The Loudspeaker Crossover Part II: Capacitor & Inductor Issues
Capacitors imperfections
Now let's discuss the capacitor. (For those of you who want to read more detail on the performance issues with real world capacitors, there is an excellent treatment of the subject in Wikipedia @ http://en.wikipedia.org/wiki/Types_of_capacitor).
There are many non ideal behaviors that capacitors show, but perhaps the worst is dielectric absorption. This is a fancy name for capacitor memory. The dielectric is the material which insulates the two electrically conductive rolled plates in contact with the capacitor terminals. This dielectric material is how we specify the capacitor type, e.g., mylar, polypropylene, electrolytic, ceramic, etc. With Dielectric Absorption (DA) even after the initial voltage gets removed from the capacitor terminals by shorting out the capacitor, the capacitor returns to its prior state of charge without any signal being supplied. The energy which returns comes from the electrical insulating film, or dielectric, in which it was stored. Problem is, the dielectric is not supposed to store a charge. Use of polystyrene, polypropylene and Teflon as dielectrics will keep this effect to a minimum. This effect (DA) is also known as dielectric absorption hysteresis. Hysteresis is the storage of energy in a medium. It is what makes our permanent magnets work, causes speakers to drift off center position, and what make a magnetic cored inductor distort even without saturating.
A 27 ufd polypropylene and two 22 ufd non polar electrolytic capacitors
In the photograph above are three capacitors. The two smallest are both 22 ufd, 5% tolerance and 100 Volts ratings. The blue one in the center is about twice as large (volume not length) as the small black one. You can see the relative size of the 27 ufd Solen 400 Volt Polypropylene capacitor at the top of the photo. Which one of these three do you think will handle the most power? Which will handle the least? If you want a good seat of the pants approach for determining capacitor quality, here is a clue. For a given capacitance, bigger is almost always better.
The Q or quality factor (Also known as Dissipation Factor or DF) of a capacitor is a measure of its losses of signal due to leakage and Equivalent Series Resistance (ESR for short). The HIGHER the Q of the capacitor, the less losses it will impose on the signal. Secondary to the signal loss, is that high DF capacitors will create more heat while they are passing the electrical signal. An ideal capacitor will not dissipate or absorb any electrical energy. A real capacitor will, and the resulting heat it generates, will likely mean the capacitors ESR will increase, meaning it will be easier to generate more heat and more loss. This is a little bit like the situation with a transistor getting hot, and increasing its native gain, which makes it get even hotter. With transistors this is known as thermal runaway. In short, the effect from the heat exacerbates itself, like positive feedback in a microphone feeding a loudspeaker.
Some of us will always prefer to "Roll our Own"
In a loudspeaker, the heat which increases the voice coil resistance means that the voice coil draws less power from the voltage amp as the voice coil gets hotter. (Heat in this instance acts like a compressor). With a capacitor getting hot, it starts to dissipate even more power, not less. While heat tends to make the voice coil self limiting, it makes semiconductors and capacitors likely to run away with an accelerating problem. While this effect (DF) is measurable in film dielectric capacitors, like mylar and polypropylene, it is not likely to be large enough to be audible. Dissipation Factor (DF) IS a serious issue with electrolytic capacitors. My very first consulting job in 1983 was fixing a crossover for a DJ in New Hampshire. When I opened up his speaker, I found his electrolytic capacitors had gotten SO HOT they literally blew up. All that was left of the electrolytic capacitors used was the plastic covering over the metal capacitor cases. The parts failed and exploded! (In the DJ business, it is often about how loud you are more than how good you sound).
When you are comparing electrolytic capacitors, and you notice some of these parts are much smaller than others which seem to bear the same specifications, it means you have left out one very important specification, that of DF (Dissipation Factor). This is often a good measure of the life of the part, along with its Voltage and temperature rating. This imperfection is THE compromise made with capacitors in order to keep both the size and the cost low. The initial cost that is. If it blows up in your crossover, it may not have been worth saving the initial $2 you saved at retail. Since this is something hidden inside the speaker box, the manufacturer often believes the buyer ignorant of this, so they elect to pocket the savings, hoping the cheap parts used will outlive the life of the warranty.
For a sense of scale, a flip phone, 18 ufd electrolytic (green) and 18 ufd Mylar (white)
Like the resistor, the capacitor can also be inductive at a high enough frequency. This ill effect is known as ESL (Equivalent Series Inductance). (We use the letter L to designate an inductor in a circuit diagram). In case you have wondered why Choke, Inductor and Coil is represented in electronic circuits by the letter "L" it is not solely because "C" was already taken by the capacitor.
For some background on this go to: http://en.wikipedia.org/wiki/Lenz's_law
In the world of the crossover, ESL is not likely an audible phenomenon, given the high inherent inductance of most loudspeakers. Audiophiles will likely want to argue with me on this point, so let me deflect this by saying when I discuss audibility I do not include the most sensitive audiophiles in the discussion. Some audiophiles claim hearing abilities rivaling that of bats and sonar equipment. That said, if measured you will find the typical tweeter has 100 times or more inductance than the most inductive capacitor likely to be in series with it. If one is using a very large capacitor, such as a 200 ufd electrolytic, then it may be helpful to bypass it (parallel) with a 0.1 - 0.5 ufd film capacitor to effectively eliminate the ESL. Unlike DF or DA, ESL can be eliminated by a lower value capacitor being used in parallel.
Inductors - The Most expensive & Most problematic Crossover Element
Let's consider the subject of chokes. Once again I am inclined to thank collectively the authors of Wikipedia for an excellent treatment of Inductance, and its close relatives, EMF, magnetic flux, and magnetism. There is enough physical science behind an inductor to write not just one article but several large textbooks, and many scientific journal articles.
For an excellent general treatment and links enough to keep the scientifically curious busy for days: http://en.wikipedia.org/wiki/Inductor This page shows no less than (6) different formula for calculating inductance of an air core choke. (So try not to go nuts....)
The primary figure of merit for a crossover coil is its Quality factor (or Q) for short. The quality factor of a coil is determined by:
Where
W(Omega) = 2pi*Frequency
L = Inductance in Henries
R = Resistance in Ohms
Ignoring all else but the resistance of the choke we can see as this figure goes to zero, the Quality factor (Q) approaches infinity. We can also see from this, that a choke of 1 millihenry inductance having a resistance of 0.5 ohms, has the same quality factor of a choke of 2 millihenries inductance having a resistance of 1.0 ohms. This should make it obvious to those who understand that as the crossover frequency goes lower, the size of, cost of, and importance of the quality factor (Q) of the inductor becomes more and more important. Two ohms in series with a four ohm woofer, is still a bigger problem than one ohms will be with regard to losses. This is one important reason why manufacturers sometimes shy away from systems having very low crossover points. Even when it is better for performance, it is often so costly to do it right, that a higher crossover point gets chosen for budgetary reasons.
2.0 mH air core Jantzen from Parts Express = $11.00 each = 0.80 ohms DCR
2.0 mH iron core Erse from Parts Express = $ 7.49 each = 0.26 ohms DCR
On the face of it, the magnetic core choke seems to be a better deal.
A laminated Steel Core Choke
Inductors are the biggest attention getters in the passive crossover and for good reason. They are usually the largest and most expensive parts used, and they are present in sizes and masses that have few real analogs in the electronic world except for transformers in power supplies or charging coils used in magnet chargers. Inductors are subject to losses much more so than capacitors. While one can buy a high quality mylar or polypropylene capacitor today for a few dollars, a very high quality large value air core choke is still many times more expensive than that high quality capacitor.
Like electronic components on a PCB, sometimes the inductors are not just inductors, sometimes they are transformers as well. (Just like sometimes loudspeaker voice coils are inductors when they were trying to be simple resistors). For those of you familiar with the construction of transformers, you will remember they are two separate electrical windings both put on a common magnetic core which is intended to link them together by electromagnetic field coupling, also sometimes called inductive coupling.
Let’s take a look at the following circuit:
An inexpensive LCR meter will Define the deficiencies of your parts
Let’s say we used two chokes, both 3 mH and both randomly placed on the PCB. Here in my lab on the prototyping board, they look like this:
If we curve the HP and LP function of this network, we find the following frequency responses:
Frequency Response of System with Separated Chokes
We have our expected High Pass and Low Pass function, but we might notice there is more loss in the LP than the HP filter. Of course, we say, the inductor is in series with the resistor load in the LP but in parallel on the HP circuit. That results in a significant series resistance being placed between the amplifier and the load, in this case a 5.6 ohm resistor. Now, lets’ move the inductors so that they are physically on top of one another, (see photo below) stacked so they share the same diameter and run the test again.
HP and LP Chokes Stacked so they inductively couple
Change in HP response due to stacking the HP and LP chokes
Looking at the green and red HP curves, we might notice two things here. First, we have an increasingly divergent stop-band on the HP filter section, and second, we have less rejection (below 400 Hz). Why? Because the close proximity of the two inductors means they are inductively coupled so we are getting crosstalk. Because the signal is coupled between the two inductors, the series LP choke, and the parallel HP choke, we get a lessening of the out of band signal rejection of the HP section. Two conductors are inductively coupled when they are configured such that change in current through one wire induces a voltage across the other wire. By placing one inductor on top of the other, I am inducing currents to flow in the HP choke because of the current flowing through the LP choke. It is for this reason that you will often find crossover chokes places at right angles to one another as pictured below when laid out on a PCB. This orientation eliminates most of the inductive coupling that would occur inadvertently.
A 5.6 mH magnetic core and a 3.6 mH air-core choke side by side
In the photo above we have two different kinds of Inductors. Magnetic and Air core. The magnetic core (left) is 5.6 mH and has a DCR of 0.28 ohms. It is wound from 15 AWG copper wire. The 3.0 mH air core choke, wound from 16 AWG copper wire has a DCR of 0.75 ohms, or three times the resistance and about 64% of the inductance. This means the loss in the Air core is about 4.66 times as great as the iron core choke. In order to both minimize the inductors resistance and cost, vendors have wind chokes on magnetic cores. There are different types of magnetic core materials used, depending on the frequency range the choke is to be used in. The beauty of using a magnetic core, is the huge savings in copper wire for a given inductance. (If I say laminated steel or ferrite or powdered iron, someone will feel compelled to explain to me the difference, and why one is superior to the other, so I shall simply differentiate inductors by saying magnetic or air core.) Because the magnetic core increases the permeability of the inductor, confining the magnetic field more closely and with greater intensity; you reach a given inductance with fewer turns of wire, allowing you to make a part which, for a given size, is going to have a much lower DCR than its air core counterpart. This means you will lose less power in your series LP chokes. It is this reason (plus cost) that we use magnetic cores in inductors.
On the face of it, the magnetic core choke seems to be a better deal all the way around. So, why then with all these advantages would anybody use anything but Magnetic core chokes? There are two reasons. Saturation, (an effect of running out of permeability by the ferrous core) and hysteresis, the storage of energy, which is present with all magnetic materials. Which problem is worse for the crossover designer; loss of signal due to higher resistance, or the nonlinearity of the magnetic core choke? This depends in large part upon the magnitude of the difference. This is why small value chokes are almost always air core, while very large value chokes are almost always magnetic core. I dislike taking sides in such debates when both approaches have distinct advantages. Personally, I can easily hear the distortion made by iron and steel core chokes, and would rather live with the higher cost and higher (but relatively constant) resistive losses in the air core choke than hear the distortion in a magnetic core choke. Unfortunately, at very high inductance values, air core chokes quickly become impractical because of their weight, size and cost.
Let's take a look at the following circuit, a simple first order low pass filter attached to some lab gear.
The Sine wave symbol indicates the power amp, in this case a bridged "3000 watt" power amplifier, and the V is the voltmeter, a Fluke model 45. The 5.6 mH choke is shown here as air core, but both air and magnetic core chokes were used for this experiment. Clio is a popular hardware/software system designed specifically for measuring audio. The input to the Clio box is put across a small 1 ohm resistor, placed between a pair of 40 ohm resistors so as not to load the bridged power amp, or cause an input voltage overload to the very expensive Clio box, which might cause the Clio to smoke, and me to lose my day job.
The point of this circuit is to see if I could measure distortion in the resistor load, and identify that distortion as originating from the changing impedance of the magnetic core choke. The theory is, if the core permeance is changing as it nears saturation, then the impedance of the choke will also change. Since an AC waveform varies its magnitude with time, the amount of saturation that occurs will be greater at the peak than elsewhere in the waveform. If that is true, this will generate a distortion in the voltage waveform and therefore in the resistor load, as the current flowing will not be faithful to the original input voltage. As the AC waveform varies, the current should follow it. Since the AC waveform varies its amplitude with time, even with a relatively invariant AC signal like a pure tone, how bad would it be if the signal had a crest factor of 20 db, not uncommon in music, instead of the relatively modest 3 db crest factor of a pure tone? Through the entirety of the AC waveform, the current will only be proportional to the voltage if the impedance does not vary (and like 99% of all amps, the power amplifier is a voltage amp, not a current amplifier).
I wasn't able to post my series links because my post count is only one since I just joined. Too bad. I've got better things to do than be malicious. Let me know and I'll email them to you if you'd like.
Quite frankly with my latest project the crossover sounded great first try. After experimenting with parallel designs for decades, I find the series much easier to implement and test, with only four components for a three-way and two for a two-way. I've even mixed Zeta .5 and Zeta .7 with good results. I personally shy away from Zeta 1 or lower for the same reason as a parallel slow slope, too much overlap, and most drivers don't have that wide a response to handle it. All my testing is by ear with difficult program material, voice, piano, instrumental combos and percussion, mainly classical and jazz. I just forge ahead right or wrong. It all started when I inherited a pair of Dahlquist DQ-10s. One look at that crossover schematic convinced me that almost anything goes, and they sound great. It works for me, and after all, serendipity rules. Shed those prejudices! Hope this is all helpful.
highfigh;723200
Do you have any links to info on these Zeta crossovers?
Here is a circuit of a series crossover.
Series crossovers [speakerbuilder.net] present a lot of formidable problems, as both sections of the crossover interact.
My rear backs, use series crossover in the passive part of the crossover. These speakers started in 1984, but the crossover did not get to its final form until 1994!
They are very difficult to perfect.
This was a good article, and reiterates points I have made many times over. The sad fact is most commercial designs do use miserable chokes with iron cores and wire of too thin a gauge, and electrolytic caps abound. A speaker is then severely compromised right out of the stating gate then, and I mean severely compromised. A speaker with decent components in the crossover will not be cheap. This leaves money on the table, for active speakers, which I believe with modern production methods, could give much better performance per dollar.
I really believe it is the receiver obsession that is so limiting. If you think about it, it is absurd that a pre pro generally cost more than a receiver. The only reason is production numbers. Burying the receiver is long, long over due now.
audioantique;723194
Paul,
Very informative and straight to the point, thanks. I suggest that a way to bypass the inductor series losses is to build a series crossover, where there are no components in series with the drivers. One exception to this would be a padding network for a tweeter, but that is only series and parallel resistors. I realize that this solution isn't for everyone, but I've had great success lately with Zeta .7 quasi-second order crossovers. A 3-way is only two caps and two chokes all parallel to the drivers, and the, for me, essential Zobel for the midrange is also parallel to the driver. Of course just like with a parallel crossover, it's essential to use drivers in their usable range and not push their envelopes. I'm not a series crossover zealot, but extensive listening seems to validate my efforts, at least to my ears.
Good luck, all.
Do you have any links to info on these Zeta crossovers?
Very informative and straight to the point, thanks. I suggest that a way to bypass the inductor series losses is to build a series crossover, where there are no components in series with the drivers. One exception to this would be a padding network for a tweeter, but that is only series and parallel resistors. I realize that this solution isn't for everyone, but I've had great success lately with Zeta .7 quasi-second order crossovers. A 3-way is only two caps and two chokes all parallel to the drivers, and the, for me, essential Zobel for the midrange is also parallel to the driver. Of course just like with a parallel crossover, it's essential to use drivers in their usable range and not push their envelopes. I'm not a series crossover zealot, but extensive listening seems to validate my efforts, at least to my ears.
Good luck, all.