# Special Considerations When Measuring Loudspeakers: Multiple Driver Loudspeakers

The picture on the right shows how the sound travels from the speaker to the microphone. Important is that only the direct sound should be measured and not room reflections as well. Therefore, only path a) not path b) should be considered.

No reflections coming from walls and ceiling may be included. The result of which is that the microphone should be placed quite close to the loudspeaker (approx. 70 to 140 cm).

The phase response is dependent on how the drivers are fitted and arranged. That's usually quite simple: the preferred source of radiation is located in-between tweeter and midrange. To be precise, the line with constant phase difference is actually a hyperbola, having its apex between the drivers. In the simplest case the hyperbola turns into a straight line that runs in-between the centres of tweeter and bass driver.

If the sound pressure level of the entire loudspeaker is measured on this straight line (or hyperbola), then the phase difference is recorded correctly.

It's a bit more complicated when several sound sources have to be considered (pictured below)

We are actually interested in the total sound pressure level of the loudspeaker. Now the problem arises that - depending on the distance to the loudspeaker - the phase difference between tweeter and mid / bass driver changes according to the distance.

The further away the listener is located from the loudspeaker the smaller the phase difference, that depends on the difference of x - a.

The sound path difference is:
x-a = square root (a2 + h2) - a

If h = 29 cm (we are exaggerating a bit), then the phase changes as follows:

 Distance Difference in distance Phase difference at 2 kHz 0.7 m 6 cm 122 Grad 1.0 m 4.1 cm 87 Grad 1.7 m 2.5 cm 52 Grad 2 m 2.1 cm 44 Grad 3 m 1.4 cm 30 Grad 5 m 0.8 cm 18 Grad 7 m 0.6 cm 13 Grad 10 m 0.4 cm 9 Grad

The table shows clearly that developing the speaker with a microphone distance of 70 cm is absolute nonsense when later the average listening distance is 5 metres. In later applications the phase difference between tweeter and bass driver would be 122 degrees - 13 degrees = 109 degrees different to the design in the lab. We therefore recommend the following procedure when building a multiple driver loudspeaker:

First, we just measure two neighbouring drivers in order to calculate a filter for them. The distance to both has to kept the same, therefore, the phase doesn't change with increasing distance.

That's how the crossover for just one transition. The second transition between midrange and bass driver is measured with the microphone positioned between midrange and bass driver.

Later, when the loudspeaker is finished the total frequency response has to be checked from a considerable distance. This can only be done covering a small frequency range since the time window has to be kept small to exclude room reflections.