Resource to calculate, building and measuring Hi Fi Loudspeakers and more...

zondag 20 januari 2019
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    Calculate Baffle Diffraction Loss

At high frequencies, a loudspeaker radiates sound directly forwards. At low frequencies, the sound "leaks" around the sides and rear of the enclosure, and becomes omnidirectional.
This transition manifests itself as a loss of output on the forward axis at low frequencies, and in an anechoic chamber the loss is 6dB, or a halving of SPL. With a spherical enclosure the transition approximates a gentle first order step, with its centre at a frequency f3 which is related to the baffle dimensions (Olson, 1969), but with most speaker boxes diffraction from the edges of the baffle tends to add wiggles to the response which can be as large as the step.

In a system which uses drivers in a modest-sized enclosure, when the drivers themselves are optimised for flat response in a significantly larger baffle, there will therefore be a low frequency loss in the the axial response.
Unless compensation is applied for the baffle step, the speakers will sound subjectively thin.

The 6dB transition theory assumes that all of the energy that is not radiated into the forward half-space is lost for ever, where common sense tells me that a large part of it will be reflected back from the rear and side walls of a normal listening room. An alternative solution is to compensate for half the subjective low frequency loss, or 3dB.

So what, exactly, are we looking for from a driver that makes it suitable for our Open Baffle? The first of our interests is excursion, particularly excursion through a linear operating region. The reason this is so important is that there is no restoring force on the diaphragm as there would be in an enclosure. If you are considering adding bass equalisation to extend the response of your driver, then its excursion limits become more critical as you ask the driver to do more work as the frequency is lowered.

Next we need to look at the Qts of the driver which is defined by its moving mass, the springiness of the suspension and the electrical damping from its magnetic system.
Again, for a speaker in an enclosure, we would normally select a Q > 0.3 for a closed box speaker and a Q < 0.5 for a reflex design.
For an Open Baffle speaker using a passive crossover we actually require a driver with a high Qts. A Qts > 0.77 will mean that the amplifier will find it easier to drive the speaker as the frequency becomes closer to the system resonance.

By careful choice of resonant frequency we can use this to extend the response below the baffle cut off frequency.
Finally the search for low Fs, the frequency of fundamental resonance of the driver, goes out of the window. The only reason we look for a low Fs in a driver destined for use in an enclosure is because we know full well that the resonant frequency will be raised considerably, in many cases doubled, by the reactance of the air in the enclosure.
Thus, for a bass reflex or closed box speaker we normally look for an Fs of 30Hz or lower to achieve a system resonance, once the driver is in the box, of below 60Hz.

The Open Baffle, however, is not going to influence the driver resonance in this way. So we can choose a driver Fs knowing that this is going to be close to our final system Fs. Figures in the 40-60Hz region will do just fine.

Have a look at my Open Baffle Project

Eminence Alpha 15A
  • Resonant Frequency (fs) 41Hz
  • Total Q (Qts) 1.26
  • Surface Area of Cone (Sd) 856 cm2
  • Sensitivity 97.2dB

  • Calculate Baffle Step Correction Network

    Re [ohms] Lvc [mH]
    Wb [inches] Wb [cm] attenuation required ( 1-6 ):  [decibels]
    • Re is the DC resistance of the driver voice coil [ohms]

    • Lvc is the driver's voice coil impedance [mH]

    • Wb is the width of the baffle [inches or centimeter]

    • dB is the amount of attenuation required [decibels]
    • f3 is the frequency midpoint of the transition from 4pi space to 2pi space

    • Lbsc is the calculated baffle step correction circuit Inductor [mH]
    • Rz is the calculated Zobel Resistor [ohms]

    • Cz is the calculated Zobel Capacitor [uF]

    Baffle Step Correction Network Calculations:
    f3 [Hz]  
    Correction circuit Lbsc  [mH] Rbsc  [ohms]
    Zobel Rz  [ohms] Cz  [uF]

    Baffle Step Correction Network

    You should use the Zobel correction circuit placed across the driver's input terminals to flatten out any rising impedance.

    More about the Zobel correction circuit you will find here

    Frequency Response on ICE Baffle

    Frequency Response in Box

    The driver is flushed mounted on a large surface area.
    Basically these panels have little or no Diffraction Loss above 100Hz.

    Using calculated values of circuit components, a filter can be constructed and installed between the amp and the driver as shown in the schematic. Now you need to listen and tweak until it is just right for your room, system, and personal taste. I usually perform the following steps to arrive at the final configuration.

    1. Adjust the value of Rbsc
    a) If the bass is still too weak, then the amount of attenuation is too little. The value of Rparallel should be increased until the bass seems to be balanced with the rest of the SPL spectrum.
    b) If the speaker sounds dull and lifeless, the value of Rparalllel is too high. Reduce the value of Rparallel to bring life back into the music.
    c) Continue adjusting Rparallel until the speakers sound right to your ears. It is probably best to use acoustic music as a reference during this adjustment period.
    d) To remove the effect of the baffle step correction circuit completely, substitute a piece of speaker wire for Rparallel.

    2. Adjust the value of Lbsc
    a) Depending on the final value of Rparallel, the original calculated value of LBSC might need to be changed slightly. This sets the frequency range over which the baffle step filter attenuates the midrange and high frequencies. If the mid bass sounds depressed, then a lower value of LBSC should be used. I typically perform this adjustment last once I am satisfied with the balance, between the very low bass and the midrange, I have achieved with the resistor.
    b) Decreasing the value of LBSC will tend to warm the sound of the speaker if the previous value produced a depressed mid bass response.
    c) Always round down to the next available inductor size, having too low of an inductor value is a lot less problematic then having too large of an inductor value.

    To read more about baffle step compensation and cabinet edge diffraction, try the following links:

    Loudspeaker Diffraction Loss and Compensation
    Understanding Cabinet Edge Diffraction
    Baffle Step Compensation
    Eminence Alpha 15A Experimental Open Baffle Design Open Baffle Design