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The Renegade Tweeter Theory

 

 

THE IDEAL TWEETER IS AN ACOUSTIC INVERTER

 

 

 Normally, you present your case and then get to the punch line. But to set the scene I am going to do it the other way, so here it is:

The Tweeter's acoustic phase is the opposite to the Tweeter's electrical phase. There is a precise 180 relationship.

The faster the Tweeter's rise time, the greater this scenario as the perfect Tweeter has an Infinite Rise Time.

A Tweeter with an Infinite Rise Time has all its useful acoustic output inverted.

The controversy here is the clear inference of those three statements is that we need to connect the Tweeter in the electrical negative phase to optimise the acoustic phase. If indeed we want to design linear or minimum phase speakers, especially with a controlled Step Response etc, this ought not to be ignored. Indeed in any design needs at least to be considered.

Reverse the phase to the Tweeter? Exactly. I don't expect you to accept this argument without sufficient proof. Indeed I need to make a good case and I believe I can. It can then be deduced that we need a fundamental change in approach and assumptions.

A Paradigm Shift is required.

Take The Leap


Back To Basis

In Chapter 17 where we described a holistic approach to crossover design, many have noted the out of phase Tweeter connection. They believe I have not optimised the Tweeter's phase, when in fact I believe I have. I received a number of heated emails that pointed to the reversed electrically connected Tweeter in the Elsinore speakers. How could I possibly make the claims I made when it was reversed?

(Edit: Thankfully this article has stemmed the tide)

This Chapter is really an addendum to Chapter 17.

Let us reiterate a few things from that chapter.

Here we have the traditional view of electrical phase. During the Red half of the cycle we have current flowing in one direction and during the negative Blue, the opposite current flows.

But when we come to acoustic phase things are decidedly different:

No movement, no output. So when motion is upwards in the Red zone, then the acoustic phase is positive and vice versa. So the transitional point is not some notional zero point (the zero volt median line as in electrical phase) but at the point where the change in motion takes place. Please keep this in mind as we shall revisit. Note also the not inconsequential shift in time when an acoustic sine wave is looked at in this light.

Because a sine wave only shows what happens at a single discrete frequency, let us now examine some basic characteristics of square waves.

Square waves shares one thing with sine waves, they have a frequency, so many cycles per second. But a perfect square wave encompasses an infinite number of frequencies. We shall attempt to explain.

Here we have a dead flat frequency response of a DUT. This is an acronym for Device Under Test. It can be a loudspeaker, but it would be unlikely to be that flat. More likely to be an amplifier. So what happens if we put a 1KHz square ware through our DUT? Something like this:

Nice and square. Let us now change our frequency response and see what effect this has on our square wave. Let us see what a treble boost does:

Now for our matching square wave:

Whoa! The leading edge has been emphasised.

What about Treble cut:

Now for our matching square wave:

The leading edge has been blunted. Is this not what we would have expected based on the Treble boost?

Now for Bass boost:

Now for our matching square wave:

Now the back end of the square wave is elevated. This should be expected even if not as narrow as the Treble boost (for reasons not needed here). So Treble boost increases the leading edge whereas Bass boost increases the trailing edge.

Now for Bass cut:

Now for our matching square wave:

No surprises here, the trailing edge is suppressed.

Examine the above a bit more and you will see the pattern. But let us sum up by re-showing our original 1KHz square wave and add some pointers:

There is a rule of thumb that I use. If you have a proper square wave with flat top and clear vertical lines, the response is flat from a decade below and a decade above the frequency of the square wave, two decades. Hence flat from 100 Hertz to 10KHz. Therefore the tonal balance would be neutral. Yes, we can look at a square wave and draw certain conclusions from it.

Now we get to the meat of our discussion. From sine wave to square wave and now progressing on to the Step Response.

Unlike a sine wave or a square wave, the Step Response has no frequency. It doesn't cycle up and down but is a single step in one direction, like a staircase with a single step (I know that doesn't make a staircase, but you can also think of it as a street kerb). But there is a similarity with square wave, the front of the step indicates the Treble response, then as the step progresses it goes through the Mids and then the Bass.

Here is what our step response looks like and this is what we will feed through our DUT (remember, Device Under Test):

Some have declared the the Step Response is the single most revealing test that can be applied when the DUT is a loudspeaker system. This includes the late John Dunlavy. It is certainly a most intriguing test. Note that it is the complete system that must be tested and at a position that is representative of the expected listening position.

Again, we must point out the obvious:

 

But we can also examine individual drivers and plot them to see what their exact contribution is. We can also include either the raw driver or include the crossover. So this is a great multi-level tool.

It's The Tweeter Dummy

Oh yeah! It is the Tweeter that is the issue here, so let us get back on track.

Here is the Step Response of the HDS Tweeter in the Elsinore box:

This Step Response of the raw (no crossover) Tweeter shows its attempt to match the infinitely fast rise time of the step. At the top of the rise the step flattens out to (theoretically) infinity. But that flat plateau is the electrical stimuli. But the response picked up by the microphone is the acoustic response.

We have already established that there is no acoustic output unless there is motion, and there is motion, but from this point onwards the phase is reversed.

If you consider what force is at work, it is simply ambient air pressure; the air has been loaded like spring and works in reverse.

In the example shown here the rise time is 0.0425mS (look for the purple box where Clio displays the time difference between the two markers). We can now invert that (1/0.0000425 = 23529) and it represents 23.5KHz.

Now imagine that our Tweeter was virtually perfect in the sense it had infinite rise time to match the stimuli:

Now inverting infinite will give us an infinite frequency, now ALL the Tweeter's acoustic output is in the reverse phase.

Now it would make sense to invert the Tweeter's phase:

Now where does the acoustic impulse really start?

It starts where the Blue dot is the marker. There is little difference from this and to this:

Yes, it starts with the Blue dot (but allowances needs to be made in the final design). But in reality this is not completely true as we don't have infinite rise time. But the above in totality demonstrates the point clearly. In the case of the HDS Tweeter, the frequencies below 20KHz is dominated by an opposite acoustic phase.

The Tweeter's acoustic phase is the opposite to the Tweeter's electrical phase. There is a precise 180 relationship.

The faster the Tweeter's rise time, the greater this scenario. An infinitely fast Tweeter has ALL of its useful acoustic output in the opposite phase.


At this point I will revisit some of the points discussed in Chapter 17. Sorry for the repetition, but Repetition is the Mother of Retention.

As the Tweeter in question will need a Lo-Pass filter (crossover) and also match up with a driver handing over from the Midrange, in our case about 3Khz, let us examine that in some detail.

Here is a 2-Way example, where Blue represents the MidBass and Red is the Tweeter with a deliberate reversed phase. The bottom of the inverted Red peak and hence when in time the Tweeter is going positive,  is made to coincide with the beginning of the slower rise time of the Blue MidBass.

Line Up the Blue dots in time (time alignment). Both the Tweeter (Red) and MidBass (Blue) go positive at the same point in time.

Is is extremely important to observe that there is no output (or very little) from the MidBass during the fast negative inverted rise time of the Tweeter. Effectively the idea is to get this part of the Tweeter's output well out of the way so that the positive outputs of both drivers are in sync. Physical alignment of drivers is required to optimise this.

That this also allows us to sum at the crossover by 100% is now hardly surprising. Here we have a clear visualisation explaining why.

Finally we have the complete system Step Response.

At no point are the drivers working against each other, both in time and amplitude (frequency), they are perfectly synchronised. To the left, the green area, we only have output from the Tweeter. This is the fast rise time of the Tweeter, inverted. It equates to frequencies well into the top octave and higher and is shown by other examples in Chapter 17 to be well away from the crossover. On the right side we have a time coherent picture even though our Renegade Tweeter is connected electrically out of phase and it has no 90 Butterworth error. IF we did connect the Tweeter in phase, then we would have to re-jig everything and except the Butterworth phase error and other attendant problems (did anybody say power response?).

But, because we are still getting the phase right, we are thus able to produce decent square waves at around 1KHz.

This example is actually a measured 700 Hertz

Our system minimum phase response confirms this as well (at 2 Metres):

And so does the actual measured system phase response:

Phase Response at 2 Metres - LF accuracy limited to above 200Hz

I believe a good case has been made here. The advantages of getting the Tweeter phase right are numerous, not all mentioned here. All the benefits are only available by reconsidering the electrical phase reversal as the most practical solution available to the designer. The Tweeter will correct its own acoustic phase.

The above complete system Step Response also confirms all the conclusions drawn in Chapter 17. The fact that the impulses of the Tweeter and MidBass are properly synchronised shows that 100% vector summing (at minus 6dB) is a reality and by extension provides a working solution to the off axis response problems usually caused by MidBass beaming effects, this bodes well for a more consistent Power Response.

Numerous Benefits

The additional benefits are also better power handling, especially the Tweeter, lower distortion, again the Tweeter (use a null filter as used in the Elsinore enhances this further). Lower distortion also from the MidBass driver as its output is 3 dB lower above (and below in the case of the Tweeter) the crossover point. Although less output, the MidBass sums 100% even if considerable beaming is already happening. Less demand on its bandwidth.  There is also less unnecessary current drawn from the amplifier across several octaves, the impedance and load is easier to control as no acoustic power is wasted (as opposed to VC heat, but that is another subject, but VC will still run cooler by some margin). These are but the highlights...

Physical Alignment of Drivers

The above Step Response was based on an MLS type signal equating to 1 Watt. If the step was increased by two to one, this would require 4 Watts. The rise time would also be longer, typically 60uS where it was 42uS for 1 Watt. This means a change from approximately 23.5KHz to 16.5Khz.

This leads to the physical alignment of drivers to be considered. As the time of the Tweeter to reach it maximum in time is dependant on input stimuli, then it's apparent that the relative time alignment changes with input. The above examples show that it is only very high frequencies that are affected. Hence 23.5KHz for 2.83VRMS and 16.5KHz for four times the power.

The relative slow rise time of the Midrange driver works to our advantage here. As the Tweeter output shifts the time relationship, the Midrange driver's output is virtually zero or at least very low. This means a good size time window exists and that ultra-critical alignment of drivers is not... well, so critical. This is so unlike 1st order Butterworth and also helps why the result we get has a much wider usable window (and much more desirable power response), rather than the narrow window one must aim at with Butterworth approach. It makes for a better speaker and an easier job for the designer.

Three-Way Systems

As I have mentioned elsewhere in Chapter 17 the use of Butterworth 1st order below 1KHz is far less problematic as we deal with drivers that are well within their pistonic range. So for a time aligned system, consider using Butterworth 1st order as the lower crossover and the above described approach. Please read Chapter 17 to complete the picture.

Here ends the story of the Renegade Tweeter Theory. Or does it...?

 

A  Paradigm Shift

Being Able To Move On, From One Thought To Another

The above may take several readings in order to digest the complete picture.

 

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


 

 

Send mail to joeras@vacuumstate.com with questions or comments about this web site.
Copyright 2003-10 Joe Rasmussen & JLTi
Last modified: Sunday January 05, 2014

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