a Helmholtz resonator excited by the rear side of the bass driver's diaphragm. Passive radiators can be tuned independent of their dimensions by adding or removing mass from the diaphragm of the passive radiator. This makes them useful for smaller enclosures with the same box tuning where an equivalently tuned port would be impractical. They also sidestep the midrange pipe resonances that can be an issue on ported enclosures in full range systems. However, to be effective, they require a much greater surface area on the cabinet exterior than a port. They are also considerably more expensive than a port tube, as they are effectively a speaker driver minus its voice coil and motor magnet. History The effect of the various speaker parameters, enclosure sizes and port (and duct) dimensions on the performance of bass reflex systems was not well understood until the early 1960s. Subsequently, pioneering analyses by A.N. Thiele, J.E. Benson and Richard H. Small presented the theoretical foundations for the synthesis of bass reflex loudspeaker systems to meet specified low-frequency performance criteria were developed into a series of "alignments" (sets of the relevant speaker parameters) that allowed designers to produce useful, predictable responses. Keele extended the design options by presenting a new set of 6th-order vented-box loudspeaker system alignments. All of these results made it possible for speaker manufacturers to design bass reflex loudspeakers to match various sizes of enclosures, and to match enclosures to given speakers with great predictability. Due to the physical electromechanical constraints, it is not possible to have a small speaker in a small enclosure producing extended bass response at high efficiencies (i.e., requiring only a low-powered amplifier). It is possible to have two of these attributes, but not all; this has been termed Hofmann's Iron Law after J. Anton Hofmann of KLH's summary (with Henry Kloss) of Edgar Villchur work years earlier. The sound pressure produced depends upon the efficiency of the speaker, the mechanical or thermal power handling of the driver, the power input and the size of the driver. Advantages Novak concluded that a bass reflex enclosure can have greater acoustic output for a given amount of distortion, lower total harmonic intermodulation, and transient distortion than a completely closed-box of similar size. Such a resonant system augments the bass response of the driver and, if designed properly, can extend the frequency response of the driver/enclosure combination to below the range