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by Marty McCann

Several years ago I wrote four separate articles on Loudspeaker Impedance that were published in various Peavey Monitor Magazines. Realizing that many people may not have read each of the articles, I have decided to address the subject of Impedance in audio once again. This will be a detailed technical paper that will start out with the basics so that sound system operators and technicians may have an opportunity to establish a thorough understanding of the fundamental concepts of loudspeaker impedance and their applications. I will also continue to address the subject of impedance as it applies to the interfacing of those electronic components ahead of the power amplifier. In order to completely understand the workings of impedance, one must grasp the mathematical aspects of impedance and Ohm's Law. Ohm's Law is actually quite simple. However, some people get glassy eyed when it comes to any kind of mathematics. If you want be just a roadie in the music industry, you may not need to understand Ohm's Law. However, if you want to be the best sound system engineer, you must fully appreciate the principles set forth in this paper. You don't have to understand this to operate a system, but if you are connecting sound system components together and you ignore Ohm's Law, you are destined to literally pay for your ignorance with your pocketbook. So don't let impedance be an impediment to your success.

A simple definition of impedance is "the opposition of one thing to another." For an analogy: you are in a room and you would like to leave that room, but if there were a 365-pound wrestler standing in the doorway and he didn't want you to go through the door, he would represent a significantly high impedance. He could easily impede or prevent you from going out of the room. If, one the other hand, some person much smaller and lighter than you were standing in the doorway, he would not offer much opposition to you if you truly desired to go through that doorway.

A loudspeaker's impedance is its opposition to current flow from the power amplifier. It is the current flow from the power amplifier that actually performs the work, or causes the voice coil attached to the paper cone to move back and forth in the magnetic field, which causes the loudspeaker cone to start the air molecules bumping in to each other to produce what we hear as sound. The more current that flows in the voice coil, the greater the cone's motion and the higher the sound pressure level, i.e., the louder the sound that is produced. The loudspeaker is a transducer, or a device that changes energy from one form into another.

The loudspeaker takes the electrical current produced by the amplifier and transforms it into acoustical energy, thus creating a phenomenon we recognize as sound. However, the loudspeaker is far from being 100% efficient. The electrical current that is not converted into acoustical energy is converted into another form of energy we know as heat. Since impedance is the opposition to current flow, the higher the loudspeaker's impedance, the less current flow from the power amplifier. The lower the loudspeaker's impedance, the more current will flow from the amplifier. The power amplifier produces energy in the form of both voltage and current.

Voltage is analogous to pressure or the potential to do some work. Power in watts represents the amount of work that can be accomplished. The voltage potential itself does not produce the power. Power is only produced when there is current flow. The more power, the more work that can be done.

Voltage represents the potential to create power or do work, but the power necessary to do the work is not produced until there is significant current flow. I think it is important to understand the consequences as far as power demand from the amplifier is concerned when you connect different loudspeaker loads to the output. It is for this reason that I am going to discuss the relationship between the loudspeaker's load and power before I illustrate actual loudspeakers in series and parallel. Don't panic; it's fairly simple math (multiplication and division).

Electrical power represents the amount of work accomplished by the electrical pressure (voltage) acting on the load or the loudspeaker. Another term used to describe this pressure or voltage in the past was electrical-motive-force (EMF), which has been shortened to E when representing voltage mathematically. Electric current (I) represents the rate or number of electrons flowing in an electrical circuit.

Electrical pressure of the unit of electro-motive-force is a form of potential energy that is measured in volts (voltage), named after Count Alessandro Volta (1745-1827), an Italian physicist and pioneer in electricity.

Electrical current is measured in units of amperes, named after French scientist Andre Ampere, (1775-1836). One Ampere of current (one amp) represent 6.24196 X 10 (to the 18th) electrons flowing past a given point in a electrical circuit in one second.

The opposition to current flow from a power amplifier is determined by the rated impedance (measured in ohms) of the loudspeaker system. One ohm is the unit of resistance that will limit the current flow to one ampere when an electrical pressure of one volt is applied.

The unit of measurement for Power is the Watt, so named to honor James Watt (1736-1819), a Scottish inventor and engineer. James Watt is credited for inventing the Steam Engine, which was the first self-powered machine.

George Simon Ohm (1787-1854) was a German physicist who quantified the relationship between voltage, current, and resistance. The unit of resistance was named in honor of George Ohm. One ohm is the opposition offered to the flow of current by a uniform column of mercury 106.3 centimeters in length and one square millimeter in cross-sectional area (mass = 14.4521 grams), at 32 degrees Fahrenheit or 0 degrees Centigrade.

The fundamental formula of Ohm's Law is quite simple: The amount of current flow when one Volt encounters 1 Ohm of resistance is equal to 1 Ampere of current. Another simple corollary regarding power is: 1 Volt of electrical pressure (E) times 1 Ampere of current flow (I) equals 1 Watt of power (W) or P = IE.

The amount of current flow measured in amperes (amps) is a function of how much total opposition in both DC resistance and AC impedance that the loudspeaker offers to the amplifier. Power (P), in watts, equals the voltage (E) available from the power amplifier times the amount of current flow, in amps (I), or P = I x E. Power in watts (W) is also equal to the voltage available from the power amplifier squared (E x E) divided by the resistance (R) of the loudspeaker (W = E x E / R). Resistance is measured in units of ohms.

When it comes to electrical measurements, it is much easier to measure the voltage potential across a resistive load than it is to measure current flow through the circuit itself.

Therefore, if we know the value of the load resistance, we can derive the current flow by measuring the voltage and using two related formulas for power. The power amplifier in sound reinforcement technology acts for the most part as a constant voltage source. If there is a source voltage of 40 volts of potential from the amplifier and if the loudspeaker has 8 ohms of resistance, then (W = E x E / R) 40 volts times 40 volts divided by 8 equals 1600 divided by 8, or 200 watts of power. If the same 40 volts were delivered by the amplifier to a 4 ohm loudspeaker load, then we would have 40 times 40, or 1600 divided by 4, or 400 watts of power.

W = 402 � 4 = 1600 � 4 = 400 watts

W = 402 � 8 = 1600 � 8 = 200 watts

Let's find out what the current would be: P = I x E, so I = P / E ; 400 watts divided by 40 volts would equal 10 amperes of current. Forty volts of electrical potential delivered to an 8 ohm loudspeaker would result in 5 amps of current or I = 200 watts (P) divided by 40 volts (E) equals 5 amperes of current.

I = 400 watts � 40 volts = 10 amps

I = 200 watts � 40 volts = 5 amps

There is a device used by electricians to measure current directly, it's a type of Amp-meter that employs a clamp that is placed around a single conductor in an electrical circuit. This device displays the current flow in amperes by measuring the magnetic flux field generated around the conductor. This magnetic field is directly proportional to the rate of current flow. It is designed primarily to read AC current in power distribution systems so it is not very accurate at audio frequencies above about 400 Hz.

It is much easier to treat the loudspeaker as if it were pure resistance to calculate simple power produced. A more complicated aspect of impedance is that when dealing with audio frequencies (which are essentially alternating as positive and negative voltage swings that cause the current to alternate in its direction of flow within the voice coil of the loudspeaker), the actual opposition impedance to current flow offered by the speaker is frequency-dependent.

Loudspeakers are not purely passive resistors that generate heat. Loudspeaker systems offer a reactive component in the form of inductance and capacitance, which are more complicated forms of impedance. Inductors are coils of wire that offer less opposition to low frequency current flow and more opposition to high frequency current flow. Capacitors are devices that can sustain an electrical charge and offer more opposition to low frequencies and less opposition to current flow at high frequencies.

There is a certain amount of capacitance between the actual windings of the voice coil wire itself. It is for this reason that loudspeaker manufacturers publish what is said to be nominal impedance. The nominal impedance can be used to calculate the power developed in the voice coil of the loudspeaker, and thus simplify basic loudspeaker power handling calculations.

In this next section we will show simple circuits to represent simple combinations of loudspeaker opposition to current flow.

When loudspeakers are wired in series, the impedance or opposition to current flow increases and less power is developed. An 8 ohm speaker and an 8 ohm speaker wired in series would result in 16 ohms of resistance to current flow.

Forty volts times 40 volts equals 1600. Sixteen hundred divided by 16 ohms equals 100 watts. One hundred watts divided by 40 volts equals 2.5 amps of current flow.

W = 402 � 16 = 1600 � 16 = 100 watts
I = 100 watts � 40 volts = 2.5 amps

When loudspeakers are wired in parallel, the opposition to current flow from the amplifier is decreased and more power is produced. Two 8 ohm loudspeakers wired in parallel would result in 4 ohms of resistance to current flow. Forty volts times 40 volts equals 1600. Sixteen hundred divided by 4 equals 400 watts. Four hundred watts divided by 40 bolts equals 10 amps of current.

W = 402 � 4 = 1600 � 4 = 400 watts
I = 400 watts � 40 volts = 10 amps

Actually, each loudspeaker or branch circuit develops 5 amps of current flow. Since there are two parallel branches, each develops 5 amperes of current because 40 volts times 40 volts divided by 8 ohms equals 200 watts in each parallel circuit branch, and 200 watts divided by 40 volts equals 5 amps of current flow for each speaker. Five amps of current in each branch equals 10 amps of total current flow from the power amplifier. W = 402/ 8 = 1600 / 8 = 200 watts. I = 200 watts / 40 volts = 5 amps x 2 circuit branches = 10 amps.

When working with loudspeakers, don't mix speakers with different impedances in the same enclosures. They would not be able to perform at the same power levels and therefore would not combine their acoustical outputs so as to mutually reinforce one another.

Some people who only understand the direct current aspects of loudspeaker impedance have tried to fool a speaker system by using resistors to balance out the equivalent resistive circuit. This also limits the loudspeaker's abilities to combine acoustically in a constructive manner, since resistors do not produce sound.

Therefore, if you only deal with loudspeakers of like impedances, then the rules of thumb to calculate equivalent load impedance are simplified. In series circuits, take the number of like impedance loudspeakers placed in series and multiply them by their mutual impedance. Four 8 ohm speakers in series is 8 x 4 = 32 ohms.

402 � 32 = 1600 � 32 = 50 watts

In parallel circuits, take the like impedance of the speakers wired in parallel and divide this impedance by the number of speakers placed in parallel to get the resultant impedance that the amplifier will see.

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