in Audio projects synergy horn ~ read.

Horn Modeling

Given the complexity of designing a Synergy Horn very few programs are available to model the predicted response. HornResp will work to some extent but given the complexity only Akabak really has the power to do the job. Unfortunately Akabak will be unapproachable to many people unless they have a background in programming or a good grasp of logic.

I built my Akabak models in three separate scripts for each of the driver groups. I have added comments where possible to give you an idea of what the script is doing. Akabak is not for the faint-hearted.

Synergy Horn Design Perspective

The High-Frequency Compression Driver - BMS 4555

BMS 4555 Compression Driver

This model uses the BMS 4552ND driver for reference as it is the only one that I could find the driver parameters for. Although the BMS 4555 is likely quite different I am not so worried about the compression driver response as it should be relatively straight forward compared with the midrange and low frequency driver configuration. This is one of the drivers that Danley Sound Labs use in many of their Synergy Horns so I thought it would be a good starting point.

System 'SynergyCompression'  
Def_Driver 'CompressionDriver' | (temp)BMS 4552ND compression driver  
Meas_DoNotModify  
Sd=15.52cm2  
Bl=6.21Tm  
Cms=140E-06m/N  
Rms=0.40Ns/m  
Fs=850Hz  
Le=0.09mH  
Re=6.20ohm  
ExpoLe=0.618  
Def_Const | Constants must be entered in SI format as conversions are not calculated and will error. 1cm corresponds to 1e-2  
{
CDRC_Vol  = 0.08e-3;  |Comp Driver Rear chamber volume (litres)  
CDRC_Len  = 0.84e-2;  |Comp Driver Rear chamber average length (cm)  
CDTC_Vol  = 0.75e-6;  |Comp Driver Throat chamber volume (cc)  
CDTC_Area = 15.52e-4; |Comp Driver Throat chamber cross-sectional area (sq cm)  
CDRC_Area = CDRC_Vol / CDRC_Len; |Conversions for CompDriver  
CDTC_Len  = CDTC_Vol / CDTC_Area;  
| Define Horn Segment Areas
areaSegment1 = 0016.00e-4; |Comp Driver input (sq cm)  
areaSegment2 = 0106.92e-4; |Mid Port input (sq cm)  
areaSegment3 = 0957.90e-4; |Low Port input (sq cm)  
areaSegment4 = 0957.91e-4; |Low Tap input (sq cm)  
areaSegment5 = 2222.18e-4; |Horn Mouth before flare(sq cm)  
areaSegment6 = 4379.79e-4; |Horn Mouth after flare(sq cm)  
| Define Horn Segment Lengths
lengthSegment1 = 04.48e-2; |WG1 axial length(cm)  
lengthSegment2 = 14.52e-2; |WG2 axial length(cm)  
lengthSegment3 = 00.01e-2; |WG3 axial length(cm)  
lengthSegment4 = 11.41e-2; |WG4 axial length(cm)  
lengthSegment5 = 04.43e-2; |WG5 axial length(cm)  
}
| One compression driver
Driver 'Compression Driver' Def='CompressionDriver' Node=1=0=52  
Duct 'CompFrontChamber' | Compression Driver front throat chamber  
Node=52=110  
SD={CDTC_Area}  
Len={CDTC_Len}  
Visc=0  
| Define Waveguide
Waveguide 'WG1'  
Node=110=120  
STh={areaSegment1}  
SMo={areaSegment2}  
Len={lengthSegment1}  
Conical  
Waveguide 'WG2'  
Node=120=130  
STh={areaSegment2}  
SMo={areaSegment3}  
Len={lengthSegment2}  
Conical  
Waveguide 'WG3'  
Node=130=140  
STh={areaSegment3}  
SMo={areaSegment4}  
Len={lengthSegment3}  
Conical  
Waveguide 'WG4'  
Node=140=150  
STh={areaSegment4}  
SMo={areaSegment5}  
Len={lengthSegment4}  
Conical  
Waveguide 'WG5'  
Node=150=160  
STh={areaSegment5}  
SMo={areaSegment6}  
Len={lengthSegment5}  
Conical  
Radiator 'Horn mouth'  
Node=160  
SD={areaSegment6}  

Akabak predicts the following response.

Compression Driver Predicted Response

The Midrange Drivers - Celestion TF0410MR

Celestion TF0410MR

This model uses four of the Celestion TF0410MR closed back 4" drivers firing into the horn approximately 4.5cm from the high-frequency compression driver through two 16mm diameter ports per driver.

System 'SynergyMidrange'  
Def_Driver 'MidrangeDriver' | Celestion TF0410MR - 4" woofer  
Sd=78.5cm2  
Bl=7.47Tm  
Cms=2.28E-05m/N  
Rms=1.30Ns/m  
fs=438.70Hz  
Le=0.61mH  
Re=5.69ohm  
Def_Const | Constants must be entered in SI format as conversions are not calculated and will error. 1cm corresponds to 1e-2  
{
Mc_Len=0.8e-2;  | Mid Throat Chamber length (height from cone to face)  
Mc_Dia=10.0e-2; | Mid Throat Chamber diameter (driver cone diameter)  
Mp_Len=1.8e-2;  | Mid Port length  
Mp_Dia=1.6e-2;  | Mid Port diameter  
| Define Horn Segment Areas
areaSegment1 = 0016.00e-4; |Comp Driver input (sq cm)  
areaSegment2 = 0106.92e-4; |Mid Port input (sq cm)  
areaSegment3 = 0957.90e-4; |Low Port input (sq cm)  
areaSegment4 = 0957.91e-4; |Low Tap input (sq cm)  
areaSegment5 = 2222.18e-4; |Horn Mouth before flare(sq cm)  
areaSegment6 = 4379.79e-4; |Horn Mouth after flare(sq cm)  
| Define Horn Segment Lengths
lengthSegment1 = 04.48e-2; |WG1 axial length(cm)  
lengthSegment2 = 14.52e-2; |WG2 axial length(cm)  
lengthSegment3 = 00.01e-2; |WG3 axial length(cm)  
lengthSegment4 = 11.41e-2; |WG4 axial length(cm)  
lengthSegment5 = 04.43e-2; |WG5 axial length(cm)  
| Amplifier output impedance (ohms)
Rg=0.35;  
}
| Four Closed Back Midrange Drivers mounted directly to baffle (through 'Throat Chamber')
Driver 'Mid Driver A' Def='MidrangeDriver' Node=2=10=64  
Driver 'Mid Driver B' Def='MidrangeDriver' Node=10=0=65  
Driver 'Mid Driver C' Def='MidrangeDriver' Node=2=20=66  
Driver 'Mid Driver D' Def='MidrangeDriver' Node=20=0=67  
| Four 'Throat Chambers' (i.e. the area between the driver cone and the wooden baffle)
Duct 'Mid Throat Chamber A' Node=64=68 dD={Mc_Dia} Len={Mc_Len}  
Duct 'Mid Throat Chamber B' Node=65=69 dD={Mc_Dia} Len={Mc_Len}  
Duct 'Mid Throat Chamber C' Node=66=90 dD={Mc_Dia} Len={Mc_Len}  
Duct 'Mid Throat Chamber D' Node=67=91 dD={Mc_Dia} Len={Mc_Len}  
| Eight Ports (2 per 'Throat Chamber')
Duct 'Mid Port A1' Node=68=120 dD={Mp_Dia} Len={Mp_Len}  
Duct 'Mid Port A2' Node=68=120 dD={Mp_Dia} Len={Mp_Len}  
Duct 'Mid Port B1' Node=69=120 dD={Mp_Dia} Len={Mp_Len}  
Duct 'Mid Port B2' Node=69=120 dD={Mp_Dia} Len={Mp_Len}  
Duct 'Mid Port C1' Node=90=120 dD={Mp_Dia} Len={Mp_Len}  
Duct 'Mid Port C2' Node=90=120 dD={Mp_Dia} Len={Mp_Len}  
Duct 'Mid Port D1' Node=91=120 dD={Mp_Dia} Len={Mp_Len}  
Duct 'Mid Port D2' Node=91=120 dD={Mp_Dia} Len={Mp_Len}  
| Amplifier output impedance 
Resistor 'Amplifier Rg'  
Node=1=2  
R={Rg}  
| Define Waveguide
Waveguide 'WG1'  
Node=110=120  
STh={areaSegment1}  
SMo={areaSegment2}  
Len={lengthSegment1}  
Conical  
Waveguide 'WG2'  
Node=120=130  
STh={areaSegment2}  
SMo={areaSegment3}  
Len={lengthSegment2}  
Conical  
Waveguide 'WG3'  
Node=130=140  
STh={areaSegment3}  
SMo={areaSegment4}  
Len={lengthSegment3}  
Conical  
Waveguide 'WG4'  
Node=140=150  
STh={areaSegment4}  
SMo={areaSegment5}  
Len={lengthSegment4}  
Conical  
Waveguide 'WG5'  
Node=150=160  
STh={areaSegment5}  
SMo={areaSegment6}  
Len={lengthSegment5}  
Conical  
Radiator 'Horn mouth'  
Node=160  
SD={areaSegment6}

Akabak predicts the following response. Interestingly, most models that I have seen by people on various forums have a predicted and measured dip in frequency response which is shown here in the region between 500-1000Hz. It is approximately 4dB and should be able to be equalised out with the DEQX.

You can clearly see the bandpass created by the ports as the response drops sharply below 300Hz and above 1500Hz. This bandpass effect is the beauty of the Danley design as the steep rolloff limits the driver's distortion by acoustically removing any artefacts caused by the driver producing excessive low or high frequencies. If you had a smoother response (i.e. without the 500-1000Hz dip) you probably wouldn't even need an electrical crossover.

Midrange Predicted Response

The Bass Drivers - Eminence Legend BP102

Eminence Legend BP102

I modelled many drivers with the goal of achieving maximum low frequency output whilst still being able to hit >115dB and not overload the driver or the ports. I finally found the Eminence Legend BP102 driver which was available locally, claims 92dB efficiency (or ~95dB with two drivers), reasonable power handling and a response which extends down to almost 65-70Hz.

My biggest constraint was finding locally available drivers which were not exorbitantly expensive. This ruled out Neodymium due to the massive price increases created by recent supply side issues and most of the European drivers due to high shipping prices or lack of availability.

The model uses two drivers per 40 litre cabinet firing into the horn via individual 70mm diameter ports and have a second 70mm port of 150mm length tapped into the horn at the same depth relative to the compression driver.

System 'SynergyBass'  
Def_Driver 'LowDriver' | Eminence Legend BP102  
Sd=334.5cm2  
Bl=9.47Tm  
Cms=5.72E-04m/N  
Rms=1.48Ns/m  
fs=35.0Hz  
Le=0.83mH  
Re=5.59ohm  
Def_Const | Constants must be entered in SI format as conversions are not calculated and will error. 1cm corresponds to 1e-2  
{
Lc_Len=02.5e-2; | Low Throat Chamber length (height from cone to face)  
Lc_Dia=24.0e-2; | Low Throat Chamber diameter (driver cone diameter)  
Lp_Len=01.8e-2; | Low Port length  
Lp_Dia=07.0e-2; | Low Port diameter  
Rt_Len=15.0e-2; | Low Rear Tap length  
Rt_Dia=7.0e-2;  | Low Rear Tap diameter  
| Define Horn Segment Areas
areaSegment1 = 0016.00e-4; |Comp Driver input (sq cm)  
areaSegment2 = 0106.92e-4; |Mid Port input (sq cm)  
areaSegment3 = 0957.90e-4; |Low Port input (sq cm)  
areaSegment4 = 0957.91e-4; |Low Tap input (sq cm)  
areaSegment5 = 2222.18e-4; |Horn Mouth before flare(sq cm)  
areaSegment6 = 4379.79e-4; |Horn Mouth after flare(sq cm)  
| Define Horn Segment Lengths
lengthSegment1 = 04.48e-2; |WG1 axial length(cm)  
lengthSegment2 = 14.52e-2; |WG2 axial length(cm)  
lengthSegment3 = 00.01e-2; |WG3 axial length(cm)  
lengthSegment4 = 11.41e-2; |WG4 axial length(cm)  
lengthSegment5 = 04.43e-2; |WG5 axial length(cm)  
}
| Define the Enclosure Size
Enclosure 'Low Rear Chamber' Node=70 Vb=40L Lb=20cm  
Driver 'Low Driver A' Def='LowDriver' Node=30=31=70=71  
Duct 'Low Throat Chamber A' Node=71=73 dD={Lc_Dia} Len={Lc_Len}  
Duct 'Low Port A1' Node=73=130 dD={Lp_Dia} Len={Lp_Len}  
Driver 'Low Driver B' Def='LowDriver' Node=31=0=70=72  
Duct 'Low Throat Chamber B' Node=72=74 dD={Lc_Dia} Len={Lc_Len}  
Duct 'Low Port B1' Node=74=130 dD={Lp_Dia} Len={Lp_Len}  
Duct 'Rear Tap 1' Node=70=140 dD={Rt_Dia} Len={Rt_Len}  
Duct 'Rear Tap 2' Node=70=140 dD={Rt_Dia} Len={Rt_Len}  
Waveguide 'WG1'  
Node=110=120  
STh={areaSegment1}  
SMo={areaSegment2}  
Len={lengthSegment1}  
Conical  
Waveguide 'WG2'  
Node=120=130  
STh={areaSegment2}  
SMo={areaSegment3}  
Len={lengthSegment2}  
Conical  
Waveguide 'WG3'  
Node=130=140  
STh={areaSegment3}  
SMo={areaSegment4}  
Len={lengthSegment3}  
Conical  
Waveguide 'WG4'  
Node=140=150  
STh={areaSegment4}  
SMo={areaSegment5}  
Len={lengthSegment4}  
Conical  
Waveguide 'WG5'  
Node=150=160  
STh={areaSegment5}  
SMo={areaSegment6}  
Len={lengthSegment5}  
Conical  
Radiator 'Horn mouth'  
Node=160  
SD={areaSegment6}

The resulting response prediction shows the drivers will be able to cover the ~70Hz to 300Hz (the lower end of the midrange drivers) range. My primary concern is the large response spike around 100Hz but I feel this can be dealt with with a combination of box tuning and equalisation.

My secondary concern is the strange upper end response at around 850Hz-900Hz however this is largely influenced by the volume between the driver cone and the baffle (shape of the cone) which I had to estimate until receiving the actual drivers. It is too bad as if it was a clean a roll-off as the midrange I would be very happy.

Bass Predicted Response

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