XO - Excel Crossover Design Tools
Parallel XO Series XO Tweeter Model
Target
Response Models
The target function is the acoustic design criteria for your system. In order to build a target model, you must
set the (acoustic) crossover frequency, slope, designed SPL, and section
roll-off shapes. As in all of the XO
design spreadsheets, you must initialize the frequency spectrum. Select the number of data points to use, and
the lowest and highest frequency to be calculated. Once you have set these, the output data can
be stored in ASCII text files. I have
chosen the format of one title line “* Frequency Mag Phase” followed by the
standardized format of one data line per calculated value set.
You can use the predefined shapes (Butterworth, Linkwitz-Riley, Bessel,
etc.), or model your own shapes by inputting the required coefficient
values. I have loosely followed the
convention described by W. Marshall Leach in his Filter Potpourri article.
Basically you can consider the low pass transfer functions to be: T(s) =
K/D(s), where K determines the passband SPL, and D(s) is the polynomial that
describes the transfer function. Rather than deal with a second polynomial in
the numerator, the frequency transformation for the High Pass function is p
-> 1/p where p = s/wc. Siince I have modeled a 4th
order function, the polynomial is:
D(s) = c0 + c1(s/wc)
+ c2(s/wc)2 + c3(s/wc)3
+c4(s/wc)4, where
cn are the function's coefficients,
s = jw = j*2*PI*f and
wc = 2*PI*fc
is the crossover frequency in radians.
The high pass coefficients follow the same input format as the low pass
coefficients using a 1/s transformation. For advanced users, it's possible to
build non-symmetric HP and LP sections as well. In order to force a transfer
function with different order, just select the custom shapes, input your
coefficients, and zero out any coefficients that are not used.
It is common to see a 12 dB/octave roll-off for tweeters and either 12 or 24 dB/octave roll-off for woofers depending on LF box alignment. The acoustic crossover between drivers frequently uses a 24 dB/octave Linkwitz-Riley target while sound reinforcement systems tend to use Butterworth (constant power) alignments to maintain a more uniform sound pattern.
Description
Here's a run down of the Inputs and controls that make this thing work:
F_Min / F_Max - These values set the bandwidth for all calculations. A standard range may be considered 20 - 20,000 Hz, but note that whenever a data file is imported into the destination spreadsheet, the frequency range will be interpolated to match the destination frequency range.
# Data Points – The number of data points for which calculations take place. The frequency calculations determine an increment multiplier such that the bandwidth (Fmax – Fmin) is achieved using the desired number of data points. The maximum value for the number of data points is 540.
Spl – The target SPL desired.
Fxo (Hz) - The crossover frequency is input either manually or by slide switch. All crossover value calculations are based on this crossover frequency.
LP/HP Filter types - The filter shape is controlled by using the scroll selection buttons. In addition to standardized shapes, you may input custom values by selecting “Custom” and inputting the desired transfer function coefficients.
LF Rolloff – The designed rolloff of the low frequency driver. You may select predefined shapes or use custom transfer function coefficients. See note below.
HF Rolloff – The tweeter high frequency rolloff characteristic. You may select predefined shapes or use custom transfer function coefficients. See note below.
XO Shape – The crossover rolloff characteristic. You may select predefined shapes or use custom transfer function coefficients. See note below.
Note: All white shaded data fields must contain numeric values to work in the “Custom” setting. If a space is used to blank input instead of a Zero, the calculations become corrupted. In standardized coefficient form, c=1.
“Never discourage anyone…who
continually makes progress, no matter how slow.”
Plato
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