Setting Up A Cardioid Subwoofer System: Example 1

9) Invert polarity on the back subwoofer. The phase trace can be seen to shift 180º.

10) Unmute both the back and front subwoofers. Measure the amplitude response of the adjusted system and compare to the initial measurement for the front subwoofer. If the phases have been correctly adjusted we shall see a significant reduction in level.

We recommend that you now listen to the result by walking from the front to the back, around the system. The difference should be remarkable.

You can also listen to the difference with pink noise by asking someone to mute the output of the back subwoofer.

11) Adjust the processor limiters so that both subwoofers limit at the same time.

Fig. 6. When adding delay to the blue curve, its phase trace moves down until it overlaps with the red one. Delay added to the back subwoofer in this example was 0.658ms.

In step 7 we reduced the gain on the back subwoofer output so that the output from both subwoofers were the same at the back of the arrangement (Keep in mind that, for optimum cancellation, phase difference needs to be 180º and levels need to be matched).

If we did not adjust the limiters this way, the front subwoofer would limit before the back one, so, for a moment, pressure levels would not be the same and there would be an annoying intermittent lack of cancellation.

Fig. 7. When inverting polarity on the back subwoofer, the phase trace is the same as for the front one, but shifted 180º.

This adjustment can be done with a music signal, varying the limiter threshold at the processor outputs so the limiting for the two signals takes place at the same time.

Fig. 8. This image compares the pressure curve of the front subwoofer at the measurement position (red) to the cardioid configuration (green). In this case, a difference of up to 12dB can be seen.

Sound pressure level in front of the cardioid configuration

Not all the back subwoofer energy is used for cancellation. At the front of the cardioid configuration, pressure is gained, compared to a conventional configuration (without a back subwoofer, that is).

Figure 9 shows the sound pressure difference between a single subwoofer and the cardioid configuration.

As stated above, at twice what we call reference frequency there is a cancellation. On this example the reference frequency is 382Hz, which means that cancellation will happen at 764Hz. This is why there is an increase in the slope of the curve above 500Hz.

Fig. 9. Red traces correspond to the magnitude and phase responses for the front subwoofer alone, while the green ones are for the cardioid configuration. In this specific example, we have gained approximately 3dB between 170Hz and 500Hz, while levels below 170Hz have stayed the same.

At the “Cabinet spacing” section we spoke of the phase differences at what we call reference frequency, as well as at frequencies above and below it. Figure 10 shows these phase differences. The red trace represents the front subwoofer while the blue trace corresponds to the back one.

Above the reference frequency, where the curves cross each other, phase difference increases rapidly (taking into account that a logarithmic scale is used for frequency) until twice the reference frequency is reached and cancellation happens as a result of the 180º phase difference.

In this example it can be seen that the blue phase curve is 0º at 764Hz while the red curve is 180º, i.e. a 180º phase difference. The black arrows mark both spots.

Below the reference frequency, phase difference is not as large as for the upper frequencies.