In the previous article, Model Validation, I specified the expression to be inserted in the LTSpice graphic post-processor to obtain the frequency response at one meter, which I report below:

SPL=20*log10[59000*frequency*I(VSYS)]

I emphasize that the display of the vertical axis must be set on a linear scale. Although the expression can be saved as a setting (Save Plot Settings), during the design it is necessary to graphically display also other quantities, often in full screen, and to return to the SPL display it is necessary to re-transcribe all the text. It might also be useful to show the response at different distances. Using the properties of the inductors, I have developed three test points that allow you to quickly view, normalized to the desired distance, the response of the woofer, of the opening and the complete system.

The sound pressure of the system at the distance r is given by:

where ρ_{0} is the air density, f the frequency and Usys the total volume velocity of the system. As we have seen, in our model the pressure p corresponds to the electrical voltage and the volume velocity U to the current. In an inductor, and in sinusoidal mode, the amplitude of the electric voltage is related to the current intensity by the following equation:

V = IωL

where ω is the angular frequency, 2πf.

Substituting in the previous expression we obtain:

p = Usys 2πf L

we can now obtain the correct expression of sound pressure, at distance r, by setting the inductance value as follows:

Since the sound pressure level is expressed in decibel I have inserted a reference level, p_{ref }; the most commonly used value is the human audibility threshold of 20 μPa (2×10^{-5} N/m^{2})(see image below).

F1 and F2 are current controlled current sources and are controlled respectively by the current flowing in V4 (volume speed of the woofer) and V5 (volume speed of the opening). The volume velocity of the system is measured by the VSYS ammeter.

To use the test points, which are activated by positioning the probe on the desired SPL_ flag, it is necessary to set the display of the vertical axis of the graph in decibels.