Use of voltage measurements to determine port velocity

Using Voltage measurement to determine input power

According to the WinISD support notes, input power to a speaker can be determined by the following formula:

Input power = RMS voltage squared / DC resistance of coil

This means that voltage measurement should give an accurate means of determining input power and then SPL and port velocity.

This approach was discussed with members of the diyAudio discussion forum, and with the WinISD support forum.

It neatly bypasses any problems with room nodes that can occur if an SPL meter is used.

For the round one tests, which used two 3.5ohm drivers in series:

Input power = RMS voltage squared / 7

For the round two tests, which used four 3.5ohm drivers in series / parallel:

Input power = RMS voltage squared / 3.5

Reality Check

To check on the validity of this method, a test was done comparing SPL determined by voltage measurement, versus SPL measured with an SPL meter.

The "Blast Furnace" sub was measured at 30hz, outside, on the edge of a deck, with the acoustic centre 1.25m above ground, and the SPL meter 1m away. Simultaneous measurements of SPL and voltage were taken.

The SPL was 92dB, as measured with a Radio Shack SPL meter

Adding 3dB correction for the analog Radio Shack meter @30z, gives an SPL of 95dB

The voltage across the drivers was 11.5V RMS, measured with an analog multimeter.

DC resistance of both drivers in series = 7ohms

Calculated Input power = RMS voltage squared / resistance = 18.9 watts

Put 18.9w into WinISD and read off SPL @ 30hz = 102dB

To accurately specify the input power at 30hz, the modelling in WinISD is done without any amplifier boost factored in.

This SPL figure given by WinISD is for measurement in "half-space".

Since the test was done outside with the speaker 1.25m above the ground, and the meter 1m away, a "full-space" value for SPL is closer to what will be measured

To convert a "half-space" SPL to an equivalent "full-space" value, subtract 6dB.

This gives 96dB as the value determined from voltage measurement

With the SPL being within 1dB for the two methods, we can see that voltage measurement is an acceptable method for determining input power and thus SPL and port velocity

Last update to this page 15th April 2007

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