Crossover 102 - Electronic Crossovers

By Marty McCann
© 2001

Charterheader

What is an Electronic Crossover?
The electronic crossover is an external electronic signal processor that takes the place of the passive crossover that is in a full range loudspeaker enclosure. In the world of today's high performance sound systems, the electronic crossover minimizes the distortion associated with full range passive crossovers, when the sound reinforcement application includes the complete micing up of the entire backline of stage musical instruments. The Electronic crossover allows for increased performance from the sound system by enabling the loudspeaker system to be run as an active Bi-amped two-way, Tri-amped three-way, or even a four-way (Quad-amped) sound system. The electronic crossover breaks the audio frequency spectrum into two, three, or four discrete bands of frequencies. Each defined bandpass is then actively powered by it's own dedicated power amplifier which then drives a loudspeaker component specifically designed to reproduce this portion of the spectrum. The result is a significant improvement in system performance due the tremendous increase in power amplifier and overall system headroom.

Headroom is defined as simply as possible as space remaining above the signal. It means that the voltage window that the power amplifier provides is not all used up, and there is reserve horsepower remaining above and beyond this nominal or average signal level. (Espacio ariba de senal). A power amplifier is able to produce it's rated output power because there is a positive (+) and negative (-) voltage rail or limit designed into the amplifier. The outgoing signal is said to swing or move between the positive and negative voltage tracks or rails. When either the positive or negative going signal reaches its rail or the limit of its available voltage swing, it is said to clip or stick to the power supplies rail. Power amp clipping is the biggest cause of loudspeaker failure.

Headroom Clipping

Why do I need to Bi-amp?
Full range sound systems quite frankly just do not have enough power amplifier headroom to successfully Mic the drum kit and bass guitar, as well as all of the remaining stage instruments and vocals. There are a couple of reasons for this. First of all individual musical waveforms consist of a fundamental frequency upon which the higher harmonics ride. In other words the highs frequencies are modulated by, or they ride on the fundamental as super-impositions on a composite waveform. The combined waveforms of the individual musical instruments create an even more complex composite electrical signal when mixed together. This very complex composite waveform has an in initial leading edge or transient spike that can be +12 to +20 dB above where the signal levels off at the crest or average of the waveform.

Peakcrest
Complex musical waveform

Also, there is a great deal more power used to reproduce low frequencies than high frequencies. Some people think that this is due to the differences in efficiency between the woofer and compression driver. But, the difference in their sensitivities is narrowed due to the fact that the high frequency driver is more sensitive, and the voltage to it must be attenuated or reduced to match the levels between the two transducers at the crossover point. There are others that think it takes more energy to reproduce the low frequencies, because they know that low frequency acoustical sound waves are very large, and they reason that you must push or shovel more air from the low frequency transducer. Actually it requires more energy for low frequency reproduction because we humans are nearly deaf when it comes to the perception of low frequencies. The threshold of human auditory hearing at 40 Hz is about +44 dB greater than the threshold for 4 kHz. Our ears just aren't flat, and that's a fact. The frequency response of our ears is dynamic also, in that it changes with the level of perception. Even at the loud level of a Rock & Roll performance, the low frequencies require 3 to 10 times (10 to 20 dB) more voltage than the high frequencies. See the Fletcher/Munson equal loudness contour curves below:

Chart

Now because of the very strong demands for power made on a full range system by the low frequency content of the musical program material, when a full range system runs out of headroom, it's the high frequency information that suffers. Since the highs are modulated by the lows, and ride on the lower frequency fundamentals, when clipping occurs, the high frequencies are the first to clip. Therefore the intelligibility of the vocals is the first to go. Also it is the clipping or complete lack of headroom in a full range system that is the biggest reason for high frequency compression driver failure (can you say "toasted diaphragm"). Once the sound system is crossed over electronically, even if the low pass amp clips, the highs can remain clean because they are now being powered by their own dedicated high pass amplifier.

In part one we covered the roll of inductors and capacitors and how they act as low and high pass filters in passive crossovers. In active crossovers, inductors and capacitors can do the same frequency filtering, but in many adjustable electronic crossovers, a circuit called a state variable filter replaces the inductors, which emulate the performance of inductors. It is a combination of the component values of inductors and capacitors, along with the selected values of resistance's that form the circuitry of the frequency filtering networks. The combination of a specific inductor and a specific resistor create something called an RL circuit (low pass), and a specific capacitor and specific resistor are called a RC (high pass). Varying the value of the resistance (R) with a given value of L or C will determine the high or low pass cutoff frequency of the crossover network.

In part one we introduced the concept of various orders of filters (-6 dB/Octave, -12 dB/Octave, -18 dB, -24 dB, etc.). For each filter section (pole) or order, we introduce more resistors, inductors, or capacitors. The most accepted type of circuitry for audio is something called a Butterworth filter network. We have been listening to them for 60+ some years. There have been other possible design classes, but generally they all have their shortcomings. Less than 20 years ago, a Mr. Linkwitz and a Mr. Riley CO-wrote a paper that essentially trashed Butterworth filters and the 3-rd order Butterworth filter in particular. The reason for this has to do with the inherent phase shift of the output signal that we initially mentioned in part one: Crossovers 101. We will expand upon this subject at this time.

In the technology of filter circuitry, for each order of network components, we get -6 dB per octave roll off, and a 90-degree shift in phase. Here is the chart for review:

Filter Order Attenuation per Octave Phase Shift
1st -6 dB 90 Degrees
2nd -12 dB 180
3rd -18 dB 270
4th -24 dB 360
5th -30 dB 450
6th -36 dB 540
7th -42 dB 630
8th -48 dB 720


Odd order filter networks will always introduce a situation where the output of the network is either +/- 90 degrees out of phase with the input signal. For instance the 3-rd order filter will introduce 270 degrees of phase shift, which is still 90 degrees short of 360. If the output of an electrical circuit exhibits a 360-degree change in phase, you are essentially back "In-phase." However the signal does spend a finite amount of time passing through four high or low pass filter circuit networks. This is something called group delay (in my day group delay meant that the band was late). Even though it took a small amount of time to pass through the filter stages, since you ultimately made a 360-degree turn, you are now headed in the same direction; i.e. the output is in-phase with its input.

Even order filter networks will always give you a multiple of either a 180-degree or 360 degree shift in phase. It is accepted practice in professional audio that it is desirable to maintain a unity of phase through out the system, in other words, the output should be in-phase or headed in the same direction as the original input signal. When a 2nd order filter network is introduced, the outputs are 180 degrees out-of-phase. This is not really a problem, because we can switch or reverse either the outputs of the crossover circuit itself, or switch the leads to the loudspeaker itself (but not both), to restore phase unity. If you try reversing the outputs of an odd order crossover filter design, since they are going to introduce a shift in output phase that is some odd number multiple of 90, you are then still dealing with +/- 90 degrees of phase shift.

Even though Linkwitz and Riley were correct in the areas outlined in their paper, we continued to use 3 rd order crossover filter networks (for the most part) throughout the remainder of the 20th century, and into the 21st. The reason is that 2nd order filters do not offer enough protection for the high frequency compression driver, and variable fourth order filter circuitry can be very difficult to accomplish precisely or accurately. In the electronic technology, there are controls called potentiometers that are used as volume or tone controls, as well as to change a crossover filter frequency. Remember we said if you vary the R with a fixed value of L or C, you will change the turnover point or crossover frequency of the filter. To have multiple poles or orders of filter networks, we repeat the value of R, L, & C, in each subsequent filter stage or order. The precision of the filter design depends on the tolerances of these component values.

There is a special type of potentiometer called a ganged control. You can have two, three, or even four variable resistors that are stacked or staged so that you can change the resistance with a common control shaft that simultaneously moves two, three, or four wipers or variable resistor contacts. One of the technological challenges involving variable ganged controls, is the typical tolerances of each potentiometer stage is usually no better than 20%.

As a result of the research done by Linkwitz and Riley, we now have a filter circuit topology that bear their names. Now you will essentially find identical component values in each filter stage of both a Butterworth and a Linkwitz Riley filter network.

However, by definition, a Linkwitz/Riley filter circuit can only be even order, where a Butterworth can be either even or odd. There is also a very important difference in how the turnover frequency or crossover point is defined. Butterworth filter networks are defined by the half power or -3 dB down points in frequency response. Where as the Linkwitz/Riley filters are determined by the -6 dB down points. I'll repeat this for you, Butterworth measure -3 dB down at the crossover frequency, while Linkwitz/Riley are -6 dB at the turnover frequency. This very important fact is often not understood by the typical sound provider. Even though a Butterworth and a Linkwitz/Riley filter set of the same order may share the same crossover point, they are going to use different value components to arrive at the common frequency.

I believe it is now time to discuss the summation of these two filters at the crossover point. First we must define coincident and non-coincident signals. If two different signals are at the same level and are not coincident (or starting from the same exact moment in time), then the most that they can add when summed together is +3 dB. This is also true if they are the same common frequency but exhibit a significant difference in degree of phase angle. If however you have two absolutely coincident signals in both frequency and level, then they will sum to +6 dB when added or mixed together.

Butterworth filters when combined are said to have a smooth power response through the crossover region. Since the crossover frequency is defined as the point at which the spectrum is attenuated or down -3 dB, the actual summation of the transducers is essentially flat when the power is averaged. There is still a little dip around the crossover frequency because the filters are not in phase with each other at this frequency. Now there are some analog electronic crossovers that introduce some signal delay in one or more outputs. However the steps can be quite broad depending on the chosen crossover frequency.

Okay, how do I set up a variable electronic crossover? First of all there is no magic crossover frequency point. The raw frequency response of each transducer or driver must first be examined, to ensure that the intended drivers can indeed effectively reproduce the chosen range of frequencies. The second and most important consideration is to know the actual sensitivities of each of the component drivers in the system. The sensitivity of a loudspeaker is the internationally accepted standard of 1 Watt @ 1 Meter. With one Watt of power sent to the driver, a measurement is made on axis at a distance of one Meter to determine how loud is the sound pressure level (SPL). Once you know the sensitivity of the drivers you can then set the gains of the crossover properly.

Let's say that we have a three-way system, and the low frequency device can handle 500 watts continuous and produce an SPL of 100 dB (1W, 1M) with a frequency response of 45 Hz to 2 kHz (+/- 3 dB). The mid frequency driver can also handle 500 Watts, but it has a sensitivity of 103 dB (1W, 1M) from 70 Hz to 2.5 kHz. The compression driver on a constant directivity high frequency horn can handle 80 Watts continuous, and has a mid-band efficiency of 112 dB from 800 Hz to 3.5 kHz, with -6 dB per octave roll off above 3.5 kHz.

According to the AES (audio engineering society) standard, a loudspeaker that can handle 500 Watts of continuous signal, can handle 1,000 of program material (average music), and 2,000 Watts of peak signal level. Now the tricky qualifier here is that the amplifier must have +3 dB of remaining headroom, above the Peak level. This would require an amplifier of 4,000 Watts. The average uncertified system operator would probably blow this loudspeaker up with a 4,000 Watt amplifier. A 2,000 Watt amplifier with a "soft limiting" circuit, such as DDT, would probably suffice, in the hands of an experienced operator. But, I would probably give an entry-level system operator an amplifier between 600 and 1200 Watts.

For our scenario, I am going to suggest that we have a 2,000 Watt amplifier for the lows, 1200 Watts for the mids, and 350 watts for the highs. Even though the compression driver is only rated at 80 Watts, because of the needed headroom to accommodate the constant directivity horn EQ (nearly +15 dB at 15 kHz), we often use an amplifier rated at 300 watts or more. The horn is padded down or attenuated -12 dB in the octave around 2.5 kHz. For the most part this means the driver would get about 20 watts (10 log 300/20 = -11.76 dB) while producing these mid-band frequencies. So, for headroom reasons, 350 Watts of power is not out of the question. However I would certainly recommend that the chosen amplifier have some sort of "soft limiter", such as the Peavey DDT circuitry. For this example we are going to assume that each amplifier has the same input sensitivity. When you have amplifiers with differences in input sensitivity (how many volts does it take to reach full power), you would have to figure the differences into the gain structure calculations.

A good choice of crossover frequencies for our example active three-way system would be 150 Hz and 2 kHz. Up to a 2/3 of an octave lower for both the Low/Mid crossover and the Mid/High crossover point, would also be within a reasonable range. None of the devices would be driven above nor below their cutoff frequency or -3 dB points. We will assume that our horn has a low frequency cutoff of 800 Hz. When it comes to high frequency horns, standard practice today is to cross them over at least an octave above their respective -3 dB cutoff point on the low end. This protects the compression driver diaphragm even further, as well as minimizing distortion that can occur within the horn itself, if crossed over lower in frequency.

If we choose to use the low pass device as our reference for gain, and set the output drive level for the low pass at 0 dB, then the mid frequency output level should be set to -3 dB to match the mid to the low's sensitivity. Likewise, the high frequency output level would be set at -12 dB in order to attenuate the high frequency horn to match the sensitivity to the low and mid bands. On many variable electronic crossovers with constant directivity horn equalization, you only attenuate the mid-band energy, and the CD horn EQ then compensates for the inherent high frequency roll off. The Low Pass maximum SPL would be 133 dB (10 log 2000 + 100), Mid Pass maximum SPL would be 133.8 dB (10 log 1200 + 103), the High Pass would be based on the 80 Watt continuous rating of the driver, plus the sensitivity, for a max SPL of 131 dB (10 log 80 = 19 + 112).

Generally this would be a good starting for a Three-way or Tri-amped system. The actual optimum crossover frequencies would depend on the composition of the music being reinforced. Most of the energy in contemporary music is below 250 Hz, which is the most demanding bandpass. The second most demanding band of frequencies is between 250 Hz and 1200 Hz. Middle 'C' is 261.63 Hz and the 'D' above the melody staff is 1174.66 Hz. A Rock band with three electric guitar players may be more demanding on this system than another band with only one guitar player. It is now up to the system operator to determine which of these three bandpasses (low, mid, or high) are working hardest. This is easy of course if the amplifiers have an LED metering system. If the amplifiers do not have metering arrays, you would have to push this system until one of the three bandpasses' power amplifiers began showing limiting (or even clipping). Let's say the low pass amp is indicating that it is working the hardest. You could then lower the low/mid crossover frequency point, to allow more headroom in the lowpass amp, but now of course the midpass amp would be working harder. If you then got to a point where the mid pass amp began to show that it was now working harder, you may try lowering the mid/high crossover point a little. The idea here is to try to spread out the demand more evenly. A general rule of thumb, for fourth order and less analog crossovers, is that the crossover points should at the very least be more than 2 1/3 octaves apart. This minimizes something called out-of-bandpass by-product distortion, due to the crossover points overlapping too much.

Many uninformed system operators keep the crossover at the FOH mixer position, so that they can twiddle with it when they deem necessary. This can be a dangerous practice, particularly if you have no way of seeing how hard any of the amplifiers are working. A particularly bad practice is to raise or lower the level of an entire bandpass during a performance, as this actually changes the crossover point of the system. A low cut crossover frequency will move down when raising the gain, and a high cut will move up in frequency. In the example 3-way system below, crossed over at 200 Hz and 2 kHz, note how raising the level of the midpass changes the effective crossover points:

3-way system
Raising the output drive level changes the crossover frequency

Raising or lowering anyone of the bandpass output levels affects how the drivers interact at these crossover points. It is for this reason that once a performance begins any changes to the system should be executed via of the overall system EQ and NOT at the crossover.

In this article we have addressed most of the issues regarding the setting up of an electronic crossover for a typical sound system. Up until recently we were limited to working with the above outlined parameters when adjusting the typical analog variable electronic crossover. In recent years so much has changed with the introduction of high quality affordable electronic digital signal processors or DSP. In the next article (Part III) "Crossovers 2001+", we will address the world of DSP. Much of traditional thinking regarding crossover operation is pretty much out-the-window when it comes to signal processing in the digital domain. There are a lot more variables and many more ways to mess things up. However, the power of today's DSP technology allows those with the proper knowledge and measurement tools, to calibrate sound reinforcement systems to a degree of accuracy never before possible. Please read Part III for the information that will bring you into the 21st Century regarding digital signal processing.