PSpice crossover design

[Rocky]

I'm doing my first PSpice-guided speaker design, and one thing baffles me about it: when I want to sum up two channels (tweeter and woofer), I calculated the SPLs could be joined by: 10*LOG10(V(bass)*V(bass)+V(tweeter)*V(tweeter)). I concluded this from the fact that SPLtotal=10*LOG10(10^(SPL1/10)+10^(SPL2/10)), and since SPLn=20*LOG10(V(signal)/1Vref), I get 10*LOG10(10^(20*LOG10(V(bass))/10)+10^(20*LOG10(V(tweeter))/10)), shortened down to the formula I mentioned in bold typewriting.

Now, this seems to give a weird result. I get SPLtotal below the tweeter SPL at one point , how can this be? All seems fine when I sum the outputs with the two-input sum component, and then plotting it by DB(sum), but I can't understand why that should be the way to go about it.. Can anyone explain this please?

EDIT: (note) I'm using the OrCAD 10.3 version, Capture CIS and PSpice A/D.

[MJK]

It has been probably almost 20 years since I messed around with PSpice doing exactly what you are doing. So my observation may be totally off the mark. In your final equation

SPL = 10*LOG10(V(bass)*V(bass)+V(tweeter)*V(tweeter))

should you be multiplying complex conjugates. You really want the square of the pressure magnitude to calculate SPL. By multiplying the voltages by themselves you are not calculating the magnitude, I am surprised the code did not puke trying to take the LOG of a number with an imaginary part or a phase.

There, that exhausts my limited knowledge (or ignorance) of PSpice.

[poobah]

Should be:

SPL = 10 * [LOG10(Vb^2) + LOG10(Vt^2)]

OR:

SPL = 20 * [LOG10(Vb) + LOG10(Vt)]

COMES FROM:

2 LOG (X) = LOG (X^2)

You have to convert the contributions of bass & tweeter to dB BEFORE you add them together.

[phase_accurate]

It is as simple as that: In Probe you add the two voltages (i.e. traces) in question. P-Spice will automatically do the complex summation. Then you set the Y-axis to log. A factor of 10 is equal 20 dB.

Regards

Charles

[bjorno]

Rocky,

It is not my intention to further confuse you, but if you do crossover design with Spice, FR measurements included, you should not forget the physical distances that comes with the real world for a useful result.

Then you must sum the sound pressure (magnitudes) from physical separated drivers at the specific real listening distance, before you calculate the SPL.

I think the sum of the sound pressure magnitude at a listening position; theta degrees of axis can be calculated from the equation

M= Sqrt(( L^2 + H^2 + 2*L*H*cos(x)); L and H are magnitudes of the crossover sections at crossover frequency and independent of theta.

Note this equation is only valid if the driver magnitudes are equal.

x=C+D+360*h/lamda+360*v*tan (theta)/lamda degrees, where C is the phase difference between High and Low crossover sections and D is the actual phase difference between the woofer and tweeter drivers, independent measured.

v and h are the vertical and horizontal separation between the centres of the drivers and lambda the wavelength of the frequency of interest.

My 2-cent contribution, ignoring baffle and room interaction.

B

[Rocky]

Thanks for the feedback, all of you. I need to chew a little on this info to resolve some of my (new) stupid questions before asking them out in public..

EDIT: one question..; In my Cadence CIS (full version, no demo), all entries in the PSpice->Markers->Advanced is grayed out (disabled). This is annoying as I'd like to try some of them, but can't figure out how to enable them..

[Calvin]

Hi,

I´m working with CircuitMaker. Here You can change scaling and do some mathematical operations with a right click in the waves-field.

What I like to know is, how You can add a special frequency response for example inverse RIAA or a speakers measured response?

jauu
Calvin

[Svante]

Assuming that the woofer and tweeter have the exact same sensitivity and that the both have an exactly flat response, even a bit outside their passbands, you could add the two voltages (using a complex add, including their phases) and calculate the level from that sum:

Lv=20*log10(Vt+Vw)

This equation will hold when the distances to the drivers' acoustical centre are equal. Off axis, vertically, they are typically not.

In real life you should also consider the contributions from the drivers' frequency responses (including phase which can be very important near the crossover frequency) and also their electrical impedances (also including phase), which will affect the resulting voltages across the drivers' terminals.

Designing crossovers is tricky business.

[Rocky]

Originally posted by Svante
Assuming that the woofer and tweeter have the exact same sensitivity and that the both have an exactly flat response, even a bit outside their passbands...(snip)

Ha, ha. The tweeter is flat enough, the woofer is another story (Seas L15RLY 5'' alu woofer). It has a 100Hz-300Hz peak of roughly 2dB. The voice coil inductance of 0.61mH makes sure the impedance rises really fast up in the band, and as of now, I don't use a zobel (I need the rising impedance for the filter to really bite at the cone breakups). Since the cone breaks up with a 12dB peak at 9kHz, I was forced to take action on it with a LC strap across the speaker terminals, resonating at the breakup peak, a 1.3mH coil looks into this. As the rising VC impedance makes the coil start to take effect below the crossover frequency (wich by the way sits on a small peak), I get a wide dip of a few dB centered around 1000Hz, where the peak of the baffle step will be located (i hope ). crossover is a bit above 2kHz, it varies mith my mood

Which leads me to my question to you, Svante.. I have used your "edge" for baffle step simulation, and it shows a huge 8dB peak centered around 1200Hz and a 6dB gain at high frequencies. This is for freespace, yes? Can I just divide those numbers by two for a reasonable prediction of what the response will be sitting close to a wall? (this is a bookshelf project. Not just bookshelf size.. and the bookshelf in question sits on a wall..)

EDIT: and there will probably be books next to it too.. I mean stacked close effectively widening the baffle.....(?)

Originally posted by Svante
In real life you should also consider the contributions from the drivers' frequency responses (including phase which can be very important near the crossover frequency) and also their electrical impedances (also including phase), which will affect the resulting voltages across the drivers' terminals.

I wonder how you guys get the phases to match up. Mine never seem to match regardless how many times I change polarity of the tweeter

In my phase plots so far, I have included a shift composed of a estimated physical offset between the voice coils of the two drivers (on axis), and how far a sound wave of the crossover frequency leads out from the tweeter as a result of this offset... correct?

Originally posted by Svante
Designing crossovers is tricky business.

Thanx, I did notice that already.

[bjorno]

I wonder how you guys get the phases to match up. Mine never seem to match regardless how many times I change polarity of the tweeter

Maybe this paper will help you find out what is necessary to take into consideration:

http://www.geocities.com/kreskovs/Phase-B.html

B