**Main Pages**

North Reading Engineering

The Audio Engineering League

North Reading Engineering

The Audio Engineering League

Loudspeakers in Vented Boxes Part II

The magnitude of Vb is the internal volume minus the
sum total of the volumes associated with the vent duct(s), bracing and
speaker. By assuming a magnitude for Vb,
the compliance ratio, alpha, is then determined (=Vas/Vb). The magnitude of Ql is
a function of the total
enclosure losses associated with absorption, leakage and the vent(s).
Of the three, leakage losses are significant and Ql values
between 5-20 are typical. By using the spreadsheet calculator, a
range of enclosure Ql values, for a given set
of system parameters is easily model as shown below (left). The
impedance modulus, as a function of the electrical equivalent
resistance, Rel, associated with the given
Ql, is shown below (right). As is evident in the graph, the
motional impedance of the driver increases as the resistive losses associated with leakage decrease
(green Ql=5,
fuscia Ql=10,
red Ql=20).

The electrical equivalent circuit of a loudspeaker mounted in a vented enclosure ignoring mutual coupling between the diaphragm and vent is modeled in LTSPICE IV and shown below. The additional components Lceb, Rel and Cmep are the electrical equivalent inductance of the enclosure compliance, the electrical equivalent resistance of the enclosure leakage losses and the electrical equivalent capacitance of the air mass present in the vent, respectively. An Excel

The vented-box equivalent circuit is a 4th-order high-pass filter function, G(s), where s is the complex frequency variable (=

Examples of the spreadsheet plots of magnitude versus frequency response derived from the general form of the high-pass transfer function, G(

The equations and coefficient used in the spreadsheet are
consistent in form with those published by Small. We have
provided copies of Small's papers in the dropdown menu
below and, for comparison purposes, included the earlier papers of
A. N. Thiele. Both papers examine the 4th order
high-pass filter transfer function that is derived from
equivalent circuits. For example, multiplying the top
and bottom of Thiele's Eq. (21) by
*p*^{4}*T*_{o}^{4}
(i.e. multipication by unity), and setting the coefficients
x1, x2 and x3 to a1, a2 and a3, respectively, the result is Small's Eq. (57).
Small extends Thiele's work by considering efficiency,
large-signal behavior, enclosure losses and interactions
between the diaphgram and vent.