Assisted Alignments of Order 8

Example 13: Eighth-Order Chebyshev Class {1, 2} Alignment

A plot of the dB SPL at 1 meter and displacement vs. frequency of an eighth-order Chebyshev class {1, 2} alignment is shown below in Figure 17.

Example 13 Frequency Response and Cone Displacement vs. Frequency — Figure 17. Frequency Response and Cone Displacement vs. Frequency of Eighth-Order Chebyshev Class {1, 2} Alignment

Performance Summary for Example 13

The eighth-order Chebyshev class {1, 2} alignment has the following data:
V_B = 10.7ft³
f_B = 14.5Hz
System f₃ = 7.5Hz
Reference SPL = 77.9dB
dB ripple = 0.12dB
k value = 0.2998
Filter 1 undamped resonant frequency = 7.62Hz
Filter 1 Q = 8.3990
Filter 2 undamped resonant frequency = 8.83Hz
Filter 2 Q = 2.5455

Example 13 is the worst example so far of the synthesis software giving a completely impractical result due to excessive low-frequency displacement. As was the case for the sixth-order class 1 Chebyshev alignment, the excessive displacement is caused by excessive filter boost below the box tuning frequency. This is illustrated below in Figure 18.

Example 13 Filter Frequency Response and Cone Displacement vs. Frequency — Figure 18. Filter Frequency Response and Cone Displacement per Volt vs. Frequency of Eighth-Order Chebyshev Class {1, 2} Alignment

The bottom trace is the cone displacement in mm per volt at the loudspeaker terminals. The top trace is the frequency response of the filter itself, which has a boost of 23.7dB at 7.7Hz. This design demonstrates again the dangers of using the synthesis software without verifying displacement performance in simulation.

Example 14: Eighth-Order Chebyshev Class {1, 3} Alignment

A plot of the dB SPL at 1 meter and displacement vs. frequency of an eighth-order Chebyshev class {1, 3} alignment is shown below in Figure 19.

Example 14 Frequency Response and Cone Displacement vs. Frequency — Figure 19. Frequency Response and Cone Displacement vs. Frequency of Eighth-Order Chebyshev Class {1, 3} Alignment

Performance Summary for Example 14

The eighth-order Chebyshev class {1, 3} alignment has the following data:
V_B = 14.5ft³
f_B = 13.7Hz
System f₃ = 10.8Hz
Reference SPL = 98.0dB
dB ripple < 0.01dB
k value = 0.5126
Filter 1 undamped resonant frequency = 10.95Hz
Filter 1 Q = 4.9289
Filter 2 undamped resonant frequency = 15.41Hz
Filter 2 Q = 0.8214

This is another example of badly compromised reference SPL due to excessive filter boost at low frequencies, although it isn't nearly as bad as example 13.

Example 15: Eighth-Order Chebyshev Class {1, 4} Alignment

A plot of the dB SPL at 1 meter and displacement vs. frequency of an eighth-order Chebyshev class {1, 4} alignment is shown below in Figure 20.

Example 15 Frequency Response and Cone Displacement vs. Frequency — Figure 20. Frequency Response and Cone Displacement vs. Frequency of Eighth-Order Chebyshev Class {1, 4} Alignment

Performance Summary for Example 15

The eighth-order Chebyshev class {1, 4} alignment has the following data:
V_B = 9.3ft³
f_B = 17.7Hz
System f₃ = 16.6Hz
Reference SPL = 111.6dB
dB ripple < 0.01dB
k value = 0.8514
Filter 1 undamped resonant frequency = 16.65Hz
Filter 1 Q = 2.9944
Filter 2 undamped resonant frequency = 19.32Hz
Filter 2 Q = 0.5135

This alignment has very good potential. Compared to the unassisted alignment with fourth-order Butterworth filter added, its volume is smaller, its -3dB frequency lower, and its reference SPL is only lower by a negligible 0.3dB. It is interesting to look at a plot of the filter frequency response, the response of the loudspeaker plus box only, and the combined response. This is shown below in Figure 21.

Example 15 Frequency Response of Filter, Loudspeaker and Overall System — Figure 21. Frequency Response and Cone Displacement vs. Frequency of Eighth-Order Chebyshev Class {1, 4} Alignment

The black trace labeled V(amp_in)/V(filt_in) is the filter transfer function. It has a mild peak of 2.9dB at 17.8Hz. The transfer function of the loudspeaker plus box without filter is the blue trace labeled V(tf_scaled)/V(in). It sags slightly, but is flattened out by the gentle peak of the filter. Note the box tuning frequency f_B is 17.7Hz, right where the peak of the filter response is. This means the filter boost is occuring in a frequency band near where the loudspeaker displacement function is a minimum - a very desirable situation. The overall transfer function of loudspeaker plus box plus external filter is the red trace labeled V(transfer_function).

Example 16: Eighth-Order Sub-Chebyshev Class {2, 3} Alignment

A plot of the dB SPL at 1 meter and displacement vs. frequency of an eighth-order sub-Chebyshev class {2, 3} alignment is shown below in Figure 22.

Example 16 Frequency Response and Cone Displacement vs. Frequency — Figure 22. Frequency Response and Cone Displacement vs. Frequency of Eighth-Order Sub-Chebyshev Class {2, 3} Alignment

Performance Summary for Example 16

The eighth-order sub-Chebyshev class {2, 3} alignment has the following data:
V_B = 11.2ft³
f_B = 22.7Hz
System f₃ = 24.6Hz
Reference SPL = 116.2dB
dB ripple = 0dB
k value = 1.4562
Filter 1 undamped resonant frequency = 21.13Hz
Filter 1 Q = 0.7147
Filter 2 undamped resonant frequency = 18.37Hz
Filter 2 Q = 0.5495

Example 17: Eighth-Order Sub-Chebyshev Class {2, 4} Alignment

A plot of the dB SPL at 1 meter and displacement vs. frequency of an eighth-order sub-Chebyshev class {2, 4} alignment is shown below in Figure 23.

Example 17 Frequency Response and Cone Displacement vs. Frequency — Figure 23. Frequency Response and Cone Displacement vs. Frequency of Eighth-Order Sub-Chebyshev Class {2, 4} Alignment

Performance Summary for Example 17

The eighth-order sub-Chebyshev class {2, 4} alignment has the following data:
V_B = 9.1ft³
f_B = 22.6Hz
System f₃ = 25.7Hz
Reference SPL = 116.5dB
dB ripple = 0dB
k value = 1.7537
Filter 1 undamped resonant frequency = 20.06Hz
Filter 1 Q = 0.6573
Filter 2 undamped resonant frequency = 14.84Hz
Filter 2 Q = 0.5032

Example 18: Eighth-Order Sub-Chebyshev Class {3, 4} Alignment

A plot of the dB SPL at 1 meter and displacement vs. frequency of an eighth-order sub-Chebyshev class {3, 4} alignment is shown below in Figure 23.

Example 18 Frequency Response and Cone Displacement vs. Frequency — Figure 24. Frequency Response and Cone Displacement vs. Frequency of Eighth-Order Sub-Chebyshev Class {3, 4} Alignment

Performance Summary for Example 18

The eighth-order sub-Chebyshev class {3, 4} alignment has the following data:
V_B = 8.2ft³
f_B = 20.7Hz
System f₃ = 24.9Hz
Reference SPL = 115.5dB
dB ripple = 0dB
k value = 2.3413
Filter 1 undamped resonant frequency = 12.32Hz
Filter 1 Q = 0.5200
Filter 2 undamped resonant frequency = 10.82Hz
Filter 2 Q = 0.5018