Locating the tweeter to reduce diffraction effects
IntroductionIn this section I will discuss how locating the tweeter on the baffle affects the tweeter's response and the best way to place the tweeter to minimize these diffraction effects. This analysis will assume that a standard 1" dome tweeter is mounted on a 9" wide rectangular baffle which is an average width for most two-way speaker designs. The theories in this analysis are applicable to any reasonable baffle width and configuration. It is also assumed for this analysis that the edges of the baffle are NOT rounded over thus representing the worst case baffle diffraction situation.
To understand the baffle diffraction plots presented in this section I'll give a quick overview of concept of baffle diffraction and baffle step. Lets assume a baseline condition of a tweeter operating with no baffle at all, not even any flange, just the dome. This characterizes the tweeter as operating in 4pi space or free field. In this scenario the output of the tweeter is allowed to radiate in all directions. Now when a baffle is added to the equation the tweeter is considered to be operating in 2pi space assuming that the baffle is infinitely wide and tall. The output of the tweeter operating in 2pi space will be 6dB greater than that of it operating in 4pi space. This is due to the fact that any soundwaves that would normally travel behind the tweeter are being reflected forward and effectively double the output of the tweeter as a result. When the baffle is of finite size, the distance between the tweeter and the edge of the baffle determines what frequency the tweeter's soundwaves transition from 2pi to 4pi space. In other words, if the wavelength of the tweeter's output is shorter than this distance then those wavelengths are operating in 2pi space. This is because they are short enough to be reflected off of the baffle and thus those frequencies experience a 6dB gain due to the baffle. If the wavelength of the tweeter's output is greater than the distance between the tweeter and the edge of the baffle then those wavelengths (or corresponding frequencies) are operating in 4pi space. These frequencies do not experience a 6dB gain because the soundwaves are effectively "wrapping" around the baffle instead of reflecting forward. In the transition between 2pi and 4pi space near the baffle edge (and corresponding wavelength) a phenomenon known as baffle diffraction occurs. I won't go into the detail of baffle diffraction but there are resources on the net that discuss this topic. Essentially, baffle diffraction causes peaks and dips in the response in the frequency region near the 2pi to 4pi space transition. The plots that I will present below represent how much the tweeter's response will be altered due to baffle diffraction effects relative to a tweeter operating in free-space (otherwise known as 4pi space).
Worst case scenario - equidistant
Tweeter shifted up
Best case scenario - Golden Ratio
ConclusionIn this discussion I demonstrated how critical the location of the tweeter on the speaker baffle is with regards to baffle diffraction effects. The key to reducing these baffle diffraction effects is to place the tweeter at different distances from each side and to avoid distances which are multiples of each other. These baffle diffraction effects are based on an on-axis listening position. Off-axis these baffle diffraction effects are reduced and it is a good idea to design the crossover with the off-axis response in mind as well but that's another topic for another day.