovers was the acoustic phase at the crossover point should be the same (not to be confused with electrical phase). We want this also to be the case with 1st order designs. This also needs explanation as it is not conventionally (and theoretically) true with respect to 1st order.
 

Butter Not Worth All it Seems?

Those interested in 1st order crossovers use Butterworth filters, because of the claimed 'correct phase' and also when taken to the very extreme, drivers staggered properly in time (so-called time alignment) is able to produce either a single Stepped response and/or square waves.

But these are Butterworth filters and they only sum the response half of the time - which will be explained as we go on. This is why L-R filters are minus 6dB when producing a flat summed response but Butterworth are only minus 3dB. Butterworth have 90
° phase shift at the crossover point that prevents full summing (they are also incapable of achieving a proper symmetrical polar response which is a direct result of getting the phase right - another thing that concerned Linkwitz and Riley). This will come back to haunt us at a later stage.

Why does Butterworth only sum half the time? Because it is a fact that they have a severe phase deficiency. Butterworth? Phase deficiency? How can you say that? Surely this is Heresy!

It may be in some quarters and it should not be, as it will act as a deterrent if we become inflexible, by which we cannot then observe the complete picture. Curious fact: Butterworth filters sum flat whether or not the drivers are connected in phase? This will be proved to be not such a good thing. Because of this 90
° phase shift they behave as follows.


Let's Start an Experiment:

Imagine two surfaces representing the two cones. The grey line represents the natural resting point of the cone as well as the box. Note there will be no output unless the cones actually move. Since this is a Butterworth filter that precedes the drivers, the bottom driver is 90° behind the top driver.

The same signal is applied to both drivers. Here they are both moving forward together. The top tier cone is now in the forward position. The bottom driver has moved forward to the centre position. This represents the first quarter of our cycle. Note the grey curve indicating forward pressure. So during this quarter of a cycle the drivers are summing (also angling down the radiation pattern that can prove another problem to symmetrical polar response - but that is another subject).

Now something interesting has happened on our second quarter of the cycle (each quarter represents 90°). The bottom driver continues to move forward as in the previous quarter, but the top driver now only has one way to move and that is backwards. It is easy to see that during this quarter they are cancelling each other’s output. They sum zero. In fact, at that moment there is no sound emanating at the centre of the crossover frequency!

 

Audio Interruptus?

On every second quarter of the cycle the speaker is effectively dead at the centre frequency of the crossover - it is not just reducing output but a total cancellation, zero output. This is hardly desirable. Also cancels off axis, exasperating that as a problem as well, more about that later.

Let us continue:

Now both driver cones are moving backwards. This time they cause rarefaction of the air, the air is moving in reverse as we have reached minus 180°. They are summing (also changing the angle of radiation again and preventing that radiation from becoming perpendicular to the front panel).

The final quarter is now obvious; the cones are doing a switcheroo again and thus cancelling. We have returned to the original state and the cycle is over. Once again, there is no sound emanating at the centre of the crossover frequency!

So the sequence is sum, cancel, sum, cancel... etc. We are only summing every second time (every second quarter of a complete cycle).

(Please see an explanation re Angle of Radiation below.)

This is why higher order L-R filters were designed to sum at the crossover point. At least they sum, sum, sum, sum etc, there is no interruptus.

I showed the above example to a well known audio engineer and he was astonished as it had never occurred to him. He could see now see that Butterworth filters that sum acoustically (or at least supposed to) are seriously flawed.

This 90
° phase shift remains the same always whether connected electrically in phase or not. Confirming this: Now try the same experiment as above, but this time put the right driver ahead of the grey line representing 180°. Instead of sum, cancel etc, it now becomes cancel, sum etc. The summed response does not change whichever phase you select. The net result is identical.

The following shows the phase response using  a Butterworth crossover @ 1KHz:

Please denote, filters (or crossovers) can only delay. The Black Bass line (which is our reference here) starts to show delay as it gets closer to the 1KHz crossover frequency. Relative to our reference Black Bass line, we have two opposite Tweeter phase plots. The Tweeter Red line , in phase,  is not delayed at high frequencies. Note the 90° split at all frequencies including the crossover frequency? Now note the Blue line. It is the Tweeter connected out of phase. Yet it is also split 90° at all frequencies including the crossover frequency. So the difference phase sum is the same whether Tweeter is in our out of phase.

It also helps to demonstrate why Butterworth sums flat whether the Tweeter is connected in or out of phase. Acoustically speaking, the error is always the same. It also explains why Butterworth must be -3dB (only 50% summing).

Of course, Butterworth constructors will stay with the in phase and time align the drivers etc, but the problem remains. What the above plots shows is that the error occurs at ALL frequencies, but what saves it is that the filter's roll-off prevents and reduces the 90° cancellations the further we get away from the crossover frequency.

Curiously, for a crossover that is supposed to be time correct, this is time error we are discussing! That it can still sum flat on axis seems good enough for the current Butterworth purist, but there are real world problems that remain, as we shall describe as we go on.
 

The Real Achilles Heel

We have not even yet discussed the real Achilles heel of Butterworth. As we know that passband in the upper midrange change drastically when comparing on and off axis responses (off axis collapse, the so-called beaming effect of midrange drivers), the incomplete summing inherent is Butterworth is a severe limitation. We usually have wide dispersion by the HF unit and we are now NOT taking advantage of that, even denying it ability to actually helping solving the problem.

We are cancelling much of the Tweeter's output where it is most needed, off axis. The beaming effect is not fully filled in when it ought to be.

Butterworth has poor Power Response.
 

By getting the phase right we should sum correctly over a much wider lateral area (filling in) and maintain good power response because our off axis response is properly maintained. Good Power Response is achievable. Butterworth is largely unable to do that.

When two drivers behave well and consistent at below and above the crossover point, on and off axis, then Butterworth filters only have one drawback, wasted energy. So the low frequency crossover in 3-way speakers, say around 300-600Hz, these can be Butterworth without much to trouble the designer. It works because you have large overlapping passbands. But the upper crossover (and usually the only one in 2-way designs) we are now working at the very edge of the midrange driver's passband.

Forget about whether the crossover is of any particular order. It might be 'electrically' first order, but look at the on and off axis and the power response of the raw driver will NEVER be first order. So much for our beloved Butterworth theory, it just doesn't fit and worse, it manages to get in the way. Do not get hung up about this or become a pursuer of a lost [Butterworth] ideal.

As stated, we need another approach, one that is workable and consistent and does not fight physics.

So this is the Introduction to a workable solution, the "Joe Rasmussen Crossover” as named such by Brad Serhan of Orpheus Loudspeakers. It wasn't me, but perhaps we should more accurately describe is as the "Joe Rasmussen Approach to Crossover." Hope you don't mind, but it seems that in this world one must do some self-promotion to get anywhere, even if it goes against the grain a bit.

This work represents much effort from the mid-nineties until now. Much of it by the seat-of-pants experiments, right through to correctly computer modelling the result. These days I would not do a design without a strict and disciplined approach, using computer capturing and modelling. It is all explained here.
 


The Sum of It All? Getting it Together?

When we do design crossovers, we ought to keep our eyes on the ball. It isn't just about flat frequency response at some single discrete point in front of the loudspeaker.

The word you hear here many times here is summing. This incorporates not just the target response being as flat as possible, but - here is another key phrase - get the driver integration right and that means getting the phase right. It must be right at a large range of distances and especially off axis. We need to gel drivers together. We could call this the stitch between the drivers. It must be predictable and not cause uncontrollable ripples in amplitude and phase. Butterworth in the upper midrange always have difficulty in getting the stich right.
 


Summing and driver integration, if a crossover cannot achieve this, it has failed. 


A Problem Within a Problem?

Let us deal with yet another factor in making 1st order crossovers difficult and hence why Butterworth is impractical. I don't mind using Butterworth below 1KHz as often the drivers are not only in their passbands but also likely to be within their piston range. This term also needs explanation. Piston range is the range of frequencies where driver cone moves as a whole, backwards and forward. Above a certain frequency called the 'knee' by E. (Ted) Jordan, the response would drop by 6dB/octave if the cone material were infinitely stiff (Allison did exactly that in the 70's). In order to extend response above the knee, the cone must start to flex in such a way that the radiating area shrinks. In theory the diameter of the radiating area should shrink and the area that shrinks should continue to move as if it was a piston and the area out side, the cone area nearer the edge, should be become stationary at those frequencies. In reality it is not that simple, as the flexing of the cone cannot easily be controlled in such a fashion. For those who want to look closer as to how cones flex, see Martin Collom's High Performance Loudspeakers Edition 6, page 66.

Now we start to see the magnitude of a 1st order Butterworth Lo-Pass filter for the midrange driver. The response beyond/above the knee is much less predictable. Here is a basic rule I follow:
 

Below 1Khz it is the diffraction loss (step baffle) that dominates, whereas the response above 1Khz, it is the effect of the knee that is most dominant.

Generally the former can be compensated by the usual methods in the crossover as described by John L. Murphy and others. But the latter is far more difficult. Let me give you a typical example of a Bass/Mid drivers response mounted in a box with typical rectangular baffle.

We can easily see the step baffle loss starting around 600 Hz. We can predict that after compensation it will average around 86-87dB sensitivity. So let us do that:

Not bad, we could have compensated slightly more. We would expect this 6.5-inch driver to have acceptable piston response below 1500 Hz, roughly the knee frequency. But the elephant in the room remains that large above the knee 4KHz peak (in many high quality drivers even much worse again). Trying to roll this off will also magnify the trough at 2KHz.

Close examination of the 4KHz peak showed something quite interesting. Is this a cone break-up mode? Is there a prominent resonance behind this peak? In this case and with this driver, the answer was no to both questions. Waterfall plots and multi-harmonic distortion tests proved the driver was largely clean.

So what exactly are we dealing with here? Well, if the problem is not mechanical (cone break-up is mechanical), then we must look to the peak as being an acoustic effect.

I am now touching in an area that I have not seen anybody write much about before. It will lead to the correct solution because we are definitely looking at an acoustic abnormality rather than mechanical failure. Take for example the baffle step response below 1KHz, it is an acoustic effect. It is not a mechanical failure of the box but rather an acoustic imprint because of the shape of the rectangular baffle. We know we can compensate for the step response in the crossover, then why not with the above knee response? I see no reason why not.

Let us now consider how acoustically the response above the knee (rather than a mechanical failure) affects the final response.

We can assume with reasonable confidence that it is the shape of the cone that causes the 4KHz peak rather than any break-up mode, of which it has already been cleared.

Reasonable confidence? Don't worry, let us see hard proof.

Two drivers, both using the same chassis and magnetic system and the same test baffle. Same test. Yet the cone material is different but the cone profiles are almost identical. There is a slight difference shown by the fact that the upper mid peak in the red sample is narrower than the black, which has a concave dust cap just a little smaller in diameter. But the cone materials are NOT the same! Just very similar cone profiles. The approximate 1dB separation is because of slightly different mass of the two cones, Red higher mass than Black.

Note: It is the shape of the cones that matter, arguably also the frame and cone terminations play a part too in shaping the acoustic response. Both were clean from any cone mechanical break-up modes, in fact top notch performers.

Just as the step response is a result of the baffle shape and dimensions, so too the response above the knee is caused by diffraction effects largely within the driver.

There are two simple conclusions to be made:

  • The ultimate roll-off does not need an additional Lo-Pass filter

  • The peak at 4Khz needs equalisation that improves both amplitude & phase

Lynn Olson comments: "I agree with Joe's comment these clean, well-defined peaks are not breakup, but are artefacts of the cone shape itself. They are especially evident in top-of-the-line cones with low inductance figures - in a more typical high-inductance driver, the peak is intentionally masked by voice-coil inductance. Since VC inductance is quite nonlinear, low inductance is a good thing - but it does make the F[requency] R[esponse] look different than you might expect." Read complete comments.


Let us take a brief detour:

[Please note, from Elsinore Mk5 onward and including current Mk6, the LCR Trap near 4-5KHz is avoided for reasons not covered here, but the acoustic phase EQ does provide suitable insight.]

Equalisation in the electrical domain will get rid of the wrinkles that shows up minimum phase plots @ 4KHz - the amplitude response mirrors the phase response.

Here Blue represents before EQ and Red post EQ. Now what affect does this have on the minimum phase plots:

Identical plots, same colour code. Post EQ Red cleans up both phase and amplitude. It is much straighter and means our final crossover will track with greater predictability.


Adapt or Perish?

If cone break-up or mechanical integrity is not compromised, why does the driver have to have a 1st order filter added? Does it need it? This took me some time to absorb as it goes against what we normally do. Sure, if it is a high order crossover, they do add a 2nd , 3rd or 4th order low pass filter. But what we want is first order. Again the fact we are dealing at the edge of the passband and above the piston range, we need to be more adaptable in our thinking.

Our 4KHz peak (which we know we can EQ both amplitude and phase), and a similar peak plague most mid/bass drivers. Just go on Tymphany's website and look at drivers from Scan-Speak (expensive), Peerless and Vifa (now V-Line) and at least some upper midrange peak is common, especially on axis and sometimes ameliorated off axis. But with the right approach we can overcome these.

Here is a suggested Lo-Pass (it is not really, but tradition dies hard) of the above driver:
 

        

The LC Network is used to balance and flatten the overall response including any necessary diffraction loss caused by the box. The LC components of the LCR Trap is carefully tuned to the same frequency as our peak, the Q decides the width of the peak to be dealt with, then the resistive component applies the severeness and depth of the trap. With careful adjustment of values we can tune out the peak and gain a smoother and more rounded curve at the edge of the passband.

The Blue line is our 'raw in the box' response and the Red line after our so-called Lo-Pass filter has been applied. Look carefully at around 7-10KHz and you can see the roll-off rate is virtually identical for both plots. There is really no Lo-Pass filter as such, what we have done is contoured our driver into a more desirable response. In fact the crossover components are now really only equalisation components. We can now concentrate on the Tweeter and crossover to match up with this curve. The eye indicates that if we are to achieve full summing at -6dB, then somewhere near 3Khz looks probable and acceptable.

Here is the result with Tweeter:
 

I could have used a Tweeter with a smoother response.

This happens to be the Peerless HDS 810921 and above is on axis. The approx 5-6Khz trough is partly common for this Tweeter (we will work on this later) and the 16Khz peak reduces somewhat as you get off axis. I could have used the Vifa XT25 Tweeter, which is smoother on axis especially, but the more problematic HDS Tweeter sounds much better.

This is 15° off axis. The 5-6KHz dip is there, but the overall response is smoother. Now let us get well off axis to really test how things hold up:

OK, what are we looking for? Obviously the top octave and a bit is now down at 25° of axis. Note that the opposite response will be the same so here we are looking at a total 50° arc in front of the speaker. And the 5-6KHz is still a problem. But look at the response in the critical octave 2-4Khz. Here the Tweeter is doing a remarkable job of filling in for the beaming effect of the mid/bass driver.

Let us look at the split of the middle graph, 15° of axis:
 

We can see that we are getting 100% summing at 3Khz. The summed response is exactly 6dB above the individual drivers output at 3KHz. Note that the crossover overlaps from 1Khz to almost 10KHz.

The crossover sums positive over the whole overlap!

Hello? Now we can see that a combined response between drivers around 5-6KHz is the cause of the dip, not the tweeter alone. We can now further tweak the LCR Trap etc and see what improvement is possible.

The result is as follows:

 

A reasonable improvement. This result is quite acceptable even if not perfect. The response is -/+ 2.5dB from well below 100Hz and 20KHz. Moreover, the troughs and peaks average out well. There is a slightly less than average output in the low treble range. This can be trimmed by ear adjusting a single resistor in the High-Pass to the Tweeter.

The example shows the response with the Peerless HDS, but if the Vifa XT25 were used, the response would be significantly smoother. But the HDS's upside is significantly lower distortion exchanged for flat response and also much better off axis above 10KHz.


You Take the Low Pass and I Will Take the High Pass

[The LCR Trap above is avoided in Elsinore Mk5 and Mk5, but the Null Trap below is still being used as it is out of band and below 1KHz.]

We now come to the Tweeter's High-Pass. This too has a few surprises.

Please take the values as only indications. But it does look rather simple and only a few questions will arise. But the apparent simplicity disguises the complexities.

There is no doubt that some will have their attention brought to that Red Positive. Yes, it is connected electrically out of phase. But we shall see that it is in fact acoustically in phase. Later, as we examine the system impulse (step) response and minimum phase graph, we will establish that the acoustic, and hence correct phase, is maintained up to 10KHz plus. By that high frequency the overlap in the crossover is finished. We shall also be able to produce square waves in the 500Hz-1KHz band.

But let us examine the amplitude response first. Note the two split 5R resistors. In purest terms the second nearest the Tweeter should be omitted but in computer modelling it was found to be useful. There is a null network made from choke/capacitor series and then in parallel with the voice coil.

The pre and post null traces show that we have maintained near first order down to around 1500 Hertz. The frequency and Q of the null network has been carefully tailored to give the result shown. The null frequency is clearly 650 Hertz, which coincides with the Tweeters Fs. The choke DC resistance should be as reasonably low as possible, here it is <0.5 Ohm and in this case we have achieved a very high order effect, better than 5th order and close to 6th. The tailoring has given us low order phase characteristics for an octave below the crossover frequency. This should be a minimum.

The Peerless Tweeter now has very good power handling in comparison with conventional first order. When we say 'power handling' in Tweeters, this also equals low distortion.

Conventional odd order High-Pass networks have a common problem that 2nd and 4th orders does not. The problem is especially emphasised in 1st order. Let us use the same Peerless Tweeter as an example, although other samples could well be worse.

This is the raw impedance and the peak of 13-14 Ohm indicates Fs equals 650 Hertz. Now let us put a single series cap for a classic 1st order High-Pass. We can see that the peak is two times the base line impedance; this will indicate a potential 6dB increase at 650 Hertz unless we use an LCR trap to flatten impedance.

We shall see the results with and without LCR trap, with or without flat impedance:

This example shows a single 3uF cap as the High Pass filter, the Blue shows the response without any impedance compensation. The 3uF cap is not rolling off at the full rate of 6dB/Octave. The Red line shows what it ought to be when the filter is electrically 6dB/Octave. We then flatten out the 650 Hertz peak using an LCR trap. At the Tweeter's 650 Hertz resonance we have an improvement of 6dB. That means the Tweeter's excursion is halved and the actual heat dissipation is a quarter. That translates to lower distortion. Tweeters as a rule do not like high amplitude motion.

The problem with Butterworth High Pass filters is that they leave the Tweeter largely undamped at the Tweeter's resonance (in above case, the LCR trap helps a great deal, but things could be better).

 

The reactance of the series cap in-creases as the frequency descends.

Now compare 2nd Order:

The reactance of the parallel inductor de-creases as the frequency descends.

We won't show 3rd order (as 3rd order Butterworth), but it suffers from the same as 1st order. What about 4th order:

Again, as in 2nd order, the reactance of the final parallel inductor de-creases as the frequency descends. This coupled with high slope and the life of a Tweeter ought to be comfortable.

We can see the pattern, the final parallel inductor dampens the voice coil where as a final cap reduces the damping. Generally 3rd order does better as it does reduce amplitude, but again 1st order (they are all Butterworth) needs some additional help, and the LCR trap is only a partial solution.

Here is our Final Solution (no pun intended):

Ignore the 5R resistors, here it is the Null that interests us. This is tuned to 650 Hertz and the peak of the Tweeter's resonance. The inductor resistance needs to be as low as practicable. The values are chosen to give the desired shape which is dictated by the Q of the Null.

The final crossover and the Null is quite visible at 650 Hertz. Low order near crossover frequency and yet the Tweeter is well protected. Distortion is low.


Looking In Time

Above section has been concerned what happens in the amplitude/frequency domain. Before going on to the time domain I want to make something clear first as it will make what follows (hopefully) easier to understand.

We are all familiar with the sine wave, how it has a plus and a minus part of the whole cycle. Something like this:

The Red represents positive and  Blue represents the negative parts of the sine wave. This is a fine representation as at the zero line there is no potential. But note we are thinking in terms of potential (volts) here and that this representation does not hold true when we enter the acoustic sphere.

Here we need to consider that it is not potential but motion that is the key to understanding the sine wave.

During the period (time) shown by Red the sine wave is moving in a positive direction even before it reaches the zero or median line. Same goes for Blue except the movement is all negative.  Whereas electrically there is no potential when at zero, but acoustically it is different. It is when motion ceases.

Keep this in mind: It is the direction of movement that matters, not where it is in relation to any zero line. This also applies to the time domain, as will become clearer.

Summing It All Up - On The Step of an Impulse

This is what we are going to do: To get the drivers to integrate at the listening position, they must sum 100% at that point. Since the Tweeter will go negative (for reasons that will become apparent) and the MidBass driver will go positive, the negative going part of the Tweeter must occur before the onset of the positive pulse from the midrange.

Here is a key thought, at some point the Tweeter's negative impulse peak will be reached and at that point the Tweeter's output turns positive. It will start to sum positive with the MidBass at that point, provided they are correctly aligned in time. It is in fact only the first half of the impulse response that the Tweeter cannot sum and does not need to.

Now this part of the Tweeter's negative going pulse will equate to above 10KHz (high rise time and well above the crossover overlap) and makes it possible to reverse the Tweeter's electrical phase and yet match the phase of the midrange driver concurrently.

To make this possible the Tweeter must be time aligned specifically to line up the two impulses. At no point must the two impulses work against each other. As the negative going part from the Tweeter progresses there must be no output from the midrange. If this is confusing, please read on and the explanation should become clearer.

First step is to look at typical examples of the step response of individual drivers and how we can line up the time factor.

Tweeter first:
 

The Tweeter's electrical phase is reversed. The negative pulse means the dome is moving inward (we keep it simple even if it isn't, for clarity's sake). At a certain point it comes to a stop. As this is a step response and if DC is seen by the Tweeter's voice coil, the dome will be kept in that state (but in reality it doesn't as there is a Hi-Pass filter function). At this point the pulse has to die, as there is only an acoustic output when the dome actually moves. The air stops. The step response reverts to positive phase (caused by natural air pressure) as it is coming from a negative base, from which it can only go positive. The position of the dome has little to do with it. Naturally, in real life the Dome does return, as it does not see DC.

This may be difficult to wrap one's head around, but in reality it is quite simple. Therefore the impulse/step response looks as above.

Here is a primary rule: It is not where the impulse "is" but where it is going that interests us. That movement is either positive or negative (no movement equals no output). So the question is, is it going up (positive) or going down (negative)?

That means that the lateral broken line should not be considered a zero reference point, only as a starting point. The Tweeter's step goes negative for less than 0.1 microSecond, then all the rest of its useful output is positive. It is the Tweeter's reverse acoustic phase that dominates the total output in the end. Surprised?

Now for the MidBass:
 

Here we have delayed the starting point of the step response to coincide as closely as possible at the end of less than 0.1 microSecond so the Tweeter's output is not cancelled. Note the slower rise time (if it had fast rise time we wouldn't need a Tweeter). The positive going portion of the Tweeter's output will augment and increase this rise time by summing correctly. The MidBass must go up (positive) at the same point in time that the Tweeter does as well.

This is the combined step response. The rise time has been maximised. Now for a look of all them overlayed:


It is important to grasp that the step goes positive after 0.1uS and well before it gets to the dotted median line. The rule is not where the pulse "is" but where it is going.


The superimposed overlayed family that makes up the whole:

Can we see how this all fits together into a careful scheme of things? After the Tweeter's initial 0.1 microSecond fast rise (of which we are taking fortuitous advantage), all the drivers sum positive and together.

(Note that the slower rise time of the mid/driver Blue indicates that physical alignment of the driver array is also much less critical and that  it will sum over a greater length or depth; it be less focus critical.)

Now that is the theory, let us look at the final result:

The Red is the Tweeter's Step Response and the Blue is the MidBass.

Here Green is the Total Summed Step Response. I have left the Tweeter's in Red to show that it is syncing perfectly.

The total step response it is overwhelmingly positive even if the Tweeter's electrically is out of phase. Note where the positive Step Response starts. It starts at the bottom of the inverted peak and not the zero line.

The Tweeter's output, even if it is negative electrically, sums positive!

We can determine that the negative going part of the Tweeter's impulse takes about 0.06mS - so our calculation:

1 / 0.00006 = 16 KiloHertz

The reverse polarity only shows up well above 10KHz, below that we have perfect phase behaviour including 100% summing and driver integration (by 10KHz the 3-4 KHz crossover is no longer overlapping). No Butterworth 90° misbehaviour, good Off Axis augmentation preventing beaming and ensuring flat power response as well as flat frequency response.

These are (but only) the highlights of the Elsinore Crossover. It looked simple on the surface but 'under the bonnet' look tells a more complete story.
 


Study the following graphs closely as they show how the whole picture hangs together, not just in the frequency domain but also in the time domain.


Final Step Response, also captured at 2 Metres and 15° Off Axis


 

700 Hertz square wave captured at 2 Metres and 15° Off Axis

IIn 3-Way speaker systems we can use Butterworth Crossover between Bass and Midrange drivers, as there will be no off-axis issues below 1KHz. In the crossover from the Midrange to Tweeter use the method discussed here and we maintain the ability to produce correct Step Response and Square Waves as per 2-Way example shown above. This also applies to the 2½-Way Elsinores.

Mission Accomplished!


Minimum Phase is maintained from 20 Hertz to 16 KHz.

This indicates that the negative going pulse lasted about 0.06mS - just as was indicated above.


Note Red Line is 0° -  actual Clio phase capture @ 2Metres & 15° Off Axis

(Sub 200 Hertz not considered accurate)


Here ends our journey for now. We have not crossed all the T's and dotted all the I's. I am aware that the above needs to be read several times for a total picture to emerge and then the dots will connect themselves.

But we have given a significant insight to a methodology that not only works but can be applied consistently over many designs. So until next time, Arrivederci!

(Rev 1.0)

Joe Rasmussen


Explanation of Angle of Radiation: Please note in the above Piston movement illustration that the Angle of Radiation is perpendicular to the line that can be drawn from the centres (nominally the acoustic centres or AC) of the two Drivers. This mean that the Butterworth radiation pattern will never go straight ahead which is perpendicular to the Front Panel (and likely aimed at the listening position). It will either point above or below depending on piston movement going in or out alternatively.

(Reference: John Kreskovsky)

This asymmetrical lobing (on the left) cannot be eliminated in Butterworth designs, it is a byproduct of the 90° error associated with Butterworth 1st Order (note: Left, the straight on axis is -3dB relative to 100% summing at 90dB on the Right). Time alignment of the two Driver ACs with regard to the listener's position is not a solution. The Pistonic example above does have the ACs time aligned with the listener and yet exhibits the problem. Re-jigging it will always be a compromise.

Addendum 2016: It should be noted that the relative location of the crossover, taking in the offset between the drivers (caused by the front panel and the location of the Voice Coils of and within the respective drivers), that reversing the physical phase in fact lessens that offset. Whatever the situation in most cases, the lobing will be reduced.


Copyright © 2007 Joe Rasmussen

PS: This instalment may continue with Brad Serhan's method of computer modelling the above by optimising 1st order electrical crossovers that sums the full 6dB by using Linkwitz-Riley 2nd order optimising engine by Bodzio (SoundEasy). The topic is far from being exhausted.

 

Total Design Responsibility, Joe Rasmussen of Custom Analogue Audio & JLTi

Part Financial Sponsor & Prototype Box Construction, Bernard Chambers of Sutherland Shire

Sounding Boards, Michael Lenehan of Lenehan Acoustics & Brad Serhan of Orpheus Loudspeakers


 

 

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Copyright © 2003-10 Joe Rasmussen & JLTi
Last modified: Monday June 08, 2015

Just had a terrible thought. If "intelligent design" is unscientific, then who will design our audio equipment?