Speaker lobing calculator – Polar response
When is speaker lobing encountered?
Speaker lobing is a phenomenon which appears when there are 2 ore more speakers, that play the same frequency, and are of certain distance apart from each other. This is almost always the case in multi-way speakers. Let’s say, for example, you have a 2-way system with a mid-bass driver and a tweeter. These drivers will play the same frequencies at the crossover region. Also, they have some distance between them, because they are not coaxial drivers. Depending on the size of the drivers, the crossover frequency, and the distance between the drivers, speaker lobing effects will happen to a certain degree. Let’s take it one step at a time, and it will be clear by the end.
The polar response is a plot that reveals the speaker acoustic radiation into space. Here is a polar plot example :
Explanation of the plot :
- The speaker is considered to be placed in the center of the plot, firing sound outwards. You see a speaker in the diagram above, but it’s only present for visual reference.
- 0° marks the point of “on-axis”, or sitting directly in front of the speaker. 30°, 60° and 90° are off-axis points.
- If the response is closer to the center of the plot if means it’s lower in amplitude. You can see the decibel scale marked on the center of the plot. Points which are closer to the exterior, means they are louder.
- Different colors can be used for different frequencies.
The plot above shows a horizontal polar response, and by the looks of it, has a fairly wide dispersion.
Speaker horizontal directivity
When the speaker starts playing higher and higher frequencies, the horizontal acoustic dispersion starts to become more narrow.
Above we have a demonstration of what happens when frequency increases. On the left we have a nice wide dispersion. As we go up the frequency range (middle plot), the acoustic radiation starts to narrow down, or in other terms, it starts to “beam”. On the third plot, the beaming is even more pronounced as frequency increased even more. As a result, the on axis response is still very good, but if you switch your listening position a step to the right or to the left, you will have a severe drop in SPL at the particular frequency.
Beaming is in direct correlation with the size of the speaker. If the speaker is big it will start to beam sooner (as you go up in the frequency range), compared to speaker which has a smaller size. To calculate the frequency when the speaker will start to beam, use this formula :
f = 2 * c / π * D
- f = frequency where the speaker starts to beam (Hz).
- c = speed of sound (343 m/s).
- D = effective diameter of speaker (m).
So let’s give and example for this Seas driver :
The effective diameter of the driver is 13.16 cm so 0.1316 m. In this case
f = 2 * 343 / 3.14 * 0.1316 = 1660 Hz
In conclusion, this driver will start to narrow its horizontal acoustic dispersion, starting with 1660 Hz. As the frequency will increase, the sound radiation will narrow even more. In conclusion, if you build a 2 way speaker system using this driver, consider this fact when choosing the crossover point. If, for example, the crossover frequency is 2500 Hz, know that the mid-bass driver will have less output in the 1600 Hz – 2500 Hz region. This is true only off-axis.
Speaker vertical directivity
When discussing about vertical directivity, the type of crossover plays an important role. The type of crossover not only decides the sharpness of the roll-off, but also the acoustical radiation pattern. More about crossovers here.
Above we have a vertical radiation pattern of a typical 2 way system with 3rd order crossover. The crossover frequency is 3000 Hz, so the distance between the 2 speaker centers is 11.4 cm (wavelength of 3 kHz). The listener is positioned on-axis. You can see the multiple lobes in the acoustical radiation pattern. That’s why the term speaker lobing or acoustical lobing. On the vertical axis there are positions of high sound pressure (mark by the lobes) and positions of low sound pressure (between the lobes).
The lobes become wider as frequency decreases. So, again, higher frequencies suffer more from this effect. In the scenario above, if the listener is sitting down (on-axis), and decides to stand up, he could experience lower sound intensity for the high frequencies (because of speaker lobing).
In the example above we have the same speaker setup, but now with the a 2nd order crossover. The difference is that the 2nd order crossover has a radiation pattern which is symmetrical relative to the 0° axis. The acoustical radiation of the 3rd order crossover is slightly tilted.
The MTM speaker
One of the best solutions to minimize speaker lobing is to use an MTM speaker configuration ( mid-bass – tweeter – mid-bass).
The MTM design needs the drivers to be spaced 1 wavelength of the crossover frequency apart, and use a 3rd order crossover topology. However, practice shows that the MTM speaker design produces a symmetrical acoustical radiation pattern no matter the type of crossover it’s using.
- A – classic 3rd order crossover.
- B – 2nd order crossover produces a large symmetrical lobe. This type of radiation pattern is useful when you deliberately don’t want much off-axis response, hence less room reflections.
- C – Combines a 3rd order high pass filter for the tweeter with a 2nd order low pass filter for the mid-bass. Radiation patter similar to normal 3rd order crossover.
The MTM speaker design is very popular specifically for its special acoustical radiation properties.
When designing a speaker system, the off-axis response is quite relevant, and especially important for some. For this reason, choosing the right speaker size, how you position them and the crossover topology you pick, will dictate the speaker lobing characteristics. Keep this in mind if you are meticulous about your audio projects.
- Speaker Building 201: A Comprehensive Course in Speaker Design by Ray Alden (Audio Amateur Pubns, 2004).
- Image source : link.