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Lowther Rear-Horn SimulationHornsimulaton with the program AJ-Horn ( www.aj-systems.de ) , for the Lowther DX3 fullrange driver by MARVIN The TSP of the driver were taken from Lowther's UK - website and Speaker Unit is checking them with the crosscalc feature : 
The TSP of the driver are the basis for all the simulations here and the first setup is a backloaded - Horn that is 238cm long ( which is a quarter-wavelength of 36Hz , the drivers basic resonance ) with three different mouth-sizes - 1000cm2 , 2000cm2 , 4000cm2 . The red line is the drivers response in a closed box of 1500Liters , which is 10 times the drivers equivalent-volume Vas : 
In the status bar you can see the cursor readouts , actually the anchor is on the red line at 79Hz and at a level of 90.2dB . The difference to the position where the cursor was at the time the screenshot were taken is shown by the info bar DELTA : 0Hz - 7.9dB , this means there is 0Hz difference , so the cursor was placed at 79Hz too and the actual difference at that same frequency is +7.9dB over the reference ( which is 90.2dB ) , 90.2dB plus 7.9dB gives 98.1dB , this is the value you see at the left . The net volume of each Horn is calculated by AJHorn immediately : Mouth area - 1000cm2 = 121Ltr , 2000cm2 = 191Ltr , 4000cm2 = 308Ltr . The horn contour that has been used in the last simulation is purely exponential , for the investigation of the effects of other contours please look at one of the next pictures . OK , now the same situation as above but only a frontloading of the driver , to give an impression how the ripple changes with different mouth - areas : 
Well , not much influence on the ripple … and the price to pay for a slightly lower ripple is a very large cabinet volume of over 300Liters . ( ripple = Q-factor of the horn-resonances ; i. e. the ratio between the height and the width of every resonance can be expressed by the factor Q ) The frequency responses of most bass-horns are pretty uneven , not only due to the ripple but also coming from dips that occur when the time-delay of the backwards radiated wave into the horn creeps out of the horn mouth , in principle a comb-filter effect . The comb-filter effect comes into existence when two broadband-signals are summed up somewhere but one signal is delayed in time which results in canceling at all frequencies where the time-delay is equal to a half wavelength of a frequency or even-multiplies of it ) . At this point of the simulation it seems to be a good idea to take a look what influence other horn-contours will have , AJHorn has several contours to offer : ( we do not use the parabolic expansion , it is of no use for horns ) 
The following comparison show four responses of the actual frontloaded DX3 driver , each one with a different contour : 
Net volume of each contour is : 120Ltr = exponential , 100Ltr = hyperbolic , 99Ltr = tractrix , 132Ltr = Conical . Please notice that the tractrix contour used here do not open at the mouth with an angle of 180 degree as it is common with full sized midrange horns ( frontloaded designs and no foldings ) . Means some people would expect the most gain will be generated by the tractrix contour , but I think this is only the case when the length/diameter - ratio of the horn is better well-suited to the wavelength of the lower cut-off , we should simulate this with AkAbak on another fine simulation day … The 10% increase of the net volume by using the conical contour seems to be very acceptable , because it generates over 4dB more output , so we use it in the further design process . Now let's look how the response changes for the frontloaded condition when a pressure-chamber is used : 
… and now the change in response when the same backchamber ( = pressure chamber ) sizes are used , but we have switched to a backloaded - horn : 
You see by the picture above why a larger pixel format has been chosen , the overlay of all curves in a smaller picture would be a real mess … For those who are interested in the drivers cone-excursion at 2.83 input voltage and the input impedance for the 4Ltr backchamber version , they can check the actual design in the next picture : 
Most of the terms above in German can be guessed by a little bit of thinking what can be the equivalent english term , so it seems not really necessary to explain the last screenshot further … but to be more fair some words should be translated : Konisch = conical ; Halbraum = 2pi radiation ; Betha1/Betha2 = resistive damping factor "Betha" in the first or last or both halfs of the horn contour ( a factor of 1000 is a maximum ) ; Abstand = distance ( in meters ) ; VHorn = net volume of the actual calculated Horn/TL ; VVK = net volume of the pressure chamber ( backchamber ) ; AH = area of the throat ; dl = an optional time-delay to account for different locations of the horn mouth , this value can be positive or negative ( depends on how different the position of the mouth is , relative to the distance of the virtual reference point , which is given by the distance "Abstand" , the effect is to move the mouth virtually back or forth , on some designs an important factor ) ; h , b = height * width = mouth area ( in any case AJHorn calculates a round Horn , only for the contour-file of Horn-designs who use a constant width for the cabinet this is of some importance ) , b = width / remark = the mouth size can be smaller than the drivers area , tapered TL's can be simulated that way , and also the beginning of the TL or Horn can be larger than the drivers area ) ; Anzahl = how much drivers are used or simply the number of drivers connected in parallel , TSP's are automatically corrected by using more than one driver ; Xmax = the drivers maximum cone travel ( can be linear or only a mechanical excursion , no information yet if this is a one-way peak excursion in the simulation or anything else .. ) ; Eff. Membranauslenkung in mm = effective excursion of the diaphragm in millimeters ( whatever "effektiv" means , Mr. Jost should be more precise here , we are *pro's* and we want pro-stuff all of the time .. :-) ; l = simply the length of the Horn ( or TL ) - it seems Mr. Jost has added +5% or so to account for an end correction , therefore the length which the user inserts into the input box is an *effective* length , but no hint about it in the manual , it seems Mr. Jost likes to keep some stuff unpublished … :-) ; Elektrische Impedanz in Ohm = electrical impedance in Ohms ; Ue = input voltage in volts ; Kontour listen = list of values for the actual Horn/TL - contour : Horn/TL - length > Horn/TL - diameter >> expansion of the contour with a cabinet of constant width . OK , back to real horn design : What happens when the mouth is placed 30 or 60cm forth to the reference point ?? See what it is going to be : 
Now the reverse situation , location of horn mouth is set back : 
Explanation of the simulations who were shown in the last two pictures : Any simulation that AJHorn does is done under the ( hidden ) prerequisite , that the sound radiates as such as it were in free space ( no room gain or standing waves or early reflections or discrete reflections like floor reflection ) and also no directivity of the mouth has an effect . In practice the location of the mouth on the back of the cabinet would surely not lead to an increase of 6dB @ 60Hz of the overall efficiency of the speaker in any room ( standing free in the room , so that room-gain is no issue here ) . What the simulation simply does , is to make the phase difference larger around the lower cut-off , between the outputs from driver and mouth , this means the radiation is more efficient in this range . In both cases ( positive or negative additional delay ) , there is an improvement regarding the first time-delay induced dip in the response , with a better tendency when the mouth is located further back ( for pro's : the phase rotation is faster with increasing frequency , resulting in lesser and smoother dips ) . When I write another article , it will be more concentrated on how variations of the drivers Thiele-Small-Parameters have an influence on the overall performance , especially linearity , lower cut-off and efficiency , in parallel we compare the F3 - frequency of reflex designs with horn designs , with respect to the net volume . Means for a given efficiency and lower cut-off frequency , what size must the reflex box have and what driver - TSP's are needed when the net volume is equal for both bass-loading principles . For every doubling of the efficiency you must also double the box volume , but lowering F3 one octave requires the increase of the box volume by a factor of 8 !! Now the question is , at what point will a horn of a certain size perform better regarding F3 and efficiency ??? Actually we don't know , but should be fun to simulate … Is someone willing to make a prediction what principle win the contest ?? Maybe we are surprised , maybe not - who knows … Goodbye for now - MARVIN Top
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