Which Impedance? Nominal Minimum / Maximum Average
This article addresses three dominant reasons for measuring the impedance of a loudspeaker.
The impedance of a loudspeaker characterizes the opposition that it presents to current flowing from the amplifier. The impedance is both complex and frequency-dependent. Complex means that it is not a pure resistance, but a combination of resistance and reactance. As a result, the voltage and current waveforms from the amplifier are not in-phase. Frequency-dependence means that the opposition to current flow varies with the applied frequency – a natural occurrence in a reactive load.
The curve in Figure 1 shows the impedance of a single driver in a sealed box. The peak of the curve is the most striking feature. It is the resonant frequency of the loudspeaker/box system and usually falls near the useful low-frequency limit of the system. The minima of the impedance curve is of greater significance and lies just above resonance. It represents the maximum load (minimum impedance) that the loudspeaker places on the amplifier.
The curve in Figure 2 shows the impedance of a typical 2-way loudspeaker system. The curve is “peakier” because of the box vent and multiple drivers.
So Why Should I Care?
In many cases you don’t need to care. Consider the way that we use electricity in our homes. The wall outlet provides a fixed AC power source at a standard voltage (110VRMS sinusoid in the US) and rated available current (typically 15 ARMS). The appliances that we use are designed to operate at this rated voltage. When they are plugged in and turned on they draw some nominal amount of current as determined by their impedance. We seldom think about how much current is being drawn unless the appliance demands more than is available. In that case the circuit breaker trips and we investigate further as to the cause. Most appliances draw far less than the available 15 amps so we just plug them in and use them without a second thought. Circuits of this type are termed “constant voltage” because the voltage does not change when the load is connected. The current flow is determined by the impedance of the load, with load current increasing as impedance is reduced.
The amplifier-to-loudspeaker interface works much the same way. The amplifier is a constant voltage source for the loudspeaker. One difference between the amplifier and a household electrical outlet is that the voltage waveform from the amplifier contains information and is much more complex. Also, the voltage is not a fixed value (as with electrical outlets), but varies with the setting of the amplifier (Figure 4). A notable exception is the high voltage distribution scheme used in distributed systems. In such systems the distribution voltage is fixed in value for a sinusoidal test tone (70.7VRMS in the US and 100VRMS in Europe). The actual voltage for speech and music waveforms is more complex and typically lower in value (30VRMS typical) as shown in Figure 3.
The impedance of household appliances is seldom specified. Instead, a power or current rating is provided. This is because the available voltage is always the 
same, so the current draw or power draw is the parameter of interest to prevent circuit overload. Voltage, current and impedance are related by the Ohm’s law. Their relationship to power is described by Joule’s law (Figure 5 – often called the “power equation).1
With amplifiers a different rating scheme must be used than for household appliances. Since the available voltage is amplifier setting-dependent, there is no way to know in advance what the current draw will be. In short “It depends.” So, instead of listing the current draw or power draw, the load impedance is given. This gives the user the information that they need to assure that the amplifier is not excessively loaded by the loudspeaker(s).
The current drawn by the loudspeaker is determined by its impedance and the spectrum of the signal. Since the impedance is loudspeaker-dependent, it is good practice to measure it for the following reasons.
Reasons to Measure the Impedance
There are three dominant reasons for measuring the impedance of a loudspeaker.
Loading
The first is to assure that it does not overload the amplifier. As with household appliances, lower impedance allows more current to flow. If the loudspeaker’s impedance is very low (< 4 ohms) the amplifier may not be able to source sufficient current to accurately reproduce the audio waveform. While the peaks of the impedance curve are its most striking features, the minima of the curve are of greater significance to the amplifier. If an amplifier is driving a single loudspeaker, it is unlikely that an overload condition will exist.
Wire Gauge
The second reason is to aid in determining the required wire gauge used to connect the loudspeaker to the amplifier. If one were to place a voltmeter across the amplifier terminals and take a reading (sine wave recommended), and then place the voltmeter across the loudspeaker terminals and take another reading, the difference is the voltage drop across the loudspeaker cable. This is the unavoidable consequence of using wire to complete the circuit. While the wire resistance can never be reduced to zero, it should be minimized to assure optimum voltage transfer to the loudspeaker. A second benefit of low wire resistance is that it improves the damping factor of the amplifier/loudspeaker interface. If the level difference between the two readings exceeds 0.5dB, a larger wire gauge should be used.
Reactive Loads
The third reason for measuring the impedance of a loudspeaker is to assure that the loudspeaker is not excessively reactive. A reactive load reflects current back to the amplifier. If the reactance is excessive the amplifier may become unstable. If the phase angle approaches +-90 degrees at any frequency (a pure inductance if positive or capacitance if negative), the amplifier could be in trouble. Measuring both the magnitude and phase of the impedance requires specialized equipment.
Average, Minimum and Nominal
Since the loudspeaker impedance is frequency-dependent, it is not easily represented by a single number. To complicate things further, most audio waveforms have a constantly changing spectrum. There is no simple way to characterize the impedance of the load, a fact that does not keep us from trying. Here are some possibilities:
Average
If the program source is pink noise or music with broad spectral content, then no one point of the impedance curve is a dominating factor. If the voltage across the load is monitored, along with the current through the load, the impedance can be found by Z = E/I, where E is the average voltage and I is the average current. The calculated impedance is likely higher than expected, since the maxima of the impedance curve tend to offset the minima.
Minimum
The minima of the impedance curve represents the greatest load to the amplifier. If a narrow band waveform (i.e. a sine wave) were presented to the loudspeaker at the frequency of the minima, the amplifier may have difficulty sourcing enough current. The result is a drop in the applied voltage across the loudspeaker and a distortion of the waveform. This condition is unlikely with real-world program material, but not impossible.
Nominal
The most widely used impedance specification is that of nominal impedance. Nominal in this context means the “named” impedance of the loudspeaker. According to IEC-268-5 the nominal impedance is found by multiplying the minima of the curve (within the pass band of the loudspeaker) by 1.25. Said another way, the minima of the loudspeaker impedance shall not be less than 80 percent of its nominal value.
From careful study of the impedance curve, a system designer can know the typical load characteristic of the loudspeaker (assuming broadband program material), as well as the maximum load (assuming narrow band program material). This information can be used to judge how many loudspeakers can be safely connected to the amplifier, as well as the required gauge of wire.
The Common Loudspeaker File Format includes the loudspeaker impedance curve at one-third octave resolution (Figure 7). The average and nominal values are displayed on the impedance graph. The average, nominal and minimum impedances are listed in text boxes. This gives the loudspeaker designer a great deal of information for interfacing the loudspeaker with the amplifier. In addition to these ratings, a PDF info file can be attached to show the phase angle of the impedance (Figure 6).
As with household appliances, the main reason for knowing the load impedance is to avoid an overload condition. The amplifier is a constant voltage source. While the power output increases with decreasing load impedance, the voltage output does not. It is prudent to avoid load impedances that cause the output voltage of the amplifier to sag more than 0.5 dB (5 percent) of the no load value. pb
1 – Thanks to Paul Matthews of Rane Corp. for this clarification.