Here a SEAS L16RN-SL using a Linkwitz Pluto type mounting and a Vifa NE180W-04 suspended vertically above the woofer is used for exploring cardioid sound field. The Vifa (Tymphany) is sold as “full range woofer”. As tested by manufacturer, doubtless done in a baffle, on axis performance looks impressive to >10kHz, with rapid roll off beyond 2kHz off axis, and recommended use 40Hz-4kHz.
The SEAS woofer as mounted is highly omni directional somewhat beyond 1kHz; based on prior knowledge and a brief measurement survey the driver is used with steep crossover at 2kHz.
The Vifa driver was measured extensively to get a good grasp of its performance characteristics. A series of measurements from front and back at 27”suggest an acoustic source that starts at neck of driver cone. The driver was rotated in vertical plane through the cone’s neck at 5° intervals. Dual channel sweeps where used with one for loop back timing reference and the other for response measurement. The use of timing reference and use of measuring tape combined together helped in keeping highly fixed measurement distance. Front of driver on axis is 0°. Backside measurements were made from 90-180 degrees and front side measurements from 0-60 degrees(Yes, 75° is missing). Overlays of results indicate highly dipole radiation pattern to 2kHz. Measurements remain well organized to 4kHz. Above 4kHz cone geometry takes over.
The 0° and 15° degree shows some plausible potential use of the driver full range to 14-15kHz
Overlays 0-60 degrees:
Overlays 90-180 degrees:
A choice was made to first explore driver alignment with Vifa rim centered above SEAS dust cap. This puts Vifa acoustic center about 1” behind SEAS acoustic center. 1” represents ½ to ¼ wavelengths about an order of magnitude shorter than 2kHz upper range of driver overlap. Driver effective diameters at 1-2kHz and apparent acoustic centers in this range are likely larger factor in polar pattern formed by superposition of each driver’s polar pattern.
Vifa driver connected as microphone with 220Hz signal to SEAS was used in finding driver position minimizing driver interaction. Vifa rim above center of SEAS dust cap produced best null, indicating equal energy delivery to front and back of Vifa from SEAS. Vifa rim is 1” above SEAS driver’s dust cap.
Great results were obtained for Pluto Clone with 2” tweeter when reference measurements from single measurement point located 9” from face of tweeter, and slightly off of tweeter axis. Direct to reflected ratio is sufficient for direct inversion using Kirkeby method in achieving equalization filters. With Pluto Clone development measurements from 2’ contained too many reflected signals, mostly floor/ceiling reflections, leading to great group delay at specific frequencies. Application of Kirkeby to such measurements leads to extreme ringing at certain frequencies, readily heard when inverse filter is convolved with sweep or music signals. This type of filter is only valid at measurement location. Anticipating this and dipole behavior of reinforcement/cancellation as wavelengths become shorter than driver diameter, and tempered by cone geometry influence near/far, a single measurement point for drivers was chosen about 12” from driver centers, and chosen 15° off axis of Vifa so to capture the flatter high frequency response. Direct use of measurements with Kirkeby resulted in ringing behavior. Application of Blackman-Harris 7 term window via REW with 15ms setting prior to Kirkeby produced working results. Windowing of result to 15ms still provides low frequency information within 1dB of large window results whilst suppressing unwanted reflections. Kirkeby filters applied to respective drivers flatten their responses.
Woofer filter is band pass filtered to 50Hz-2kHz, tweeter is filtered 200Hz-15kHz. Results sum over 200Hz-2kHz range. Secondary filter is used to shelve each driver’s response down 6.02dB across 200Hz-2kHz overlap region. Applying Kirkeby inverse transform to sum of 200Hz high pass filter with 2kHz low pass filter generates the secondary filter. Result is flat sum with monopole behavior 50Hz-200Hz, cardioid behavior 200Hz-2kH, and dipole behavior above 2kHz that is shaped by cone geometry.
Raw Crossover:
DSP:
J River Media Player is used for playback of sweep signals, convolution of sweeps with filter kernels, and recording of microphone responses. Previous testing finds software bit perfect. Here are frequency response overlays of measured results 0-180 degrees at intervals of 15 degrees. Microphone is placed 9” from edge of woofer pipe at height of tweeter axis. Tip of microphone is sighted through to protractor ruling around pipe top, and against center of woofer dust cap for achieving rotational alignment. Sweeps are exponential 2Hz-22050Hz with 262144 samples. A series of four sweeps with ½ seconds of silence are used as stereo track. Signal polarity of 2nd sweep of track 1 (woofer) and 3rd sweep of track 2 (tweeter) have polarity inverted. Resultant test sequence is: 1) normal woofer with normal tweeter, 2) inverted woofer with normal tweeter, 3) normal woofer with inverted tweeter, and 4) is repeat of 1). This format allows for sums and differences for verifying integrity of data and extracting images for solo woofer and solo tweeter responses. The four sweep periods are 284194 samples. Each isolated block is convolved with inverse sweep, obtaining impulse response. Resultant IR data are ported into REW for generating overlays of frequency responses.
Using Room EQ Wizard software, frequency response overlay views of 13 measurements 0-180 degrees for normal woofer polarity and for reverse woofer polarity is set up. Flat response region for 0 degree normal woofer polarity measurement across 300Hz-800Hz is offset to 0dB and all other results shifted by same offset. The same plot colors are used for corresponding rotation angles for both overlay views:
With woofer polarity reversed:
Monopole behavior is seen centered at about 55Hz.
Strong cardioid behavior is seen 200Hz-1kHz, indicative both of good monopole driver behavior and of good dipole behavior.
Measurements with microphone at reference point:

The SEAS woofer as mounted is highly omni directional somewhat beyond 1kHz; based on prior knowledge and a brief measurement survey the driver is used with steep crossover at 2kHz.
The Vifa driver was measured extensively to get a good grasp of its performance characteristics. A series of measurements from front and back at 27”suggest an acoustic source that starts at neck of driver cone. The driver was rotated in vertical plane through the cone’s neck at 5° intervals. Dual channel sweeps where used with one for loop back timing reference and the other for response measurement. The use of timing reference and use of measuring tape combined together helped in keeping highly fixed measurement distance. Front of driver on axis is 0°. Backside measurements were made from 90-180 degrees and front side measurements from 0-60 degrees(Yes, 75° is missing). Overlays of results indicate highly dipole radiation pattern to 2kHz. Measurements remain well organized to 4kHz. Above 4kHz cone geometry takes over.
The 0° and 15° degree shows some plausible potential use of the driver full range to 14-15kHz
Overlays 0-60 degrees:

Overlays 90-180 degrees:

A choice was made to first explore driver alignment with Vifa rim centered above SEAS dust cap. This puts Vifa acoustic center about 1” behind SEAS acoustic center. 1” represents ½ to ¼ wavelengths about an order of magnitude shorter than 2kHz upper range of driver overlap. Driver effective diameters at 1-2kHz and apparent acoustic centers in this range are likely larger factor in polar pattern formed by superposition of each driver’s polar pattern.
Vifa driver connected as microphone with 220Hz signal to SEAS was used in finding driver position minimizing driver interaction. Vifa rim above center of SEAS dust cap produced best null, indicating equal energy delivery to front and back of Vifa from SEAS. Vifa rim is 1” above SEAS driver’s dust cap.
Great results were obtained for Pluto Clone with 2” tweeter when reference measurements from single measurement point located 9” from face of tweeter, and slightly off of tweeter axis. Direct to reflected ratio is sufficient for direct inversion using Kirkeby method in achieving equalization filters. With Pluto Clone development measurements from 2’ contained too many reflected signals, mostly floor/ceiling reflections, leading to great group delay at specific frequencies. Application of Kirkeby to such measurements leads to extreme ringing at certain frequencies, readily heard when inverse filter is convolved with sweep or music signals. This type of filter is only valid at measurement location. Anticipating this and dipole behavior of reinforcement/cancellation as wavelengths become shorter than driver diameter, and tempered by cone geometry influence near/far, a single measurement point for drivers was chosen about 12” from driver centers, and chosen 15° off axis of Vifa so to capture the flatter high frequency response. Direct use of measurements with Kirkeby resulted in ringing behavior. Application of Blackman-Harris 7 term window via REW with 15ms setting prior to Kirkeby produced working results. Windowing of result to 15ms still provides low frequency information within 1dB of large window results whilst suppressing unwanted reflections. Kirkeby filters applied to respective drivers flatten their responses.
Woofer filter is band pass filtered to 50Hz-2kHz, tweeter is filtered 200Hz-15kHz. Results sum over 200Hz-2kHz range. Secondary filter is used to shelve each driver’s response down 6.02dB across 200Hz-2kHz overlap region. Applying Kirkeby inverse transform to sum of 200Hz high pass filter with 2kHz low pass filter generates the secondary filter. Result is flat sum with monopole behavior 50Hz-200Hz, cardioid behavior 200Hz-2kH, and dipole behavior above 2kHz that is shaped by cone geometry.
Raw Crossover:

DSP:
J River Media Player is used for playback of sweep signals, convolution of sweeps with filter kernels, and recording of microphone responses. Previous testing finds software bit perfect. Here are frequency response overlays of measured results 0-180 degrees at intervals of 15 degrees. Microphone is placed 9” from edge of woofer pipe at height of tweeter axis. Tip of microphone is sighted through to protractor ruling around pipe top, and against center of woofer dust cap for achieving rotational alignment. Sweeps are exponential 2Hz-22050Hz with 262144 samples. A series of four sweeps with ½ seconds of silence are used as stereo track. Signal polarity of 2nd sweep of track 1 (woofer) and 3rd sweep of track 2 (tweeter) have polarity inverted. Resultant test sequence is: 1) normal woofer with normal tweeter, 2) inverted woofer with normal tweeter, 3) normal woofer with inverted tweeter, and 4) is repeat of 1). This format allows for sums and differences for verifying integrity of data and extracting images for solo woofer and solo tweeter responses. The four sweep periods are 284194 samples. Each isolated block is convolved with inverse sweep, obtaining impulse response. Resultant IR data are ported into REW for generating overlays of frequency responses.
Using Room EQ Wizard software, frequency response overlay views of 13 measurements 0-180 degrees for normal woofer polarity and for reverse woofer polarity is set up. Flat response region for 0 degree normal woofer polarity measurement across 300Hz-800Hz is offset to 0dB and all other results shifted by same offset. The same plot colors are used for corresponding rotation angles for both overlay views:

With woofer polarity reversed:

Monopole behavior is seen centered at about 55Hz.
Strong cardioid behavior is seen 200Hz-1kHz, indicative both of good monopole driver behavior and of good dipole behavior.
Measurements with microphone at reference point:

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