Thursday, July 3, 2014

Crossover Networks, Zobels, and Life Lessons

With my newest adventure with the ongoing Bozak restoration project, I had a terrible time taming the interaction between drivers and I questioned the wisdom behind the manufacturer's choice of a first-order (-6dB/octave) crossover network. It is true that the technology of the time (1958) is not state-of-the-art but there are a lot of design considerations then that still hold true today.

For example, Bozak's use of a light-weight cones provides better transient response than one of greater mass. Newton's second law of physics reads "Force is equal to Mass times Acceleration (F=MA)" meaning that if you increase the mass, it requires more force to get the same amount of acceleration. For loudspeakers this is still true today and it is why light-weight ribbon technologies are still superior sounding (cleaner or crisper) when compared to heavier cone or dome technologies.

One of My Hero's: Sir Isaac Newton

But how did I decide this? Did I just want to "give it a go" or was there more? Sir Isaac himself was quoted as saying (paraphrased here) "There is a huge difference between believing (or suspecting) something and knowing something to be true" and his efforts helped mankind better grasp its understanding of our complex world. Reading about my situation and what I did may help you know whether or not to make changes in your speakers. If nothing else, it will help you better understand why any manufacturer chooses the crossover network design that they do. So let's see what my issues were, what I did, and the reasoning behind my choices.

Remember, when changing something, you can always put it back to the way it was so don't be too worried about making a mistake. Just take notes, take a lot of before-after pictures, and remember what you did. Make one change at a time and who knows? Maybe you can make a silk purse out of a sow's ear! So with that, let's begin. This is a very simple thing you can do to improve the sound of your own speakers.

The RTA measurement below is of my Bozak B-209A midrange driver in its enclosure with no crossover network attached. This tell you a lot about this particular driver, especially how aggressive it is above the manufacturer's chosen crossover frequency of 2.4KHz. Remember to disregard the data below 300Hz since my cell phone (an AT&T Samsung Galaxy S-III) incorporates a built-in non-defeatable bandwidth limiter to make voice recognition easier. It is reasonably accurate above 300Hz and you can observe the relative changes rather than make absolute conclusions.

Bozak B-209A with No Network

This is a 6.5" conventional dynamic driver with an aluminum cone and an aluminum dome functioning as the central dust cap. This means that there is a certain amount of acoustic energy contributed by both the cone and the dust cap each acting independently of the other. This is also why the driver's sound pressure extends uniformly well above the manufacturer's 2.4KHz crossover point (most of the higher-frequency energy is emitted by the metallic dome). However, it is wise not to push any driver to operate at its limits (operating at a range well inside its capability). To do this, an engineer typically chooses a crossover point generally an octave below that upper limit and an octave above that lower limit.

Sounds pretty simple, right? Well, there are other issues at play that interfere with a "perfect" world. You see, when a crossover network begins to attenuate (roll off) the signal to an attached driver, the driver may produce non-linear sound pressure levels for any number of reasons. Lower-order attenuation slopes may be inadequate to prevent any non-linearity from interfering with the operation of other drivers.

For example, the Bozak B-209A has a good characteristic frequency response to about 7KHz, a highly desirable property. However, when connecting the driver to the manufacturer's designed first-order network (a 2.4KHz crossover frequency), the driver inappropriately colors the sound of the tweeter in its 4-7KHz operating region. Below is a stand-alone measurement of this driver connected to this manufacturer's designed first-order network.

B-209A with -6dB/octave Attenuation above 2.4KHz

What the heck happened? This looks terrible and indeed it sounds awful. As you can see, there is a significant change in the uniformity of the driver's sound pressure as compared to when it is not connected to any crossover network. Most notable is the rising response of the driver (white dots) above the network's predicted attenuation level (red line). Although somewhat attenuated by the crossover network, the driver still contributes a CONSIDERABLE amount of acoustic energy in a region in which it is not desired. This undesired contribution will color the sound of the other driver (here the tweeter) causing non-uniformity in sound pressure and phase distortions all over the map. Yuck! No wonder it sounds bad.

To understand why this happens, we must look at what other electro-mechanical influences could disrupt the behavior of the crossover network itself. After all, it should have worked, right? The network should have attenuated the acoustic output of the driver above the crossover point as predicted. What changed that defeated the networks ability to control the driver?

Crossover networks are designed to operate at a certain impedance, here 8 ohms. However, any dynamic driver has a rising impedance which basically pulls the rug out from under the crossover network and eliminates its ability to attenuate sonic energy from the driver. The Bozak B-209A driver has a measured impedance of 8.3 ohms at 2.4KHz, 14 ohms at 8KHz, and 22 ohms at 16KHz, a value almost three times the value anticipated by the crossover network design. Could this rising impedance be the culprit? Yes it is!

So the first issue to be addressed is the rising impedance of this driver. A Bourcherot cell (commonly called a Zobel network) stabilizes the rising resistance of the driver. In reality, a Zobel network is another first-order network that introduces a mirrored resistance value to that of the rising impedance thereby normalizing the resistance observed by the crossover network (i.e., it stabilizes the rising impedance). This allows the crossover network to properly operate at its anticipated 8 ohm value. Below is a measurement of this same driver with a Zobel network in place.

B-209A with Zobel and -12dB/octave Attenuation above 2.4KHz

Adding the Zobel network helps to resolve this tweeter-interaction issue but the sound level just before the crossover point also suffers. While the Zobel is a very good idea, its influence can adversely impact the linearity of sound pressure desired from a driver. In other words, a Zobel is not a magic bullet but it can help the crossover network better control the driver's behavior. Changing the Zobel values can marginally correct for this non-linearity in the desired operating band at the expense of increasing the sound pressure above the crossover point. The only way to have it both ways (uniformity without coloring the tweeter's sound) is to move to a higher-order (steeper sloped) crossover network design (i.e., -12dB/octave or greater).

However, making the crossover network slopes steeper creates other issues such as increased cost for components and additional phase distortion at the crossover frequency (remember, in audio and in life you rarely if ever get anything for nothing). The only other option is to change the driver, something I did not want to do for this project. The logical choice to control better control this driver is to abandon the manufacturer's designed first-order network.

Finally we have reached the logical steps I followed in making the decision to change the crossover network design from manufacturer's choice of a first-order design. Although my gut originally told me something was wrong, like Newton I needed to prove the truth to myself rather than just follow my hunch. Although my hunch was indeed correct (a plus in the column for trusting your gut) objectively testing my intuition proved the truth to me (a plus in the column for trusting your mind). Both my intuition and my logic were necessary in discovering the truth for without either the truth would not have been discovered.

WARNING: Stepping on my soap box now. This is a micro life lesson. And so it is in other walks of life where opinions, ideas, and convictions can cloud your understanding of the truth. These are sometimes called biases and have absolutely no place in science - or in life if what you desire is your highest good. Finding value and a balance in both is where solutions lie. Stepping off my soap box again.

In my case, moving to a second-order (-12dB/octave) network significantly improved the operation of the driver but more than doubled the cost of the components in the crossover network. Even though the steeper slope helped in this design, a Zobel network was still required to control the driver's rising resistance.

BTW, with a second-order network, the phase of the sound pressure at the crossover frequency also changes by 180 degrees. This means that the piston movement of the B-209A would appear to be moving backwards as the tweeter movement was forwards. To resolve this is a simple matter of swapping the polarity of the driver (put the plus wire on the minus terminal). Below is the final measurement of this driver with a well designed second-order Bessel network including a properly engineered Zobel.

RTA Measurement of the Final Design

Whoa! Where did that nasty 1KHz peak come from? As I mentioned earlier, you never get anything for nothing and the peak is one of those unexpected "gifts" (and probably why Bozak never used a second-order network). Mathematically predicting behavior and measuring reality is often two very different things as demonstrated here. There is an interaction between the higher-order network and a natural resonance and so yet another level of tuning is needed. Called a parallel notch filter, a few components in series with the driver can help tame such annoyances - at the expense of additional phase distortion. However, when such a peak persists, there is little choice to the matter.

The good news is that with the introduction of a properly designed notch filter (one involving more iteration), a driver's irregular behavior can be tempered. Below is the result of all modifications to the Bozak B-209A driver as observed from the measurement of the entire system.

System RTA Measurement 7-3-14

Although not ruler flat, the performance is vastly improved despite the remaining anomalies. Instruments have that natural timbre reminding you that you are now one step closer to headphones at the mixing console.


What I wanted to demonstrate to you was how the behavior of drivers changes when connecting them to passive crossover networks. Mathematically calculating a Zobel's value and then adjusting that value to make it work properly is an iterative operation, one requiring patience on your part to get it right. Remember, after making changes and reaffirming the chosen values, ALWAYS confirm measurements with prolonged listening tests. I cannot tell you how many times I could make the RTA measurement look ruler flat and appear visually fantastic but have the system sound absolutely terrible. Needless to say I backed out of these modification as fast as dropping a hot potato (yikes!) while learning yet another valuable life lesson.

The toughest challenge you will face in designing or redesigning your speakers is to be brutally honest with yourself. Ask yourself, "Is what you just did make your system sound better or worse?" Then, answer this question both objectively (listening) and subjectively (measuring). Just because something is predicted to work will it do so. Engage both sides of your brain and listen to your music with your ears, and not just your eyes. Get your ego out of the way and listen with your heart.

There are two quotes I find appropriate for this life lesson:

Not everything that counts can be counted, and not everything that can be counted counts.
Sign in the office of Albert Einstein

Not all that matters can be measured; not all that can be measured matters.
Elliot Eisner, Artist, Author

From these two quotes, it appears that the left and right brains can come to an agreement. I challenge you to find yours.

Related ArticlesSee all entries about speaker enclosures in Part 1Part 2Part 3, and Part 4. Also, a related article on the effects of crossover network components on driver performance.

Yours for higher fidelity,
Philip Rastocny

I do not use ads in this blog to help support my efforts. If you like what you are reading, please remember to reciprocate, My newest title is called Where, oh Where did the Star of Bethlehem Go? It’s an astronomer’s look at what this celestial object may have been, who the "Wise Men" were, and where they came from. Written in an investigative journalism style, it targets one star that has never been considered before and builds a solid case for its candidacy.

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