Impedance and its influence (electrical)

Many types of amplifiers will benefit greatly from a 12, 16 or even 32 ohm loudspeakers—even solid-state and even if they are only printed to work with 4 or 8 ohm speakers; going higher is generally not a problem, higher impedance presents less load to the amp, going too low is typically the problem. Higher impedance loudspeaker designs can and often do sound better than demanding low impedance designs. Here’s why:

First, it’s Ohm’s law. Many loudspeaker designers, reviewers, hobbyist, and consumers, fail to recognize some basic points about how a loudspeaker should be measured and what effects the amplifier can have on tests and measures as well as the musical performance, timbre, bandwidth, presence and so on. This article address the basic electrical relations between amplifier and loudspeaker, which together form an intimate relationship—get it wrong and your sound will suck. The Article does not attempt to detail the more complex dynamic behavior of the loudspeaker system, thermal changes at the transducers motor, loudspeaker cable influences, environmental conditions, nor how an audio power amplifier’s design will react to these dynamic impedance variables.

2.8 volts equal 1 watt, right? Only for true 8 ohm loudspeakers.

Ohm’s law, power, and SI units of measure:

V=IR     I=V/R     R=V/I
W=IV     I=W/R     R=V2/W
efficiency = output / input

Electric potential is voltage V, current is amperes I, resistance is ohms R, power is wattage W.

Loudspeakers are generally reactive AC devises. Power factors and impedance differentials between amplifier and loudspeaker must  be considered. Solving for power, watts not voltage, is essential for understanding relationships. Power in watts is current times voltage. Phase angles can be ignored in basic loudspeaker testing but does factor in more complex dynamic behavior modeling. Without the correct understanding of basic power transfer, a complete detailing of the system and device under test, measures and data cannot be accurately correlated into observed fidelity. It should also be pointed out that without a basic understanding of test system, device, procedure and marketing can easily manipulate the tests, data and you.

The amplifier is a major factor in how a loudspeaker system performances, both technically and sonically. If testing the efficiency of a driver in an infinite baffle, correctly mapping the impedance across its bandwidth, then at least distilling the string of points into a nominal number is essential. You cannot simply pump in 2.8 volts and call it. Data acquired this way has little correlative meaning. Once impedance is known and plotted power and system efficiency can then be tested and the results can be useful.

Many Zu loudspeakers measure 12 ohms nominal. (Remember, the speaker driver’s measures and performance are in large part determined by the acoustic impedance system: box, horn, baffle... that they are mated with and raw driver or infinite baffle plots are not system impedance measures.) To get a basic measure of system efficiency we first solve for current, then voltage, all measures being at the loudspeaker’s input.

First solve for amperes; square-root of wattage over resistance (ignoring phase) which equals 0.289 amps. Then take amps times resistance to solve for voltage and we arrive at 3.5 volts input. So a 12 ohm load (older Zu Druid, Omen, Essence...) requires 3.5 volts at input to reach 1 watt. An input of 2.83 volts into a 12 ohm load yields 0.66 watts. Nearly all modern tests and measures on loudspeakers simply input 2.8 volts (assumption of an 8 ohm standard) which has almost no lay correlation to actual transduction efficiency and power. If all loudspeakers had a nominal impedance of 8 ohms then a 2.83 volt input would be fine and does in fact result in a nominal 1 watt of input power. With 4 ohm nominal loudspeakers we get; 2.83 volts input which equals 2 watts of electrical power at input, at 16 ohms its 1/2 watt and 32 ohm you are down to a 1/4 watt. Knowing power in and accurately measuring power out of a system you can then know efficiency. Voltage sensitivity is not efficiency, it is a subset of efficiency. Voltage sensitivity is a useful tool in specific applications and conditions but is typically the domain of the engineer.

Now add the amplifier and its design—it’s all about the matchup

Designers and reviewers should be working with power and impedance and not sensitivity and uncorrelated measures. Let’s take an ideally optimized class-A solid-state direct transistor drive power amplifier running wide open, best case when properly matched up to a loudspeaker designed for that amp is 25% electrical power efficiency, this is amplifier only efficiency and not system or loudspeaker. But when you take the same or similar class-A design and transformer couple the output transistors to the loudspeaker you can reach an electrical power efficiency up to 50%, again amplifier only. This is if everything is optimally designed and once understood a designer can then apply similar engineering and reason to transformer/loudspeaker optimization to further improve power transfer to the loudspeaker and net additional fidelity gains. With vacuum tubes this whole matchup is even more critical.

These are maximum percent efficiencies for series-fed class-A amplifiers occurring only under ideal conditions and for maximum signal swing.

Note, with class-A solid-state it’s important to always have your loudspeakers connected, driving your class-A amps without the load will result in excess heat generation within the power transistors. If the loudspeaker draws some of the power then the transistor has to handle proportionately less. The transistor has to dissipate the most power when the loudspeaker is disconnected. It’s always preferable to keep the load connected as long as the class-A amplifier, transformer coupled or not, is switched on.

Understanding power transfer dynamics will hint to why power amplifiers have such a huge impact on the playback systems timbre, dynamic range, bass response, presence, treble, how loud it sounds, and so on. Remember, the reactivity of a dynamic driver is dramatically effected by the loudspeaker design and the driver loading used (box, horn, baffle...) and the necessity for measuring the device as a complete loudspeaker system. This also reveals how the exaggerated “sensitivity” measures are being generated by the majority of brands. Now that we understand the basic relations between impedances voltage and current we can approach how a given power amplifier might behave and influence the tone, power, and presence of playback.