Passive crossover problems in audio
Premise
A passive crossover is intended as a network of inductances, capacitors, and resistors placed before the electro-acoustic transducer (loudspeaker) and after the output of the power amplifier.
The purpose of the crossover is to make frequency cuts, in order to allow a specific band of alternating current signals to pass, and, in some cases, to linearize the bandwidth itself.
Other types of crossover, placed before amplification or before the source instead of the speaker, are called “active crossovers”.
There are different ways of applying passive components before loudspeaker, some of these do not provide a frequency cut and therefore could not be called “crossover”: an example could be the Zobel compensation cell, useful for linearizing the speaker impedance module.
In this regard, it is important to remember that a loudspeaker is a complex load, whose electrical model can be mathematically described as a network of inductors, capacitors and resistors.
However, the problems of passive crossovers are so significant that they would adversely affect even if the speaker were a simple resistive load. Some of the demonstrations in this paper will be done through real measurements and others through a circuit simulator.
In the simulations, the components used are ideal, and the speaker a simple resistive load. This means that in reality, the results are even much worse: since the components have tolerances and parasitic variables, and the speaker is a much more complex load.
Here the problems found are listed and analyzed one by one. These are really relevant, and include but are not limited to: increased distortion, decreased speed, decreased correction factor, bandwidth peaks, phase shifts, tolerances etc.
Problems [1]: reduced damping factor
Without going into specifics and explaining in detail how the damping factor works, we must keep in mind that the damping factor decreases as the impedance between the feedback point of the amplifier and the coil of the loudspeaker rises.
Attention: the damping factor is not only determined by what is present from the amplifier terminals to the speaker box terminals, but more precisely by all the impedance present between the amplifier feedback point (therefore before the output terminals, since those also add impedance) and the speaker coil.
This means that literally everything in between adds impedance: the terminals, the cables (including return cables), and, above all, the crossover.
A passive crossover reduces or nearly nullifies the effectiveness of an amplifier’s damping factor by adding a large amount of impedance between the amplifier’s feedback point and the speaker coil ends.
For example, in standard inductors, it is incredibly difficult to find commercial coils that have an impedance that falls below 0.5 Ohm, this happens because, in order not to use magnetic cores, it is necessary to use a large amount of turns of enamelled wire in order to achieve the desired inductance.
Which means, even with a damping factor of 10000, the total damping factor has now dropped to 16 on 8 Ohm loudspeaker.
It should also be considered that the output impedance of an amplifier rises as the load falls. Hence, the lower the load impedance, the lower the damping factor: ideally the damping factor is reduced by half if the load impedance is halved, but in reality it gets worse.
In sound, the damping factor is extremely important in the low frequencies, which is where the speaker is much more prone to spring. The more it is reduced, the more the low frequencies become shaky and inaccurate. The effects of varying the damping factor are well documented in the scientific literature and many measurements have been made.
Another effect of reducing the damping factor is also the reduction of the speaker’s bandwidth linearity. The damping factor is basically the amount of control the amplifier has over the speaker: if the control becomes too low, the effective bandwidth becomes a servant of the impedance module of the speaker itself.
Problems [2]: artifacts in frequency response
The task of a crossover is mainly to make a frequency cut. In a resistive load this is done effectively using inductors and capacitors.
In the case of a simple high pass, this filter should pass a specific band of frequencies higher than the cutoff frequency and attenuate the rest.
However, the mathematical and electrical model of a speaker is much more complex than just a resistance. Thus, our filter will never have the same effect. Rather, the effects on the speaker band will be far more inaccurate and problematic.
Let’s take the frequency response of an example loudspeaker, and apply a simple high-pass capacitor to it.
The dotted line corresponds to the frequency response of the original speaker, the continuous line the resulting one after the filter has been added. The blue line, on the other hand, represents its impedance module.
As you can see, the slope is present, but above all, that the result is not what we expected: in fact, there is no constant attenuation, and there is a peak on the resonant frequency of the speaker.
Now let’s say to increase our cut, also applying an inductor, and varying the cut slope from 6dB/oct to 12dB/oct.
Thanks to a higher slope, now our crossover works almost well. However, the entire remaining frequency response has been changed. Now our loudspeaker is no longer linear, or rather, much less so than before.
Problems [3]: tolerances
Like all electronic components in commerce, the crossover elements also have tolerances. In a simple simulation of a high pass filter, where a 100uF capacitor with 10% tolerance was placed in series to a simple resistor, due to tolerance, although the sources and speakers are perfectly identical, the resulting frequency response will never be the same.
Tolerances of 10% are standard for capacitors, high for resistors, but very optimistic for inductors. This would lead the channels to have disparities of a few decibels in cuts.Although it is possible to infinitely select the components to build the crossover, as the voltage or the let-through current varies, and as the temperature varies, the tolerance will continue to vary and the result too.
To consider, that even the loudspeakers have tolerances, and that it is practically impossible to produce two identical ones. However, adding to these tolerances also those of a crossover would mean increasing the damage.
Problems [4]: phase shifts
Considering the loudspeaker taken alone, and placed in half space (infinite baffle), we obtain from it two phases: one acoustic and one electric.
The first is related to its frequency response.
While the colored lines represent the frequency response at different angles, the gray line represents the phase of this frequency response. As you can see, the phase does not vary much during the speaker’s usable band.
The second phase, on the other hand, the electrical one, is linked to the speaker impedance module.
The blue line represents its impedance module, while the pink one represents the electrical phase. As you can obviously see, the electrical phase of a loudspeaker is not very linear. However, there are systems to linearize it, such as, for example, Zobel compensation cells.
After the application of a Zobel cell, the speaker impedance module is linearized, and consequently its phase. Which unfortunately, however, remains curved in the area of the resonant frequency.
Phase follows always the bandwidth in the theory of the signals, if a there is a cut-off frequency, there is a phase change.
A passive crossover is no exception, as is an active one: the variation of the electrical phase is inevitable when making a cut.
Problems [5]: Performance and specs changing in current and temperature rising
The changing of the specifications of an electronic component as the amount of current and temperature varies is not a new concept in electronics.
Each electronic component varies its performance as these two variables vary. Normally, the percentage of variation is expressed in ppm/C° and is available in the datasheet of any component.
As the current passes, there is an inevitable rise in temperature, due to a resistive factor of the component. As the component heats up, its specifications vary. In this simulation, it is noted that from the same component there are different frequency responses to varying temperatures (respectively: 10°, 30° and 60° Celsius).
Furthermore, as in the case of electrolytic capacitors, the performance of the dielectric varies according to the voltage, current and frequency applied to the ends. An electrolytic capacitor, for example, greatly varies its capacity as the three conditions written above vary, as well as the temperature.
The other capacitors also have the same problems, albeit to a very limited extent.
Problems [6]: Added distortions
A crossover filter induces various types of distortion:
- Distortion due to frequency cut (slew distortion)
- Distortion due to the passage of the signal through the components
- Memory distortion
- Hysteresis distortion
To understand exactly how a passive crossover does not simply provide attenuation, but rather distorts the signal, let’s take the most obvious case: a square wave through a low pass.
Certainly a crossover cannot be defined as a low pass, if it does not reduce the speed of the current flow. The consequence of reducing this speed has the effect of attenuating the higher frequencies: bandwidth and speed go hand in hand, if the bandwidth is reduced, the speed is reduced.
In the case of passing a signal, the crossover not simply attenuates, as we can verify, but distorts the signal. The speed reduction of the signal is also called “slew induced distortion”, and is present in switching amplifiers as well as crossovers.
Although this is the most obvious case, signal distortion occurs in all cases. And it is greater as you move away from the cutoff frequency, outside the passing band.
Also, passing a signal from an electronic component increases noise and final distortion. As in the case of capacitors.
As can be seen from the measurements, using the exact same signal with the exact same load, two different capacitors have two different distortions simply changing the dielectric type.
Note that, in this case, the load had a high impedance, and the current flow was therefore minimal. Despite this, even the MKP type capacitor (often used in passive crossovers) introduces its own distortion, which increases, and by a lot, with increasing voltage and current.
By placing an ideal inductor on a resistive load, the distortion of a simple sinusoid is theoretically zero. However, when the component becomes real, its variables strongly affect the signal. The distortion comes from the signal passing through the component itself, not from the cutoff frequency or even from slew-induced distortion.
Memory distortion is yet another type of distortion introduced by electronic components. It consists of signal-induced thermal drifts.
The circuit memory is the ability of a circuit to remember the past states of a signal. Here are some examples of memories:
- A capacitor: has memory, it integrates current into voltage
- An inductor: has memory, it integrates voltage into current
If we were to listen to music through this, however, we would notice that, after several seconds of low amplitude signals, the cap has discharged and will completely clip the crescendo that follows. This circuit has memory: the cap voltage is an image of past amplitude peaks.
In addition to the memory effect, at the passage of a non-constant signal we also have the variation of the temperature and of the current through the component, and therefore the variation of the electrical characteristics of the component itself. This, added to the component’s own distortion, creates enormous distortion damage.
Passing on, hysteresis distortion is a type of distortion that happens only when an inductor does have a magnetic core. It has always been known in the world of electronics and signals, and lately it is much discussed in the world of class D amplification.
The figure above highlights the issue. The signal traverses the B-H curve in each direction as given in the graph. The flux (and thus the voltage) at a specific point on the curve can be different depending how you arrive at that point. For instance, following the path 5 to 7 takes you through point 6, and although points 5 and 7 are identical on the B-H curve, the voltage at that point is not. The same situation occurs when you go from 2 to 4 through 3; the voltage values at identical points 2 and 4 are different depending on the path you took to arrive there. Clearly, there are voltage ‘jumps’ when, after traversing a minor B-H loop, you arrive at the same point at the major loop where you were before. So, there is an element of which causes strong non-linearity.
Problems [7]: Power attenuation and heat dissipation
It must also be remembered that all electronic components are not ideal. If, for example, inductors were ideal, we would have only the inductive component, instead, we also have other characteristics, and more complex mathematical models.
All the impedance in series with the load, in addition to decreasing the damping factor, represents a real attenuation.
The higher the impedance of the component, the less current flows from it: in this way the load requires more power to be able to operate at steady state. In cases where the crossovers are very complex, the sensitivity per volt of the speaker is greatly reduced, forcing the use of very powerful amplifiers.
Furthermore, all the power used by these crossovers is dissipated in heat, representing a loss of efficiency.
Another consideration is the power factor for alternating current signals. Above all, it should be considered that the power in alternating current signals is also given by the phase between the voltage module and the current module. Upon adding a passive crossover, the current and voltage are no longer in phase, resulting in a large loss of output power.
Furthermore, the final output power no longer has the same shape as the current and voltage, and again results in a distorted signal.
Conclusions
Probably a book would be needed to deal in detail with all the defects and problems induced by passive crossovers in the audio field. However, what we can draw from it is that in an audio system, passive crossovers are the real weak link in the chain, even though the speakers already have strong non-linearities and high tolerances.
It should be noted that the problems of passive crossovers are also encountered in specific types of active crossovers, such as phase shift and added noise.
It must be remembered that there are two types of active crossovers: analog and digital. Digital active crossovers work by cutting and reprocessing a digital signal (before the source, if this is a DAC, or between source and amplifier if this is an ADC-DAC). Active analog crossovers, on the other hand, act on a purely analog signal before it enters the power amplifier.
Active analog crossovers suffer almost from the same problems as passive crossovers: they do not damage damping and do not create response artifacts, but they have tolerances, have distortion problems, have phase rotations, change performance as the temperature changes and they also suffer. of memory distortion.