Real-Life Measurements

As mentioned by two readers in this month's "Letters," amplifiers are used to drive loudspeakers but are almost exclusively measured into resistive loads. The reasons for this are twofold: 1) real loudspeakers both produce neighbor-annoying sound levels and tend to break when driven with typical amplifier test signals; and 2) the question as to which "standard" loudspeaker should be used is impossible to answer---at least the conventional resistive loads are consistent and repeatable.

However, the general point that an amplifier should be measured into a load similar to that of a real loudspeaker is a valid one. Loudspeakers can be much more demanding than resistive loads, as evidenced by Eric Benjamin's 1993 AES paper, "Audio Power Amplifiers for Loudspeaker Loads." We had been thinking about how to implement this for some time, when, as a result of a chance conversation, Ken Kantor of NHT and International Jensen sent us a speaker simulator he had been using.

Its circuit diagram is shown in fig.1. Combinations of resistors, inductors, and capacitors produce a load with an impedance magnitude and phase plot (fig.2) intended to represent a typical two-way, sealed-box, 8 ohm loudspeaker. (The small-value resistors shown are the measured series resistances of the coils.) The impedance peak in the bass is the equivalent of the woofer's enclosure resonance; the peak in the low treble is identical to that produced by a crossover filter. The phase angles are also typical; note that the worst-case phase never coincides with the lowest magnitude.

Fig.1 Circuit of Ken Kantor loudspeaker simulator, intended to represent a two-way, sealed-box minimonitor with a nominal impedance of 8 ohms.

Fig.2 Kantor speaker simulator, electrical impedance (solid) and phase (dashed) (2 ohms/vertical div.).


6j5's picture

I found this model rather useful for a spice simulation of power Amp output transistor loading. JA's addition of the series RC net to better represent loading at HF was interesting because these Zobel nets are usually part of the amplifier not the speakers and used together with the mandatory series inductance to stabilize the amp against capacitive loading.

The point I'm trying to make is that some crossover designs are of the 'constant resistance' (CR) types which try to flatten the peaks and troughs across the range this may be the reason why JA added the zobel net not because that's part of the speaker model but because CR crossovers do that if they can be called CR.

I redesigned my Klipshorn mid/HF crossovers to a CR type as with the original XO's they could hardly be called 8 ohm speakers! The penalty is loss of efficiency (stated as 104dB/m) which hardly matters these days. CR XO's are more desirable with valve amps that need decent load lines for best linearity. Use of an autotransformer in the XO is useful if not mandatory to this end which is far from common. McIntosh use autotransformers in their SS amps because they know its the best way to make life easier for the output devices.

I would argue that amplifier testing at constant 4 or 8 ohms will not tell the full story in terms of how it will handle the wild dynamic load changes a real speaker will present. But neither would testing at sub 2 ohm loads as these occur over discrete bands and are not sustained excitations. Any decent amplifier should however be able to handle those sub 2 ohm levels for prescribed durations derived from real music statistics across the audio band at rated power.

At any rate the issues arising with an amplifier driving reactive loads is far from novel or peculiar to audio amps, the electrical power distribution companies have know about it for well over a century which they handle by encouraging POWER FACTOR CORRECTION. You can connect a 10uf across the amp o/p delivering ZERO power yet the output devices will likely be screaming hot. Of course PF correction in the same way is highly impractical in audio amps unless you are operating it at a single frequency say 50 or 60 Hz ... just to make the point. The nearest thing to PF correction would be a CR crossover.