Calibration for the Ribbon Simulation

The Pioneer ribbon was measure for 0, 30, 60deg. off-axis horizontally and 0, 15, 30, 60 deg. vertically to provide a comparison for a ribbon simulation.

The approximate dimensions of the ribbon element are 0.2cm x 5.5cm. and a horn of 2.5cm x 7.4cm of 1.2cm depth. The horn has a cross like phase plug. The horn is centered on a baffle of 7.6 x 10.5cm.

The horn profile is complex: in the vertical axis it is conical and in the horizontal axis it is a modified catenoid. Due to this complexity the simulation model will be done in 3 parts. The basic ribbon response as a planar piston. The horizontal response as a catenoid horn profile and the vertical as a conical shape. Hopefully this will allow an insight in the components of the measured response.

The horizontal radiation pattern will be defined by the conical horn profile. The vertical should be dominated by the exponential profile. However the modeled response seems to suggest that the response is for a conical profile.

Note that the physical ribbon is recessed some distance from the throat and would form a pre-chamber volume. However the dimensions are not known and the model does not seem to require a Vf variable.

Since the horn has a phase plug, I’ll make a comparable measurement without the cross like phase plug to determine its contribution to the measured response.

The dimension that seems to be critical is the width of the horn throat. This will change both the gain peak and the off-axis response.



Measured Data

The measured data will form the response constrains for the ribbon model.


Fig.1 Horizontal Ribbon Response 		File: Rhv00.bmp

Horizontal 0,+30,+60 deg.

The response has a peak of ~ 8dB @ 15kHz. and a series of nulls @ 2.8, 3.5, 4.3kHz. for 60 deg. axis.

These are the primary signatures that the horn model will attempt to reproduce.

The f3 ~ 2kHz.

The high frequency attenuation knee will be assumed @ 17kHz.

Fig.2 Horizontal Ribbon Response, - angles.
 File: Rhv01.bmp
Horizontal 0,-30,-60 deg.

The +/- symmetry is only approximate. The negative side shows much clearer the off-axis nulls @ 2.7, 3.5 and 4.3kHz.


Vertical Off-Axis Response

Fig.3 Vertical Ribbon Response 		File: Rhv02bmp

The 30deg. off-axis shows a lobbingresponse past 5kHz.

At 60 deg. you see null harmonics past 2kHz. This signature should be sufficient to define the geometry of the horn.


Dispersion Model Data

Fig.4 Horizontal Ribbon Response 60deg. off-axis

Horizontal 60 deg. off-axis

The response shows a series of cancelations starting around 2.2, 2.8, 3.6 kHz. etc.

What is causing these Does not seem that baffle diffraction would cause them and the basic response is defined by horn geometry.
The Phase Plug was removed for the following data comparison.

Fig.5 Horizontal Ribbon Response

File: Rp00.bmp

Horizontal On-Axis Comparison

The primary change is that the peak @ 14kHz is reduced by about 1 dB.

Fig.6 Horizontal Ribbon Response 		File: Rp01.bmp
Horizontal 60deg. Off-Axis Comparison

The series of nulls/peaks starting @ 2.2kHz are not present for the horn with the phase plug removed.

This suggest that@ 60deg the dimensions of the phase plug has a shadowing effect resulting in the nulls. Therefore the conical model for off-axis directivity plots can be assumed to be accurate.

The response without the phase plug is to be compared to fig.7


Development of the Ribbon Modeled

Ribbon Width=0.2cm
Height=5.5cm
Qms=1.0
fs=1.5kHz
Mms=0.01g
Re=5ohm
Le=0.01mH

Fig.7 Modeled Ribbon Horizontal Response
 File: PRH00.bmp
Basic Ribbon Model
Note the response is for the ribbon only, without the horn geometry.
The gain @ 8kHz. is 82dB.
f3~2.05kHz.
The 0, 30, 60 deg. off-axis is essentially the same.

Fig.8 Modeled Ribbon Vertical Response
 File: Prh00A.bmp
Vertical Response of Basic Ribbon.
The 30 deg. off-axis has the 1st. null @ 12.5kHz.
The 60 deg. off-axis has nulls @ 7.2 and 14.4kHz.
Comparing to fig.3 measures data, the off-axis response is good.

Fig.9 Modeled Ribbon Vertical Directivity
 File: Prh00b.bmp
Vertical Directivity Pattern
Note the very prominent cancellation pattern for the basic ribbon. This pattern is not present when the ribbon and horn response is measured.
This data emphasizes that the response of the ribbon + horn is defined by the geometry of the horn.

Fig.10 Modeled Ribbon Horizontal Response
 File: PRH01.bmp
Ribbon + Horn Model, on axis.
If the horizontal horn response is modeled as modified conical the response has a 8.5dB peak @ 12kHz. This explains the peak in the measured data.
Note the horn has about 3dB gain above the basic ribbon response.
The addition of the horn model to that of the ribbon’s response reproduces the on axis HF gain measured in figs.2 and 2.


Horizontal Horn Model: conical
Throat Width=0.2cm
Height =5.5cm
Mouth Width=2.5cm
Height=7.5cm
Horn Length=1.2cm

Fig.11 Modeled Ribbon with Horn, Horizontal Response
 File: Prh02.bmp
Horizontal Axis Response.
The conical horn model reproduces the peaked response of the measured horizontal data as well as the best approximation of the off-axis response.
The modeled response is without baffle diffraction.
Referenced to 5KHz.
0 off-axis peak @ 14kHz. 5.5dB.
30 off-axis -2.3 dB.
60 off-axis .6dB.

Fig.12 Modeled Ribbon with Horn, Vertical Response
 File: Prh03.bmp
Vertical Axis Response
Conical Horn Model.
The off-axis gain are a bit too small, however Rhv03 for 60 deg. off-axis shows a series of cancellation nulls that are not reproduced.
Modeled data:
peak @ 14kHz, +5.3dB.
30deg. off-axis .9dB.
60deg. off-axis .3dB.
Measured data:
peak @ 14kHz. +8dB.
15deg. off-axis.
2dB @ 10kHz.
5dB @ 14kHz.

30deg. off-axis
~10dB. @ 10kHz.
60deg. off-axis
~15dB. @ 10kHz.

Fig.13 Modeled Ribbon with Horn, Vertical Response
 File: Prh04.bmp
Baffle Diffraction
The comparison with the measured data Rhv02 is very good. The 60 deg. off axis has the deep null reproduced.
See the directivity pattern bellow.

Directivity Patterns.

The directivity pattern shows a 6dB. shallow null @ 60 deg. for the 14kHz. curve. This corresponds to the measured vertical off-axis response.

Fig. 14 Without Baffle Diffraction
Fig. 15 With Baffle Diffraction


Ribbon Wavefront Patterns
Polar Response

Last updated: October 5, 2005 9:28 PM