Crossover Filter Shape Comparisons A White Paper from Linea Research Paul Williams July 2013 Overview In this paper, we consider the various active crossover Fig.1 - Well behaved Magnitude Response filter types that are in general use and compare the 6 properties of these which are relevant to professional audio. We also look at a new crossover filter type and 0 consider how this compares with the more traditional 6 types. 12 Why do we need crossover filtering? 18 Professional loudspeaker systems invariably require two or more drivers with differing properties to enable the Magnitude,dB 24 system to cover the wide audio frequency range effectively. Low frequencies require large volumes of air 30 to be moved, requiring diaphragms with a large surface 36 3 4 area. Such large diaphragms would be unsuitable for 100 1 .10 1 .10 high frequencies because the large mass of the Frequency, Hz diaphragm could not be efficiently accelerated to the Low required velocities. It is clear then that we need to use High drivers with different properties in combination to cover Sum the frequency range, and to split the audio signal into bands appropriate for each driver, using a filter bank. In Phase response its simplest form, this filtering would comprise a This is a measure of how much the phase shift suffered high-pass filter for the high frequency driver and a by a signal passing from input to the summed acoustic low-pass filter for the low frequency driver. This is our output (again assuming ideal drivers) varies with crossover filter bank (or crossover network, or just changing frequency. The group delay is a parameter crossover). derived from phase response which describes how different frequencies are delayed. Since the group delay Common Requirements is proportional to the gradient of the phase response When choosing an appropriate crossover filter type, curve, it follows that a linear phase response produces a there are several factors to be considered. flat group delay, meaning that all frequencies are delayed by the same amount. We would therefore like Magnitude response the phase response to be as linear as possible. Commonly referred to as "frequency response", this is a However, lack of phase linearity is not necessarily measure of to what degree the combined acoustic audible. response of the system (assuming ideal drivers) remains Polar response at a constant level with respect to changing frequency. We would ideally like there to be no variation, but small In most loudspeaker systems, the drivers are not deviations can usually be tolerated, particularly if other normally in the same vertical and horizontal position (in more desirable properties can be attained. Although other words they are not coincident), the exception being perhaps the most obvious parameter, it is not the Dual Concentric type. Assuming the drivers are necessarily the most important. It is after all the most separated in the vertical place, then it is clear that the readily corrected using equalisation on the 'input' to the distance between the listener and each driver can only system (or alternatively identical equalisation applied to be the same in one position. If the listener is above or each of the outputs from the crossover). However, one below the centreline of the driver pair, then there will be needs to be aware that applying such equalisation will a difference in distance, and therefore a difference in have an effect on the Phase Response. Figure 1 shows delay which the signal arriving at the listener from the the Magnitude Response of a well behaved crossover drivers will suffer. These delay differences will cause filter pair. attenuation, and ultimately cancellation at certain frequencies. On the centreline however will be the main lobe where there is no such attenuation. Any differential Page 1 of 13 phase shift between crossover filter bands will cause this attenuation. The latter is rarely an issue, but the rate of main lobe of the acoustic beam from the loudspeaker attenuation (often referred to as the cut-off slope, or system to tilt. If such phase shift varies with frequency, cut-off rate) is usually seen as an important this tilting will be frequency dependant, resulting in consideration. Driver design, like many aspects of colouration of the sound which will be strongly engineering, involve many carefully balanced design dependant on the listening position. The ideal filter bank decisions. Problems such as cone break-up and will therefore maintain zero degrees phase difference narrowing of the acoustic beam at high frequencies between adjacent outputs across the crossover region, present the designer with challenges, while and ideally at all frequencies. over-excursion distortion or damage can become an issue at low frequencies, particularly below the effective A Polar Response plot is essentially the magnitude loading frequency of horn loaded drivers. More effective response at different observation angles. The Polar stop-band attenuation in the crossover filters will allow Response is often referred to as the D ispersion Pattern , the driver to be better protected from the problematic which can be different between the vertical plane and frequencies. the horizontal plane for a given system. Here, we are interested in the vertical dispersion . Figure 2 shows the Frequently, some of these requirements are mutually Polar Response of a system with vertically separated exclusive, forcing designers to choose the best drivers, using a crossover filter pair in which the phase compromise. response is identical. This is plotted at the crossover frequency with driver separation equal to the wavelength Active or Passive of the crossover frequency. The scale lines are at 10 A crossover filter bank (network) can of course be degree and 10dB intervals. It does not take individual implemented with purely passive components. In driver directionality into account. In this case, we can professional high-power systems which employ high see that the centre of the main lobe is at 0dB at all voltages and high currents, the size and cost of the frequencies. We have plotted the Polar Response at passive components can become prohibitive, and can three different frequencies. Note that the cancellation lead to distortion, losses and degradation of the damping that is evident on the 1kHz plot has nothing to do with factor. These problems tend to be exacerbated when crossover filters, and would indeed be the same if the high filter orders are required. filters were taken out. This is purely a function of the It is often desirable instead to employ an active dissimilar distance between the drivers and the crossover filter bank, where the band-splitting is done observer, which will clearly change significantly for before the amplification, requiring amplification to be differing distances between drivers. provided for each frequency band (conceptually on each driver). Such systems are sometimes referred to as Fig.2 - Well behaved Polar Response "Bi-Amping" (for two-way active crossovers), or "Tri-Amping" (for three-way active crossovers). Such systems also benefit from the ability to match the power rating of the amplifier to the power requirements of a driver; lower frequency drivers usually requiring an amplifier with a higher power rating than high frequency drivers. Furthermore in such a system, one crossover filter bank might be delivering a driver signal to several amplifiers, thus requiring fewer crossovers. Sometimes, passive and active crossover filters are used together in different parts of a multi-driver loudspeaker system, the passive filters being used on the highest frequency crossover, where voltages and currents are lower. Only active crossover filters will be considered in any 750Hz detail in this paper, although much of the discussion 1kHz applies to both active and passive implementations. 1.5kHz 0dB Digital Or Analogue It is a commonly held misconception that digital Separation/Band-Stop effectiveness implementation of filters in Digital Signal Processors This is a measure of how effectively a filter output (DSPs) behave in a fundamentally different way to their attenuates frequencies which are not intended for its analogue counterparts. In fact, if a digital filter is driver. There are two issues: The rate at which the designed properly to imitate an analogue filter design, attenuation increases as the frequency gets further away then it will duplicate the magnitude, phase and group from the intended band edge, and the ultimate Page 2 of 13 delay characteristics perfectly; there will be no Fig.4 - 4th Order L-R Phase difference. 360 Digital filters can however start to depart from their analogue cousins when the filter frequency is set at very 240 high values - particularly when this frequency approaches half the sample rate. Towards this region, 120 the magnitude response and phase response of the filter will fail to perfectly match the analogue filter. There are 0 various ways of mitigating this problem, the most effective being to simply use a high sample rate. A 120 Phase,Degrees 96kHz sample rate almost completely eliminates the 240 problem. Of course, the digital version will be superior in terms of 360 3 4 5 accuracy, and in terms of consistency from one instance 1 .10 1 .10 1 .10 of a product to another because it does not suffer the Frequency, Hz inconsistencies of component value tolerance that will 48kHz sample rate plague the analogue filter. This inconsistency can often 96kHz sample rate be experienced as shifts in the stereo image, where Analogue component value differences between the channels can cause small, but acoustically significant phase Digital Filter Classes differences. When implementing filters digitally, there are two primary classes of digital filter which can be used: Infinite Figure 3 shows the magnitude responses of three Impulse Response (IIR), and Finite Impulse Response different filter designs; a digital filter at 48kHz sample (FIR).