Minimal Delay Phase Control
March 2024
Wanting to improve the coverage of the low-frequency range in curved arrays while avoiding significant delays of 5ms or 10ms is a common concern. How can we control the phase response between modules in the array with minimal delay?
1. Separating the Low and High Frequencies
As a preliminary step in controlling the phase for low frequencies, input signals are divided into high and low frequencies using a crossover. A 3rd order Butterworth filter, with its level at -3dB and phase at -135 degrees for the Low Pass Filter (LPF) and +135 degrees for the High Pass Filter (HPF) at the cutoff frequency, can be used. Mixing an LPF and an HPF with the same cutoff frequency results in an All Pass Filter that has a 360-degree rotation around the cutoff frequency.
The diagrams below show the transfer functions of signals passed through LPFs and HPFs at a 250Hz cutoff frequency in a 3rd order Butterworth (BW), and their mixed output.
2. Shifting the Low Frequencies
Next, to shift the phase of the low frequencies, a delay is added to the LPF side. The diagrams show the transfer functions when increasing the delay from 0.0ms to 0.5ms in 0.1ms increments on the LF. The delay shifts the phase response at low frequencies, but also leads to changes in the magnitude response.
3. Compensating the Magnitude Response
To compensate for the magnitude response caused by adding the delay, a Parametric Equalizer (PEQ) is inserted before the crossover as a Compensation EQ. PEQs not only alter the level but also shift the phase response. Although this shift is minor compared to the phase shift caused by the delay, at frequencies lower than the most significant level change, the shift leans towards a further delay, and at higher frequencies, towards an advancement.
The diagrams below display the transfer functions of six filters with a 0.0 to 0.5 ms delay applied to the low frequencies, followed by up to 5 bands of EQ to give a nearly flat magnitude response.
Comparing each filter, with delays from 0.0 to 0.5ms in the low frequencies, to the reference (no delay : 0.0ms), it is evident that while maintaining a nearly flat level, the phase responses in the low frequencies can be adjusted relative to each other.
Observing these filters' relative phase delays reveals that the phase characteristics start to change around 500Hz and are nearly constant at frequencies below 160Hz. Moreover, corrections made by the EQ result in a slightly greater phase delay below the cutoff frequency than the imposed delay time, while at frequencies above, the phase delay caused by the delay is compensated.
Although these filters were created with IIR filters and delay, it is also possible to create filters with almost identical characteristics using (almost delay-free) FIR filters.
*Note: It has been confirmed that the .csv files can be imported into PowerSoft Armonia+.
*Disclaimer: We cannot be held responsible for any issues arising from the use of these filters.
Application Example of LF Phase Shift Filters
This section applies the filters for shifting the phase characteristics of the low frequencies to a curved array composed of seven elements with 8-inch woofers. Designed to provide sound to an audience area approximately 25m deep, the array delivers a uniform response across the entire seating area at 4kHz Direct SPL map. However, at 160Hz, the SPL near the audience area increases significantly.
To reduce the radiation of low frequencies towards the front of the audience area, the array is shifted in phase to function as a straight array towards the back of the seating. By observing the displacement of the array from the side, a filter with close phase delay using the bottom box as a reference is applied. As illustrated below, LF0.5ms filter is selected for the upper four boxes, LF0.4ms for the fifth, LF0.2ms for the sixth, and LF0.0ms for the bottom box.
Viewing the 160Hz Direct SPL map demonstrates that coverage can be improved with the LF Phase Shift filters.
In summary, the filters introduced here offer relative control of the phase characteristics between the filters without introducing substantial delay. While there is a trade-off of 360-degree rotation in phase responses in the mid-low range, these filters provide an option for those wishing to control phase in low frequencies without tolerating significant delays.
About Other Crossovers :
In this article, we used a 3rd order Butterworth crossover to separate the high and low frequencies, but there might be better filters available. However, several crossovers I wanted to try did not work well for this purpose.
For example, a 1st order crossover (shown in the upper right figure) results in a flat phase and level frequency response when high and low frequencies are added together. However, being a gentle filter, it allows the effects of applying a delay to the low frequencies to extend into the high frequencies.
Alternatively, reversing the polarity of the low frequencies in a 3rd order Butterworth crossover and adding it to the high frequencies creates an all-pass filter with a 180-degree rotation around the cutoff frequency, but applying a delay to the low frequencies causes a drop in level around the cutoff frequency (shown in the lower right figure). Boosting this with a PEQ will advance the phase at frequencies below the cutoff and delay it at frequencies above. As a result, the phase delay in the low frequencies we want to control becomes smaller than the applied delay, whereas the phase delay in the high frequencies, which are not the target of control, becomes larger.
