# Formula request - Power required for driver at xmax by frequency

#### Dave Bullet

I'm trying to model maximum excursion for several drivers in a spreadsheet.

I have Max SPL per frequency as a function of Sd and Xmax. Max SPL obviously increases as frequency increases, leading to power / thermal handling limits - credit to a Jeff Bagby post:

SPL= 20 * log(10) (1.18 / 0.00002 * Sd * Xmax / SQRT(2) * 2 * PI * F^2)

Where Sd is in Meters^2
Xmax is in Meters one-way linear travel
And F is the frequency you want to solve for.

What I now want is the power limited formula equivalent (such that I can "cap" driver output above the point where Xmax would demand more power than the voice coil can handle in heat).

I have a power formula that uses driver Sd, Mms, BL and Re, but it seems to be about ~6dB out when calculating max SPL given max continuous driver power.

I tried to reverse engineer Linkwitz' closed box spreadsheet, but failed (maybe too tired). Linkwitz' model is better in the sense it caters for per frequency variable impedance, but I'm more concerned at the top end, not necessarily driver Fs or cabinet loading impedance changes.

Thanks!

#### tktran303

Paid Member
Dave,

Please consider using the Enclosure tool in VituixCAD2. It really is very powerful and with a few keystrokes (Up or Down arrow keys) or the scroll of a mouse wheel you will have a visual and numerical representation of the answer to your queries, and more.

The Excel spreadsheet were good when Jeff and Siegfried made them but @kimmo has grabbed loudspeaker modelling and dragged it into C21, welcomed by many.

Donateware software for educational use.

1 user

#### Dave Bullet

Thanks - I am a VituixCAD user. I was going to just solely rely on software sims for this, but want to understand the math behind and be able to multi-simulate several drivers to overlay the "weakest link" amongst them for SPL.

I realise there are other factors in play (BL curve lineraity and impact on non-linear distortion, enclosure loading, baffle signature, natural driver response etc...). I may yet abandon my attempt

#### markbakk

The manual for Basta! may help you further here. The app itself is -while a bit old- still very elegant and well thought out.

#### weltersys

I realise there are other factors in play (BL curve lineraity and impact on non-linear distortion, enclosure loading, baffle signature, natural driver response etc...). I may yet abandon my attempt
The AES2-1984 (r2003) power rating has the LF driver mounted in free air.
Power is determined as the square of applied rms voltage, divided by Zmin. The driver is driven with pink noise extending one decade upward from the manufacturer’s stated LF limit of the device. The noise is bandpass filtered at 12dB per octave and the peak-to-rms voltage ratio of the noise signal is 2:1 (6 dB).

One problem with that rating is Zmin (the minimum impedance) is generally much lower than the average impedance over that range, so the power generated by the voltage may only be a fraction of the rated “power”.

Considering the power and excursion ratings for speakers are derived from a completely different circumstance than what you are attempting to derive, abandonment seems prudent ;^)

1 user