Handbook for Sound Engineers

Loudspeakers 625

response goes through a 720° wrap through the cross-
over region. From what we have observed so far, it is
evident that higher-order symmetric filters can intro-
duce nonideal transient response behavior when used as
crossover filters. Based on observations of the delaying
effect of the low-pass filters, one might be tempted to
introduce electrical delay into the high-frequency signal
in an attempt to better synchronize low- and high-
frequency signals. In the case of the LR filter family,
such attempts will only serve to compromise the ampli-
tude response of the loudspeaker while offering
minimal improvement in the impulse response. As with
crossover-frequency anomalies caused by noncoinci-
dent transducers, one way of addressing the nonideal
behavior of higher-order symmetric filters is to assert
that the problems are not audible. It is also possible to
address transient response issues and at the same time
retain a steep filter slope for one of each pair of neigh-
boring bands in a multiway loudspeaker. Crossovers of
this type are termed constant voltage crossovers and are
discussed in Section 17.8.5.3. The simulations above
are based on ideal filter behavior and ideal transducers.
As one makes the simulation more realistic, accounting
for the bandpass behavior of real-world transducers, the
performance of all of the modeled crossovers will dete-
riorate, but the relative attributes of constant voltage
filters remain.

17.8.5.4 Beyond Two-Way Systems

As the number of spectral bands in a loudspeaker
increases, the issues that must be dealt with in crossover
design multiply. In a system with three or more bands,
at least one of the crossover filters is a bandpass, usually
formed by cascading low-pass and high-pass filters of
the desired characteristics. The low-pass portion of the
arrangement will introduce delay in its passband, which
can create misalignment between the band in question

and its lower neighbor. In addition to this issue, there is

also the possibility of interactions between transducers

that are not neighbors in the audio spectrum (e.g., the

woofer in a three-way system can contribute enough

energy in the high-frequency horn’s passband to make

its presence known). This type of interaction is often

undesirable, as it has generally deleterious effects on the

response and directivity of the system.

17.8.5.5 Passive versus Active Crossovers

When designing a passive crossover—one that receives

the power amplifier’s output and applies appropriately

filtered signals to each transducer—the designer must

account for the frequency dependence of the imped-

ances of each transducer in the system. In the case of

most cone transducers, the impedance curve has a peak

at the resonant frequency, above which it decreases to a

minimum and then rises with frequency in similar

fashion to the impedance of an inductor. This variation

of impedance with frequency is often minimized

through the use of a parallel, or shunt, network. Once

the device’s impedance has been stabilized in this

manner, the actual crossover filter may be designed to

drive a purely resistive load with excellent results.

Active crossovers —those that divide the spectrum at

line level and apply the band signals to the inputs of

power amplifiers— have the advantage of the buffering

effect provided by the power amplifier. Imped-

ance-related issues are far less significant in this case,

and active filters—particularly DSP-based ones—offer

a number of options not readily available in passive

versions. These include frequency-independent delay,

all-pass filters, and dynamics processing (compres-

sion/limiting). The price that is paid in an active system

is in additional channels of power amplification and

wiring.

17.8.6 Acoustic Boundaries

Generally, one considers that acoustic boundaries are

part of the space into which a loudspeaker is radiating.

The field of architectural acoustics is largely concerned

with the acoustic behaviors such boundaries cause.

However, every loudspeaker has a collection of acoustic

boundaries independent of the external environment in

which it is operated, and these boundaries make a

surprisingly large contribution to the loudspeaker’s

response and directivity.

Most of the boundaries associated with loud-

speakers constitute reflective surfaces: enclosure walls

are designed to be rigid and generally have hard

Figure 17-48. Impulse response family of fourth Link-
witz-Reilly filters.

Input

Low pass

High pass

Sum

0.0 0.4 0.8 1.2 1.6 2.0

10

0

10