Polar and Directivity Response


The principal purpose is to provide the directivity data files for the conical projection plots. A secondary issue was the documentation of the change in the point source radiation with the onset of lobbing. The wavelength calculation would seem to support the concept that the lobbing peaks as a function of off-axis angle can be viewed as equivalent to distinct radiation of sources separated by 2x the wavelength.

The directivity data can be used for the [X Y Z}=contout(r,n) function.

Response plots for a 2.54cm dome File: PH00

Frequency Response.

The polar plot correspond to this response model and is only for the horizontal axis.

Note the rapid narrowing of the main lobe from 15 to 16kHz and the lobbing @ 17,18kHz. The wavelength corresponding to the dome dia. @ 13.56kHz. and the pencil beam @ 18kHz has a wavelength ~ 1.91cm.

Note the growth of the side lobes between 17 and 18kHz.

At 19kHz. the sidelobes merge and become dominant. The critical change in response from the 15kHz. to the 22kHz. is in the phase.

Dome Directivity Patterns.
File: Phase0

Response for Dome Model.

The off-axis response wasfor 85 and 45 deg. to show the correlation to the initiation of lobbing.

@ 85deg. off axis

ft = 16.02kHz, phase=-61.3 deg.

@ 45deg. off axis.

ft = 16.74kHz. phase= -63.6deg.
File: Phase1

Directivity Response.

@ ~ 80deg. the appearance of side lobes, the main lobe = 49dB the side lobes = -7dB and the peak/null ~ 80dB. Phase = 117/-63 deg.
File: Phase2

Directivity Response.

At close to the minimum magnitude of the main lobe (width ~ 3deg.), the side lobes = 46dB and the main lobe =-5.8dB. Note that the phase transition corresponds to the main lobe.
Higher than 18.81kHz the side lobes begin to merge.
File: Ph07

Directivity Response.

This plot illustrates the response before the onset of lobbing, @ lobbing and past the 1 st lobbing frequency range.
Cone Polar and Directivity Response(low freq. lobbing response)

Driver model: Focal 6K 4411, 6.5" woofer
Outer diaphragm diameter = 14.1cm.
Inner diaphragm diameter 5.0cm.
Cone depth =3.4cm.
File: Phase3

Cone Response

Lobbing commences about 3kHz. and primary on axis null = 4.5kHz.
Note that @ 4.5kHz the main lobe is completely suppressed and a deep null is @ 0deg.

File: Phase6

Directivity Response.

The driver’s dia ~ 14cm.

@ l = 17.2cm some directivity is apparent

@ l = 9.8cm lobbing is prominent. 69.8% cone dia.
File: Phase7

Directivity Response

@ l = 11.5cm main lobe ~ 70deg. 81% cone diameter.

@ l = 9.8cm main lobe ~ 45deg. 70% cone diameter.

@ l = 8.6cm main lobe ~ 29deg. 61% cone diameter.

Response becomes a pencil beam (+/-2deg.)around 4.504kHz. 32% cone diameter.
Note modeling the lobbing as defined by 2point sources separated horizontally by 6cm.,lobbing commences at 2.9kHz, l = 11.9cm. The pattern in the vertical axis is similar but the magnitude of the null of the higher frequency, is larger (model’s HF slope attenuation)

This says that lobbing starts @ 2X the source separation and can be view as equivalent from 2 sources. Note that inverting the phase of the 2nd. source moves the commencement of lobbing to ~27kHz.
File: Phase8

Directivity Response

Past 4.5kHz the side lobes merge and @ 10kHz a 2 nd. set of side lobes are generated.

Polar Response Equation


Beranek pg.102
J1is the 1st.order Bessel function.
Note the radiator model is a piston.

Ribbon Wavefront Patterns
Ribbon Simulation Calibration

Last updated: October 5, 2005 9:28 PM