Introduction

Have you ever wondered what makes a loudspeaker “difficult to drive”? Do you wonder what’s so special about an amplifier that is stable into a 4 ohm load? If these are the kinds of questions that leave you mystified, this may be the article for you. Fortunately, there is nothing extraordinarily difficult involved in answering these questions: as long as you have rudimentary math skills and knowledge of the right equations, you will be able to look at a few basic measurements of a loudspeaker, namely the impedance curve, electrical phase curve, and voltage sensitivity, and determine what kind of amplification you’ll need to get the job done.

Terminology

Before we get too far, it’s important to define some terms:

Voltage: The difference in electrical potential between two points measured in volts (V); a measurement of the energy contained per unit of charge.

Current/Amperage: the total flow of electric charges through a surface at the rate of coulomb per time unit. The flow of current through a circuit is usually measured in amps (A) or milliamps (mA).

Resistance: Opposition to the flow of current through a conductor measured in ohms (Ω).

Capacitance: The ability to store an electrical charge measured in Farads (F) or micro Farads (uF).

Inductance: The property of a conductor in which a change in current flow within the conductor creates voltage within itself as well as other nearby conductors. Inductance is measured in Henries (H)

Impedance: Similar to resistance, impedance is the opposition of AC current flow through a conductor in a reactive circuit (i.e. one exhibiting elements of capacitance and inductance).

Phase Angle: The degree to which current flow will lead or lag the voltage waveform in a reactive circuit element.

From left to right, a set of resistors, a capacitor, and an air core inductor.

Ohm's Law

To really kick things off, we will first want to examine Ohm’s Law; in plain English, the law says that the current flow/amperage through a conductor is directly proportional to the voltage potential, with the factor between them being the conductor’s resistance, or in the case of a complex circuit, its impedance. Mathematically, this is simply written as:

V = I * R (1)





where V=Voltage, I=Current, and R=Resistance. In a complex load, we substitute Z for resistance, where Z=Impedance.

The Ohm’s Law Triangle demonstrates the interchangeability of the variables. The line dividing the left and right sections of the triangle represents multiplication; the line between the top and bottom sections represents division. Active Power One other important equation to keep in mind is:

P = V * I * COS(Ф) (2)

where P=Power and Ф (Phi) = phase angle. Looking at our prior equations, you’ll find you could also re-write this as:

P = I^2 * Z * COS(Ф) (3)

and

P = (V^2 / Z) * COS(Ф) (4)

It’s worth pointing out here that power will always be positive, given that it is proportional to the square of the current or voltage; that is to say, energy is always dissipated inside of an electrical circuit, though one may note inductance and capacitance in and of themselves store, but do not dissipate energy. With any luck, these equations haven’t scared you off just yet. Suffice it to say, a strong understanding of the relationships they represent are a key component to answering the questions at the beginning of this article. The Power Triangle visually demonstrates the power lost due to phase shift between voltage and amperage, and is given above as Reactive power. The Application

So now that we know these rules exist, how do we apply them to audio? Well, let’s start with the magic number of 2.83 volts. You may see that number pop up in speaker specifications a lot with respect to voltage sensitivity. You’ll also find that the majority of loudspeakers are specified as an 8 ohm nominal load. Going back to equation (1), we can plug in 2.83 volts = X amperes * 8 ohms. To solve for X, we simply divide 2.83 by 8, which yields amperage as 0.354, and gives us the statement 2.83 volts = 0.354 amperes x 8 Ohms. Plugging those numbers into equation (2) to solve for power (and ignoring the phase angle for now), you’ll find that 2.83 volts translates into 1 watt with an 8 ohm load.