How big an amplifier do I need for my woofers?.
One of the most common questions, and perhaps misunderstood aspects of loudspeakers, is the power
requirement for a sealed box woofer system. Is a 100 w/8ohm amplifier powerful enough? Do I need 200
watts? Perhaps 500 watts? Part of the problem is that power, per say, is not necessarily the issue. Woofer
systems operate around the peak in the impedance curve and therefore the actual power delivered into
them around the woofer Fs can be very small. At Fs the impedance is a maximum and purely resistive, thus
the power delivered at Fs is the voltage across the woofer times the current though the voice coil, P = VI.
Ohms law tells us the I = V/R. It follows that P = V^2 / R. Form this we can determine an amplifiers RMS
output voltage capability based on its power rating, Vrms = Sqrt(Pr x Rr) , where Pr is the rated power into
the specified load resistance Rr (for example, 100W into 8 ohms).
Given that driver specifications are typically provided as a voltage sensitivity (or referenced to 1 w into 8
ohms) relative to their flat band output, it is a simple matter to determine the SPL as a function of
frequency and the required excursion given the T/S parameters of the driver in the enclosure (Qtc and Fc)
for an amplifier with a given power rating. Or, conversely, determine the required voltage swing to produce
the displacement limited SPL at a specified frequency.
The Excel base spread sheet which can be downloaded performs such tasks. The user must enter the
woofer alignment (Fc and Qtc for a sealed box or Fs and Qts for free air or open baffle), the voltage
sensitivity, Xmax and the effective cone area, SD. He can then enter the desired frequency at which the
required amplifier voltage sing is to be calculated. The spread sheet will then compute the displacement
limited SPL for 2 Pi monopole operation, the peak and RMS voltage required across the driver to achieve
this displacement, and the required power ratings for the amplifier to reach these levels. The user may also
specify the rated amplifier power into 8 ohms and the curves to the right will be displayed. If the woofer is of
lower impedance and the amplifier power into 4 ohms is not twice the 8 ohm rating then 1/2 the 4 ohm rating
should be entered. Provided that the woofer impedance remains above the amplifier's rated load the
amplifier should be able to produce the output shown in the plots.