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Part Eight

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

Notes On Computer Modelling

The following page was written with Mark 1 Elsinores in mind:

As mentioned earlier, the driver's acoustic measurements are all gathered from a single microphone position. This simplifies the computer modelling. It is not always understood that a measured frequency response also carries the phase information.  But both the amplitude and phase are only relative to that position and no other. So let us revisit that earlier illustration:


To sum up, the top three drivers are in Point Source configuration (but the captured acoustic data assumes all drivers are Point Source). So we need to model the tweeter by capturing both its acoustic response and its impedance. These are imported in our modelling program, SoundEasy Version 11. The two drivers above and below the tweeter are connected in series and once again acoustic response and impedance measured. Finally the two lower bass drivers, also connected in series, are also measured in the same manner.

The software then is able to produce three files, these contain the Complex Transfer Characteristics based on those measurements, both acoustic and electrical (the last is the impedance and impedance phase of the drivers in sets/series wiring). We shall call these the driver CTC from here on.

Note: The MidBass Drivers are paired and measured as if a single driver. Both their acoustic and electrical characteristics are combined.

This approach and the single position microphone reference enormously simplifies modelling and allow us to measure four sets of modelling using the reference mic positions with much greater ease.

Four Times Modelling

Yes, four times. The diagram below shows two ON axis and two OFF axis. One set at 1 Metre and the other at two Metres.

For those familiar with the principle of weighing, there is an interesting conclusion we can make from the above four reference positions. The one and two metre On Axis measure the frequency response. These are discrete measurements only. But the one and two metre Off Axis reveal something more akin to the power response. In fact this off axis measurement should be weighed as much as two times more valid as the on axis one. Why? Because if we measure off axis, then we are really doing two measurements in one. If we did the same measurement from the other off axis, then this would be identical (this is because the vertical alignment of the drivers in the centre of the box, i.e. lateral symmetry). Can you understand this? Well, understand this, the off axis is twice as revealing as the on axis. This is indisputable.

Stripped Down Modelling (Point Source)

A quick explanation what is meant by 'Stripped Down Modelling' - this could also described as 'Bare Minimum Modelling.' A minimal approach where both measurements and modelling assumes Point Source.

Today's software can simulate so many variables in speaker design. The SoundEasy modelling program has a bewildering array of these, a huge feature set. While these are not without benefit (they are great for research and discovery of all sorts of interesting things), the fact is that real data is better than simulated data. Perhaps better put this way, real data is more reliable, you can bank on it. You can model it more reliably.

Brad Serhan and myself developed an approach that minimises simulation, relies on measured data that is gathered in situ, so the driver must be in box, the microphone in potential listening position etc. Thus we don't have to model the box and driver position, but can concentrate on modelling the crossover only.

This means that the box must be modelled first separately, sort out the box alignment, the physical location of drivers on the baffle, in fact everything box related. NOW we can use the two illustrations above and we have a workable methodology.

The Process

MidBass Driver: The electrical data is effectively the same for all four, but the acoustic data are not (because they have different physical locations they have different acoustic outputs). These must be collected as sets. Note I call them sets as the following data has been collected.

1. Tweeter - on its own

2. Top two MidBass Drivers (nearest Tweeter), in series as one set (16 Ohm)

3. Bottom two MidBass Drivers, also connected in series and as one set (16 Ohm)

Above three must be measured four times and hence four sets. So now we generate CTCs of all of them, that is a total of twelve CTCs.

The Software used for this is SoundEasy Version 11. See SoundEasy Home Page.

To look at the Driver Parameter Editor for the MidBass combination, see here.

To look at the Driver Parameter Editor for the Bass (bottom two) combination, here.

To look at the Driver Parameter Editor for the Tweeter, see here.

To look at the Crossover CAD, see here.

After constructing our CTCs from the Driver Parameter section, then it is the Crossover CAD where most of the action takes place. But it is important that when we get to this stage that we must be absolutely certain that we have captured all data correctly and with extreme discipline. It will have been all for nothing and the many hours that will be spent in the Crossover CAD will have been a wasted period of your life that will amount to nought.

The CTCs contain all the necessary data, these are all in situ characteristics. Yes, the data files we call CTCs even contain the data of the box, even though these are named after the driver or driver combination that makes the CTCs. This is because these are influenced by the box and thus the box is integrated into the CTCs (so we do not need to model the box characteristics and driver positions in SoundEasy). This includes the box tuning (alignment), the diffraction effects of the box, the way the box changes both the acoustic and electrical response of the Bass/MidBass drivers and the acoustic response (not so much the electrical, because the rear is sealed) of the Tweeter.

So assume that we have checked, double checked and even triple checked that our collected data is all totally valid, we can now construct our crossover.

Here we can now start to see the benefits of the Stripped Down Modelling method.

In our above example of the Crossover CAD, we can see that the Bass (bottom two drivers) are modelled as a single WO, the MidBass (upper two) as M6 and the Tweeter is T13 (don't be superstitious).

We draw the Crossover into the CAD using the symbols on the right. We assign the three driver symbols, WO, M6 and T13, to the CTC files which are imported by giving the modelling program the file path to those files. This means that we can make the initial crossover for all four by pointing to different file paths and files containing CTCs. Then we save into four Projects:

Project A:     1 Metre On Axis

Project B:     1 Metre Off Axis

Project C:     2 Metre On Axis

Project D:     2 Metre Off Axis

From here on, when we make on change in one crossover, we must replicate it in the other three. So if one value of resistor etc changes, then that change needs repeating in the others. What if we make a mistake? One simple trick is to plot the system impedance as they, unlike the system response, should always be the same in all four. It is also easy to check visually as any inconsistencies are immediately obvious to the eye. Any good system must have checks and balances and this is ours.

As with gathering data, discipline must be continued and constant check consistency of both data and results. Confirm and re-affirm that all four projects have identical crossover layout and values. The end product is worth the effort and also do not pre-allocate the amount of time necessary. Many times you will go back and test, try, compare and refine. Take your time!

All graphs shown will be 5dB per division.

We shall mainly use "Project A" as the example - but in reality there four in total.


Why Use Computer Modelling?

Certainly it is possible to design speakers without modelling, so why do it? It boils down to flexibility and the ability to explore many possibilities that would otherwise be time consuming and tedious. As we limit ourselves to model the crossover only, there are still a near infinite range of possibilities that could not all be explored if we had to physically build a crossover (and rebuild) over and over again. What if you don't have the components or the values you want to try. It could be costly in both time and money - how many inductors, capacitors and resistors do you want to keep in stock? In modelling we can use any value, any type of crossover and any idea you may want to try.

In the following we shall concentrate, for simplicity's sake, on the 1 Metre On Axis acoustic results, while keeping in mind that we were also looking at the other three sets (as mentioned above) as part of the process. It was important to keep the whole picture in mind. As it is, the on axis measurements do easily demonstrate the modelling.


Let us look at the Tweeter's modelling. We want to use low order and non-reactive Hi-Pass filter. But we also need to suppress the fundamental 500Hz resonance. The XT25 tweeter does not use ferro-fluid damping in the voice coil gap. Many prefer that, but it means that the crossover must suppress the resonance in order to get low distortion. Tweeters, as a general rule, do not like amplitude, they are happy with velocity. In a first order filter the series element is a capacitor which has a rising reactance (in Ohms) as we descend in frequency. Think about that, if the crossover is 3-4Khz and a 6.8uF cap has a reactance around 7 Ohm, then by the time we get to 500 Hertz it will have risen to 47 Ohm. This will now appear in series with the DC resistance of the voice coil and erode the Qe (electrical Q) so badly that only Qm (mechanical Q) is now controlling the tweeter's amplitude at 500 Hertz. The result is a violent amplitude reaction at the Tweeter's resonance with little to control it and a large increase in audible distortion.

So we need to dampen that resonance, effectively try to short this out or very close to it. That would require high order and even order has an advantage over odd order. The advantage lies in the fact that a choke ends up in parallel with the voice coil in even order filters - a good thing. But first order is odd order, no parallel choke. The solution is a notch filter at the right frequency and correct Q. Think of Q in this context as the width of the notch filter. Also, a notch filter is also parallel, just like a choke - again a good thing.

Effectively the response above the desirable crossover point 3-4KHz is reasonably flat. The normal response should continue in a flat direction below that. The Diffraction Wedge is here clearly elevating the response in the area we want. It peaks at 1500 Hertz (+6dB approx) and would have continued below that if not for the notch cancellation at 750 Hertz. This notch was expected and is a function of the Diffraction Wedge, but as long as it was well under 1KHz, no harm.

This rise between 3.5KHz and 1500 Hertz is exactly what we want as that is the transition between the drivers handling the midrange and where the Tweeter's response will be gradually rolled in. In other words, it's in the crossover's overlap and where the off axis of the midrange drivers output gradually fails.

The acoustic impedance is altered in such a way that it effectively is increasing the radiation area of the Tweeter's diaphragm - to be closer to matching that of the midranges in the crossover overlap between 1500 Hertz and 3.5Khz.

Tweeter Crossover

The parallel network of 300uF and 0.33mH (keep DC resistance below 0.4R) is the 500 Hertz Notch Filter. This has a Q value that has been adjusted, as we shall see next:


The 500 Hertz Notch can be seen as can the one at 750 Hertz caused by the Diffraction Wedge. One needs to comment on the 2R2 (for Nomex HDS or 2R7 for PPB HDS) as the Notch Filter would normally be right across the voice coil of the Tweeter. So 2R2 is in the wrong position?

Here is a classic example of the power of computer modelling. It turns out that placing 2R2 after the Notch Filter gives better results in two areas.

This example uses 2R7 padding value. In the Pink the 2R7 is before (theoretically correct) the Notch Filter and the Red is (theoretically incorrect) after. Yet the results are clear. The Notch Filter is more effective in the after example. The Pink line would also indicate that the series capacitor would need to be larger in value (added expense) which would worsen the performance of the Notch Filter further. The Red gives us the best result all round. It does have a slight downside that it gives a lower Z and negative phase angle in the crossover region. We shall revisit that topic later.

Bass (Lower Two)

The bottom two drivers are in series but rolled off gradually using a single choke. The top two drivers are also in series but not rolled off as such. Yes, there is a choke but the parallel resistor prevents it becoming a proper low pass filter, so the ultimate roll of is that of the driver itself.

The four drivers work as a Line Source at low frequencies and gradually becomes a Point Source (with the Tweeter) as we move into the mid and high frequencies. It is the following crossover (sans the Tweeter crossover already shown above) that makes this possible.

This is the raw response of the bottom two bass drivers:

The single 9mH choke gives us the following response:

The peak @ 150 Hertz should be ignored somewhat, but the choke is actually less than first order. No attempt to compensate for the inductance in the voice coils. The dip at 2KHz is caused by the difference in distance as shown in the very first diagram in this chapter. At one metre on axis, the top driver is 1095mm and bottom driver is 1175mm. The difference is 80mm which happens to be half the wavelength at 2KHz, hence the cancellation at that frequency. But do people listen at one metre? Not really. Look next:

That's better. This is the two metre measurement and that raises cancellation to almost 4KHz and in most cases it will be 5KHz or higher. We can now see the shape the choke imparts.

Next the MidBass that is fed by a somewhat more complex crossover (it is actually not a crossover as it is a contour network - the ultimate lo-pass function is missing).

Here are the two raw response before crossover components applied. We see that there is gradual diffraction loss starting about 700 Hertz and below, the peak at 150 Hertz tends to hide it, but it is definitely there.

Now we have our crossover (contour network) in place. We have not compensated for the diffraction loss, look closely and it will become apparent. The bottom two bass only drivers will easily compensate for that. This is important as it will help keep the overall sensitivity (and efficiency) high.

Look at the slope at 10 KHz, it is the same. The two drivers are rolling off at their natural rate. The parallel choke and resistor in conjunction with LCR parallel network eliminates the 4KHz peak. This peak is not a cone resonance (waterfall plots shown elsewhere proves that) but seems to be a result of the concave dust-cap, a kind of diffraction effect. The LCR network not only smoothes it out but also corrects the acoustic phase anomaly caused by the peak. This was a minor revelation of it own. Almost major, actually.

The combined response:

Nice! I could not have hoped for much better than that. By combining the drivers the diffraction loss has disappeared and leaving sensitivity up near 90dB while retaining 8 Ohm system impedance. Keep in mind that the basic single driver is around 88dB before typical 4dB compensation loss. So we have gained 2dB above that plus the 4dB that would normally needed to be expended, hence 6dB gain. Yes, other speaker system do the same but they cheat. They gain is 6dB by paralleling  8 Ohm drivers. That too gets 6dB, but system impedance is now 4 Ohm and the real gain is only 3dB (the extra 3dBis caused by doubling the current). But we have gained a genuine 6dB because we have kept system impedance high.

Now it has to be admitted that the last graph was due to a lot of hard work, but not really all that hard as we could constantly change and shift values till we got the best results, which we have just presented on a plate here. Again, this is the power of computer modelling.

Combined Total Response

Let us put it all together, all five drivers:

Almost classic first order (almost sub order) but with interesting features: The Tweeter goes from first order to almost fifth order at around 1500 Hertz to 500 Hertz. Aside from the 150 Hertz (please ignore it as a measurement quirk only) the room boost of the 2Pi response shows that we only need 5dB boundary boost to have flat response down to 30 Hertz and -3dB near 25 Hertz. We have easily achieved our in-room target of 25Hz-20Khz frequency response.

Here is our summed response:


We have only covered "Project A" which was On Axis and at One Metre On Axis. Let me assure you that all other three, B-C-D, check out OK. Here is Project B - the Off Axis at One Metre:

Other than some energy loss at 6-7Khz, the overall slope is acceptable. Some, like Michael Lenehan, feels that a speaker should measure this way. Also keep in mind, this is 25 Off Axis, the preferred listening angle is 10-15. But this graph shows that we have a wide and reasonable flat power response into the room.

Let us over-lay the last two graphs:

Let us magnify that graph from 5dB/division to 3dB/division:

We can see that the summing of the drivers are near perfect. Drawing the Tweeter's output Orange makes this clearer to see. Look in the transition between 1200 Hertz and 8KHz - at no point is the any driver's output subtracted from the other, neither does any single driver exceed the summed output at any frequency. Small peaks and troughs add up in the summed response throughout the transition.

This result is what we would want from a Point Source and we would also expect this to hold up in the Off Axis response:

Driver integration, a paramount issue, and what we see indicates what we and others have heard, it is in the top drawer performance wise.

Not Yet The Complete Story

We have only really looked at one side of the story. The other is the electrical domain, by which we mean impedance and phase angle. As was mentioned in the chapter dealing with speaker design issues, where we have a frequency where the Z (which is the impedance) and the phase angle goes significantly negative, this creates additional demands on the amplifier.

We will plot three-in-one:

The plot is limited to two decades for clarity. Please note the numbers in the margins as they will tell you what the graphs are doing. The Red is the amplitude (frequency) response. The Blue is the Z and the thin Pink line is the Phase angle.

Clearly the minimum Z is at 5-6KHz and it's 4.3 Ohm. The minimum Phase angle is at 1900 Hertz and minus 50. So it is the latter that is of concern. Yet at that frequency  the Z is nearly 9 Ohm. This helps a lot.

But let us not just be satisfied there, we need to know what is the source of the large negative phase angle at 1900 Hertz. Let us plot the four larger drivers:

I did plot also beneath 100 Hertz and can tell you that the second greatest negative phase angle is at 95 Hertz and minus 40. Yet the Z is a whopping 17 Ohms here. So it is still 1900 Hertz that we want to know a bit more about. This time we had taken the Tweeter out and we can see that the Phase angle is positive from 190 Hertz up. This makes the load inductive rather than capacitive. At 1900 Hertz we have a Z of 20 Ohm and the Phase is plus 15.

So it must be the Tweeter, let us take a look:

Sure enough, there it is. Since we can largely discount the Bass and MiBass drivers as having a rather benign load, then we can examine the Tweeter in isolation. I don't know about you, but I have looked at a lot of Tweeter voice coils over the years. They are typically 25mm in diameter (one inch types) and not heavy gauge wire as you don't want a lot of mass. It only takes a few hard watts to damage them. Clearly Tweeters do not have the ability to get amplifiers into trouble. The amplifier will win every time!

OK, what does our graph reveal? The large negative Phase angle is the result of a first order filter with a single large filter cap. The Notch Filter centred on 500 Hertz is also adding to that, but not by a huge margin. But at 1900 Hertz the Tweeter's Z is 10 Ohm and at the same time is 10dB down in the response (relative to 90dB). The Blue line (Z) is rising steeply at 1900 Hertz as the increasing reactance of the capacitor is offsetting its increasing capacitive effect.

On a whole I am not unhappy at this when the picture is seen in its entirety. At 1900 Hertz the primary transducer is the two top MidBass drivers and they are happily in benign load mode. The Tweeter's contribution at 1900 Hertz is unlikely to stress the amplifier. It's not a bad trade-off.

Concluding Remarks

We have covered quite a bit of territory but by any means have not exhausted this topic. I hope it has given some insight into the workings of speaker design. The Elsinore Project has been an ambitious design combining a Line Source in the lower frequencies and then gradually becoming a Point Source at mid and higher frequencies. It also incorporates a method where the acoustic impedance of the Tweeter is enhanced in the crossover region for a smoother and more gradual transition, more gradual than the usual  commercial products so far.

What is important here is that we can model this so accurately - it is really worth the effort to master the tools that are now available, and at a reasonable cost. It is how you use these tools that matter. An apprentice may have the best tools you can buy, but would you not rather have a master than an apprentice? The tools are important (try to hammer a nail in without a hammer) but the wielder of the tool is what matters.

We are very much in favour of this minimal approach. Once understood it is also the easiest to learn and master. So if you have the opportunity, go for it!


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

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

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


Send mail to joeras@vacuumstate.com with questions or comments about this web site.
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?