section 10 of article —

Referring to the complex impedance of a loudspeaker, Vance Dickason states [2] that, “Phase angles in excess of 40° at low frequencies, and the same at frequencies about 1-2 kHz, can be considered as a somewhat difficult load for an amplifier to drive.” Also on p.129 of the same book he says “The extent to which the load is either capacitively or inductively reactive at different frequencies determines how happy or unhappy an amplifier will be driving a particular loudspeaker.”

Michael Renardson in his paper [3] states that, “Although many loudspeakers are specified as having an impedance of 8Ω there is usually large variation throughout the audio frequency range with typical variations in a given loudspeaker from 5 to 40 ohms and significant reactive components. The distortion produced by an amplifier with a loudspeaker load will therefore be different from that with an 8 ohm resistor and the total harmonic distortion figure is typically 10 dB higher over much of the frequency range and in some cases considerably worse.”

Impedance of woofer LS1 of Figure 4 equals 10Ω at a frequency of 150 Hz, increases to a maximum of 29Ω at 80 Hz and equals 21Ω at 60 Hz. Thus, without excessive impairment of the accuracy of the analysis, the phase angle and impedance of the load presented to an amplifier driving the speaker system of Figure 4 can be calculated disregarding the impedance of LS1 connected across the series connection of capacitors C1~ C4 and resistor R2. At frequency equal to 40 Hz and 55 Hz, phase angle of the response-shaping network consisting of resistor R1, capacitors C1~ C4 and resistor R2 equals (respectively) 45° and 36°. At frequencies greater than 500 Hz the phase angle is 0°. Impedance of the response shaping network at frequency equal to 40 Hz and 500 Hz is respectively 6.4Ω and 4.5Ω.

For frequency equal to or greater than the cut-off frequency f3 of the system of Figure 2 or 55 Hz, the phase angle of the load of that system is less than 40° and thus according to Dickason should be less of a difficult load for an amplifier to drive than is sometimes encountered. Variation of impedance of the system of Figure 2 is only from about (slightly less than) 4.5Ω to 6.4Ω which is much less of an impedance swing than normal. The small impedance swing of the system of Figure 2 presumably reduces total harmonic distortion based on the statement of Renardson.