Horn Loading

Horn Loading and Efficiency: Frequency Dependence

Horn loading is a technique used in loudspeakers to improve the efficiency and directivity of sound radiation. A horn acts as an acoustic waveguide, channeling the sound waves from the driver (speaker) in a specific direction. This focusing effect can significantly increase the sound pressure level compared to a simple driver without a horn.

We will describe technical terms here but loading works like this:

• Impact Loading: The closer and smaller the air surface near a horn’s throat, the greater the impact loading.

• Directivity Control: Loading cannot be “sent” beyond the horn’s directivity control end; this would be ineffective. Horns exhibiting good loading effects often have a strong cutoff approaching the horn’s control end, due to this effect, allowing for a lower crossover frequency that can be defined by Group Delay, in addition to directivity matching and driver distortion. This interplay between directivity and loading can also result in a “bell response” due to the interplay of constant directivity and loading.

• Loading and Frequency: Loading effect decreases with increasing frequency. Consequently, the “anchor point” (14/15kHz) SPL, used for our horn EQ, remains unaffected by loading but will be influenced by directivity, as discussed in the next point.

• Off-Axis Energy: At a given frequency, energy present off-axis is no more present on-axis. This is one of the reasons why pursuing constant directivity up to 20kHz is not necessary, especially when considering audibility and psychoacoustics.

• Loading Uniformity: Loading is not uniform at all. The characteristics mentioned above define a frequency range of loading effects, with a given dB pressure level, forming a curve that will interact with driver one. Surface area size, expansion, and directivity significantly influence these effects.

• Example of Loading Effect: Lengthening the horn throat can significantly alter loading. However, these manipulations must be approached cautiously as they impact wavefront propagation and, consequently, directivity. This is why FEA simulations are essential for accurate predictions.

Acoustic Impedance

Acoustic impedance (Z) is defined as the ratio of sound pressure (Pa) to particle velocity (v):

Z = Pa/v

It characterizes how easily an acoustic wave propagates through a medium or across a boundary between two media. In practice, acoustic impedance measures the adaptation between two acoustic environments, such as a loudspeaker coupling into a room, or a compression driver coupling into a horn.

Acoustic impedance is not directly audible. Instead, it governs how much of the acoustic energy is transmitted versus reflected at a boundary. A well-matched acoustic impedance maximizes energy transfer and minimizes unwanted reflections.

In horn-loaded loudspeakers:

• At low frequencies, where the wavelength is larger than the horn dimensions, the horn does not load efficiently and the acoustic impedance mismatch leads to reduced efficiency.
• At mid frequencies, the horn improves the impedance match, boosting efficiency and controlling directivity.
• At high frequencies, the impedance tends to rise again due to smaller wavelengths and internal viscous losses, reducing the overall gain.

Additionally, directivity impacts impedance: as a source becomes more directional (naturally or by design), the radiated impedance increases. Horns use this effect intentionally to “concentrate” the energy, but it must be controlled to avoid creating too much mismatch at the horn mouth.

Finally, acoustic impedance at the horn throat typically increases with frequency, and a very high impedance combined with high particle velocity can lead to thermal compression and distortion at high SPL levels.

With a horn with a roundover to avoid midrange narrowing, the impedance is near zero and close to being linear at the mouth of the horn.

Particle Velocity

Particle velocity (v) is the oscillating motion of air particles caused by a sound wave. It differs from the speed of sound (celerity), as it describes the back-and-forth movement without any net displacement.

In audio systems:

• High particle velocity occurs in narrow areas, such as bass reflex ports or horn throats.
• At constant sound pressure, higher particle velocity means lower impedance.
• In general, as the cross-section narrows, the particle velocity rises, even if the frequency or SPL remains constant.

Thus, particle velocity must be monitored when designing small apertures or highly compressed structures, to avoid excessive velocities that can cause distortion or energy losses.

Critical Mach Number

The critical Mach number describes when the particle velocity becomes a significant fraction of the speed of sound (Mach 1). In loudspeaker design, this is particularly relevant in narrow passages or throats where particle velocity can increase substantially.

The Mach number is defined as:

M = v/c

Where:

• v is the particle velocity,
• c is the speed of sound in the medium (≈ 343 m/s in air).

At a Mach number of around 0.1 to 0.3, the acoustic behavior starts to become nonlinear. Exceeding this critical Mach number results in:

• Strong nonlinearities (distortion),
• Turbulent flow,
• Thermal compression (heating due to intense localized motion),
• Potential efficiency loss and audible degradation.

Keeping particle velocity well below the critical Mach number ensures low distortion and optimal efficiency in horn-loaded designs.

For ports, we have developed a flat velocity port that allows us to keep the Mach number low.

How These Concepts Interact with Frequency

The interaction between acoustic impedance, particle velocity, and the Mach number is highly dependent on the frequency.

• At lower frequencies, sound waves have larger wavelengths. This results in lower particle velocities and reduces the risk of reaching the critical Mach number. As a result, horn-loaded systems can generally handle these frequencies more efficiently without significant distortion or turbulence.

• At higher frequencies, sound waves have shorter wavelengths, which means the particle velocity increases more rapidly. In narrow openings, such as the throat of a horn or the port of a bass reflex system, the risk of exceeding the critical Mach number increases. This can lead to nonlinearities, distortion, and even thermal compression, all of which negatively impact the efficiency and sound quality.

In horn designs, proper impedance matching is essential to minimize reflections and ensure optimal energy transfer. However, as the frequency increases, the impedance tends to increase as well, particularly at the throat of the horn, where viscous and thermal losses become more significant. This can further complicate the efficiency gains from the horn.

Thus, frequency plays a pivotal role in determining the balance between particle velocity, Mach number, and impedance. The design of the horn, its throat size, and the frequency range it is intended to operate in all contribute to how well these concepts interact to achieve optimal performance.

High-Order Modes (HOMs) in Horns

High-Order Modes (HOMs) are unwanted sound waves that can occur within a horn due to its geometry. They deviate from the ideal plane wave propagation pattern and can cause irregularities in the directivity pattern (how the sound radiates in different directions) and degrade the sound quality.

Minimizing HOM Excitation

A well-designed horn aims to:

• Maintain a flat impedance profile across the desired frequency range. This helps to suppress the excitation of HOMs.
• Have a smoothly expanding horn throat to encourage the propagation of the fundamental wave mode (desired sound wave) and discourage the excitation of higher-order modes.

Influence of Throat Geometry and Mass Corner on Horn Loading

The way a horn loads the driver is primarily dictated by the throat design and the expansion profile, but the mass corner of the diaphragm also plays an important role.

• Throat geometry and expansion: A longer, more constricted throat increases low-frequency loading by enhancing impedance matching at low frequencies. However, this comes at the cost of increased acoustic resistance at higher frequencies, which can reduce efficiency and bandwidth in the upper midrange and treble. Conversely, a rapid flare (wider throat expansion) improves high-frequency performance but sacrifices low-frequency loading because of poorer impedance matching.

• Mass corner effect: The mass corner defines the transition between compliance-controlled (spring-like) and mass-controlled (inertia-like) behavior of the diaphragm. Above the mass corner, the diaphragm operates in a mass-controlled region where energy transfer into the horn is more efficient. Below the mass corner, the diaphragm becomes increasingly compliance-controlled, making efficient horn loading more difficult.

Thus, horn loading performance results from a combination of throat geometry and diaphragm behavior relative to its mass corner. A horn may appear to “turn” around a specific frequency, but this is not solely because of the mass corner or the horn geometry alone—both contribute.

In classic direct-radiating loudspeakers with horn-loaded cones, it’s possible to optimize the impedance match between the cone and the horn’s throat by carefully designing the throat profile, like with a compression driver, thus minimizing efficiency loss around the mass-controlled transition while maintaining good loading.

Impedance Matching and Low-Frequency Considerations

For a cone driver in a horn-loaded speaker, impedance matching between the diaphragm and the throat is crucial, especially at higher frequencies, as this helps maximize SPL and minimizes energy losses due to reflections.

However, as frequency decreases toward lower midrange and bass regions, impedance matching becomes less critical for the following reasons:

• Longer wavelengths allow the throat to behave more “linearly” at lower frequencies.

• Acoustic resistance of the throat becomes less significant at lower frequencies, as pressure variations are smoother and energy propagates better over longer wavelengths.

• The horn’s low-frequency loading effect becomes more dominant, and impedance matching has less impact.

In summary:

• At high frequencies, proper impedance matching between the diaphragm and the throat is crucial for efficient energy transfer, minimizing reflections, and maintaining consistent frequency response.

• At low frequencies, imperfect impedance matching has a reduced impact on efficiency. Horn design at these frequencies is more concerned with maximizing acoustic loading and maintaining extension, rather than achieving a perfect impedance match.

How a Horn Increases Efficiency at Low Frequencies

The loading of a horn depends on several factors, including:

• Horn Geometry: The geometry of the horn, particularly the throat design and the expansion profile, strongly affects the acoustic loading and impedance matching. Surface propagation and horn depth also play a role, but the throat shape and expansion law are the primary factors.

• Mouth Size and Directivity Control: The size of the horn mouth largely defines where directivity control ends, particularly in the horizontal plane. If the horn loses control in the vertical plane too early, a portion of the acoustic energy can be lost or dispersed unpredictably, leading to reduced efficiency.

• Frequency of the Sound: Frequency fundamentally influences how the horn interacts with air impedance and controls sound radiation. Lower frequencies require larger horns to maintain good loading and directivity.

Here’s a breakdown of the key points:

• Acoustic Loading: A horn acts as an acoustic transformer, influencing the acoustic impedance “seen” by the compression driver. This allows for a better match between the driver’s impedance and the horn’s impedance profile across the desired frequency range, improving efficiency and sound radiation characteristics.

• Low Frequency Efficiency: At low frequencies, the impedance mismatch between the driver diaphragm (high impedance) and the air (low impedance) hinders efficient energy transfer.

• Matching the Air Load for Efficiency: Air has a relatively low acoustic impedance compared to the diaphragm of a compression driver. This impedance mismatch can lead to inefficient energy transfer from the driver to the air. A well-designed horn can influence the impedance profile “seen” by the driver, particularly at low frequencies. This allows for a better match between the driver’s impedance and the radiating medium (air). This improved impedance match can lead to increased efficiency, allowing the driver to operate with potentially reduced diaphragm movement for the same sound output (dB).

• Reduced Diaphragm Movement: With improved impedance matching, the driver needs to move less to produce the same sound pressure level at low frequencies. This reduces distortion and improves the overall efficiency of the driver.

Important Note:

This principle primarily applies to low frequencies. At higher frequencies, the horn’s effect on impedance matching becomes less significant, and other factors like diaphragm size and material come into play.

The “loading effect” is frequency-dependent. It has a stronger influence at lower frequencies and gradually diminishes as frequency increases.

More informations about global energy in horn: Horn and energy

A point about Constant Directivity Horns:

As energy is not “free”, a constant directivity horn cannot be straight on axis as the energy is dispatched off-axis to be constant, that we need, so the on-axis response will show a bell response curve.