21 Temmuz 2010 Çarşamba

Measurements and Crossover Design

Measurements
For the measurements, I wrote a simple code in Matlab. Using the code, the computer outputs a steady sine or sweep and takes input from the sound card or user prompt. With the help of this I could measure frequency response and other stuff like impedance, output voltage etc. Here is a piece of the code for frequency measurement where sound card input and outputs are utilized:

for measureno=1:3

N=48000;
T=10;
A=0.1;
f1=500;
f2=20000;

%generate sine with function "generatesine"
[signal,freqArray,tArray,signalwpre]=generatesine(f1,f2,N,T,1,1);

pause

%apply amplitude and plot!
signal=A.*signal;
signalwpre=A.*signalwpre;
plot(signalwpre)

%%do the recording
ai=analoginput('winsound');
mikrofon=addchannel(ai,1);
set(ai,'SampleRate',N);
set(ai,'SamplesPerTrigger',T*N);
set(ai,'TriggerChannel',mikrofon)
set(ai,'TriggerType','Software')
set(ai,'TriggerCondition','Rising')
set(ai,'TriggerConditionValue',0.01)
set(ai,'TriggerDelayUnits','Seconds')
set(ai,'TriggerDelay',0.5)

ao = analogoutput('winsound');
addchannel(ao,1:2);
set(ao,'SampleRate',N)
putdata(ao,[signalwpre' signalwpre'])
start(ao)

start(ai);
wait(ai,T+4);
stop(ao);
[rec,time] = getdata(ai);
plot(rec)

%for test purposes only
%rec=signal;

if max(rec)>=1
    warning('ADC clip etti sanki')
elseif max(rec)<0.1
    warning('Seviye çok düşük bebeğim')
end

%%do the fourier transform--dB value has no reference
cp=2/length(rec).*fft(rec*10^8);
cw=(abs(cp.^1)).^2;

%plot cw to SPL with smoothing
cw=smooth(cw,200*T-1);
Lw=10*log10(cw);
SPL(:,measureno)=abs(Lw);
freq=(1:length(cw))/T-1;
semilogx(freq,SPL);

delete(ao)
end

AXIS([f1 f2 max(max(SPL))-40 max(max(SPL))+10])

There are lots of things to add to the code (e.g. windowing, calibration, octave averaging) but it helps me quite well as it is.

The Crossover
Patrick has second order crossovers for the mid-bass speakers and the tweeter. The bandpass section has a first order low-pass filter, the side-fills have a first order high-pass filter.

The second order crossovers were intended to be in Linkwitz-Riley alignment because the speakers on the cabin are placed quite away from each other and problems with phase matching is expected. Linkwitz-Riley alignment is regarded as the alignment least sensitive to loudspeaker placement because of the -6dB crossover point. But because the Linkwitz-Riley alignment required some very large size capacitors, I decided to use Butterworth filters with distant cut-off frequencies. This wasn't as flat or as coherent as the Linkwitz-Riley alignment but I thought I could spare some from the mid frequencies.

The final responses, measured from three different points in the vertical axis are in the graphs below. Those three points were selected so that each has a 120° phase angle difference from the previous one at crossover point.

 Patrick's Frequency Response

The red-green one is the reference where two speakers are exactly in phase. This one translates to a few degrees up in the vertical axis which is the usual listening angle when Patrick is on the ground and people are standing up or sitting down in far field. To account for the poor high frequency dispersion of the tweeter a little extra gain was added using the tone controls. This helps for a more neutral response overall in open field. The effects of this gain is clearly visible above 8kHz.

Please note that the graphs above were measured using a Behringer ECM8000 microphone. This is not a very high quality microphone. Unfortunately I couldn't lay my hands on a proper microphone this time. Anyway, the measurements were done from near field with high level signals so noise was not an issue. The unflat frequency response of the microphone, on the other hand, should always be taken into account during measurements.


Frequency Response of My Measurement Microphone

Response And Power Handling In Low Frequencies
The low frequency section was modelled using Unibox loudspeaker box modelling spreadsheet. This is a complete tool for low frequency cabin design. Below are the final responses. I have added the results of the two low frequency sections using Excel, one in phase and one 90° off-phase. After setting up the speaker, I have matched phase by measuring output of both sections at the crossover frequency. They have matched pretty well (better than 30°) at crossover frequency after reversing the phase of the bandpass section. So the final response is expected to be similar to the curve with Theta=0 sum.


Low Frequency Response of Patrick Modelled With Unibox

This graph also shows maximum power handling of Patrick. The results shown are maximum attainable SPL values limited by driver excursion in the bandpass section.

The tone controls have been tuned to have a similar rise with the curves shown above so that reducing the bass level using the tone controls, a flat response is attained. This way, the loudspeaker is fit for use indoors and outdoors in open field equally. I leave the bass control at -3dB in open field which works quite well.

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