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Impedance in Audio Technology

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.

LOUDSPEAKER IMPEDANCE
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.

OHM IS NOT A CHANT!
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.

OHM's LAW
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.

SERIES CIRCUITS
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

PARALLEL CIRCUITS
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.

SERIES/PARALLEL CIRCUITS
When the loudspeakers are wired in combination of series/parallel, the opposition to current flow is determined by the resultant impedance that the amplifier sees. Two parallel circuit branches, each consisting of two 8 ohm speakers in series, become two 16 ohm circuit branches if parallel and the amplifier will see a load of 8 ohms.

W = 402 � 8 = 1600 � 8 = 200 watts
I = 200 watts � 40 volts = 5 amps = 2.5 amps per parallel branch

I have tried to keep this explanation of impedance informative while covering basic rules governing the power generated by the amplifier. When discussing a technical subject such as impedance, it is necessary to employ mathematics to illustrate the relationship between voltage, current, impedance, and the resultant power produced in the circuit. I realize that a lot of people don't' like math. You don't need the math if you are going to just be a roadie or stage technician, but if you desire to truly understand how sound equipment functions, you must accept the fact that the math works. If you want to design systems and specify equipment, then you will need to understand the math involved.

If you now understand the relationship of the speaker load to the power produced, you may think that the lower the impedance of the speaker load, the more current will flow and maximum power will be produced by the amplifier. However, in reality the amplifier can develop only so much current flow from its output stage until the point that the maximum sage output current is reached.

This is why amplifiers have a rated minimum load impedance limit, i.e. they can only develop their maximum safe power at the rated minimum load impedance.

If the amplifier were allowed to produce more current than the rated power required, it would destroy itself. The output devices would fail, due to the excess heat generated in the transistors. The more current that flows in a circuit, the hotter the conductor becomes; this is also the case for transistors that are amplifying the signal. This is why most power amplifiers today will begin to current limit in order to protect themselves when the loudspeaker load goes below the minimum rated load impedance.

Loudspeakers also have a minimum impedance that is even lower than the nominal impedance published by the manufacturer. The actual impedance varies with frequency, and it is for this reason that many manufacturers publish impedance charts that will indicate at what frequency the impedance is at its minimum.

IMPEDANCE


Example Impedance Curves

Note that the minimum impedance is lower than the nominal impedance.

Some people who check out a loudspeaker's resistance to direct current with a volt-ohm meter (VOM) become confused, because the DC resistance of a speaker is much lower than the stated nominal impedance. Remember, audio signals are alternating in their direction of current flow (AC). A typical DC resistance measurement can be 20% lower than the nominal impedance rating.

POLARITY OF LOUDSPEAKERS
I haven't discussed the electrical polarity of the loudspeaker yet. Most loudspeaker manufacturers produce speakers that move OUT when a positive referenced voltage is present at the red terminal. All of our Scorpion and Black Widow loudspeakers respond to a positive voltage at the red terminal by moving forward.

The correct wiring of loudspeakers with regards to proper polarity is shown below:

For your information, in case you aren't aware of this, at least one manufacturer's loudspeakers move IN when a positive referenced voltage is present at their red terminal. In that manufacturers' loudspeaker systems, the loudspeaker leads are reversed to place the woofers or cone loudspeakers "In-phase" with their compression drivers mounted on their high frequency horns. Their compression drivers have what is considered normal polarity-they move out when the positive voltage appears at their red terminal.

This fact about polarity is ver important when putting one manufacturer's loudspeaker in a system in conjunction with another manufacturer's components, as in adding a subwoofer. You must verify that a positive voltage, placed on what is supposed to be the positive speaker lead wire, will indeed cause that speaker to move out.

This can be accomplished with a simple nine-volt transistor radio battery. With the positive terminal of the battery placed on the positive speaker lead and the negative terminal on the negative speaker lead, the speaker should move OUT. If the speaker moves IN, the leads need to be reversed either at the loudspeaker itself, at the input jack, or at the power amplifier's output terminals.

The reason for the difference in the direction of the loudspeaker cone's movement is that some loudspeakers have opposite magnetic polarity. If you try putting two identical types of loudspeakers together where the magnets are back to back, they will repel one another. If , on the other hand, you take a Black Widow and JBL and place them back plate to back plate, they will attract one another and may be difficult to pull apart. If you reverse an electro-magnetic system's magnetic polarity, you are also reversing its electrical polarity. They are opposite sides of the same coin.

Since I have brought up the subject of magnetic/electrical polarity, let me tell you one situation that I have experienced on a couple of occasions in my twenty-seven years of active involvement in audio. If the magnet or motor structure has been accidentally placed upside down in the magnetizer, it will be charged to the opposite magnetic polarity. This speaker may then be placed in a system with other similar loudspeakers, but it will move opposite to them, causing the speaker system to sound thin. The wiring color coding may appear to be correct, but it is the mis-magnetized motor structure that is the culprit.

When wiring loudspeakers, you must orient the leads correctly. In a series circuit, the connection between loudspeakers always is made between opposite terminals, i.e., from + red to - black or vice versa (- black to + red). In paralleled circuits we always connect black to black (- to -) and red to red (+ to +).

We have a couple of low frequency enclosures in the Peavey line that employ what we call a trans-axial loudspeaker loading technique. One loudspeaker faces inward while the other faces normal. These two loudspeakers are not on opposite sides of the same baffle board. There are two separate baffle boards that are offset to allow the acoustic centers of the two opposite facing loudspeakers to be in the same plane. In this application the polarity of the rearward facing loudspeaker is reversed. Since the speaker is facing backwards, the reversed polarity causes the two loudspeakers to be acoustically in phase, i.e., they are both moving in the same direction at the same time.

There is a difference between loudspeakers that PRODUCE music (guitar amplifier loudspeakers) and loudspeakers that REPRODUCE music (sound reinforcement loudspeakers). Guitar amplifier loudspeakers are actually voiced or designed to have somewhat "soft" cone breakup, called cone cry by some transducer engineers. Cone breakup occurs at certain resonant frequencies where the cone ceases to move as a single linear piston, but moves in segments. A sound reinforcement loudspeaker should be designed to minimize all cone breakup modes, and thus perform as linear as possible.

It is acceptable to wire guitar amplifier speakers in series and parallel configurations. In guitar amplifiers, the damping factor of the power amplifier is purposely kept low. The speaker is not controlled or damped well and essentially flops around, but this is part of the sound.

However, sound reinforcement loudspeakers should NOT be wired in series. They can be wired in parallel, but they should be wired in such a manner that each speaker has its own two leads wired in parallel at the output of the power amplifier. Some people neglect to do this because it's inconvenient to run separate speaker lines for each transducer.

Tighter, punchier, more transparent kick drum and bass lines will result when the loudspeakers are individually wired in parallel at the power amplifier's output terminals. Tight bass means control of the loudspeaker or high Damping Factor. More on this later.

Sound reinforcement loudspeakers can be wired in parallel, but not internally in the loudspeaker enclosure. Each loudspeaker should have its own set of speaker wires that may be wired in parallel at the output of the power amplifier. Most loudspeaker systems have parallel input jacks on the enclosure. If we didn't include them and other manufacturers did, some salesman that didn't know any better would use this against us to sell another product. More on this later also.

Moving right along, I have even more information to help you understand impedance. We should learn by other's mistakes so we don't have to repeat them. Several years ago while working on some projects in Africa, I encountered a technician who did not understand the difference between DC resistance and AC impedance. We stated earlier that a simple definition of impedance was "the opposition of one thing to another." I also said that impedance was different and more complicated than DC resistance (or the opposition to Direct Current flow), because DC resistance is constant. Impedance varies depending on the frequency of the signal.

DC resistance is equal to the voltage drop (pressure) across the device under measurement, divided by the current flow (number of electrons) passing through the device. DC resistance is rather straightforward. In dealing with the opposition to current flow offered by components in an electrical circuit that contains varying electrical cycles of audio frequencies, the opposition to current flow is know as the more complex impedance.

There are a couple of different types of impedance. The following are some definitions of impedance from the Dictionary of Scientific and Technical Terms by McGraw-Hill:

IMPEDANCE: (PHYS) 1. The ratio of a sinusoidally varying quantity to a second quantity, which measures the response of a physical system to the first, both being considered in complex notation; examples are electrical impedance, acoustical impedance, and mechanical impedance. Also known as complex impedance. 2. The ratio of the greatest magnitude of a second quantity which measures the response of a physical system to the first; equal to the magnitude of the quantity in the first definition.

ELECTRONIC IMPEDANCE: Also known as Impedance. (ELEC) 1. The total opposition that a circuit presents to an alternating current, equal to the complex ratio of the voltage to the current in complex notation. Also known as the complex impedance. 2. The ratio of the maximum voltage in an alternating current circuit to the maximum current; equal to the magnitude of the quantity in the first definition.

ACOUSTIC IMPEDANCE: (ACOUS) The complex ratio of the sound pressure on a given surface to the sound flux through that surface, expressed in acoustic ohms.

MECHANICAL IMPEDANCE: (MECH) The complex ratio of a phasor representing a sinusoidally varying force applied to a system to a phasor representing the velocity of a point in the system.

If you find these definitions a clear as a Columbian cup of coffee, or if you feel as if you have been mentally zapped by a "Star Trek" phasor; read on. Perhaps my further explanations will help you to better understand. We did tell you they called it complex impedance.

The opposition to electrical current flow takes two forms, passive resistance (which produces heat), and an active reaction when there is capacitance or inductance in the circuit. The opposition created by capacitance or inductance is referred to as reactance.

A capacitor consists of two electrical conductors separated by a dielectric or something that will support or store an electrical charge. Air itself can support an electrical charge and is said to have a dielectric of one. A capacitor is said to have a capacitive reactance or opposition (impedance) to current flow. A capacitor blocks direct current (DC), and stores a charge, but for alternating current (AC) a capacitor has high opposition to current flow at low frequencies, and low opposition at high frequencies. When alternating current encounters a capacitor, the voltage lags behind the current.

An inductor is a coil of wire that offers high opposition to current flow at high frequencies and low opposition at low frequencies. When alternating current encounters an inductor, the current lags behind the voltage because inductance is a circuit element that opposes changes in current.

Here is an analogy for impedance in the physical world. You have loaded a wheel barrow with dirt, and now you must move the payload. When you pick up on the handles of the wheel barrow, the weight offers a resistance. However, because the handles operate with the wheel and the axle to form a kind of inclined plane (lever), the resistance is less than the actual weight. In order to get the wheel barrow moving, you must apply even more force, but the mass (real weight of the dirt) offers inertia or opposition to the force applied (Inductive reactance). Now imagine you have moved the payload to its intended location, and must now stop the wheel barrow's forward motion. But now the opposition to the deceleration is in the form of momentum or stored energy in the actual motion of the wheel barrow (Capacitive reactance).

In the case of our loudspeakers, their opposition to current flow from the power amplifier is their impedance. Audio electrical signals are electrical analogues or representations of the positive and negative fluctuations of air pressure that have been converted to positive and negative fluctuations of voltage. This fluctuating electrical signal that represents the vibrations of air or sound is by its very nature Alternating Current or AC (i.e., the direction of current flow changes directly with the number of audio cycles per second being reproduced).

Loudspeakers actually involve three forms of impedance. The first is the electrical impedance offered to the power amplifier discussed above. The second is the mechanical impedance of the loudspeaker, which is taken into account in the design of the loudspeaker enclosure. Third is the impedance of the air or the acoustic impedance that the combination loudspeaker/enclosure encounters.

The air itself, which is the medium through which we transmit sound in the form of pressure variations, has an impedance (the medium of transmission offers opposition to the vibrations of its air molecules). A loudspeaker is a transducer that changes energy from one form to another. The loudspeaker changes electrical energy into acoustical energy or sound as we know it.

A basic loudspeaker is quite a bit inefficient in that most of the energy produced is in the form of heat generated in the voice coil of the speaker. Loudspeakers intended for use as direct radiators are anywhere from 0.25% to 4% efficient, meaning that more than 96% of the energy is lost as heat and not converted into sound or acoustical energy. Loudspeakers actually make better space-heaters than they do electrical to acoustical transducers.

There are ways to somewhat improve upon the efficiency of a basic loudspeaker, and that is to use a kind of transformer to couple it with its acoustic environment. Many of you already know about electrical transformers that can isolate (1:1 ratio), step up (1: 10), or step down (10:1) electrical signals. The ratio represents the proportion of the number of turns in the primary to the number of turns in the secondary. In addition to isolating and stepping voltages up or down, a transformer can match impedances: i.e., a very high impedance source can be coupled to a low impedance load via a step down (high to low turns ratio) transformer. The source that is coupled to the primary of the transformer now sees the high turns ratio as its load impedance, while the secondaries lower turns ratio sees the device coupled to the secondary of the transformer as the actual load impedance.

In loudspeaker transducer technology, we use a horn as a transformer. The horn couples or matches the loudspeaker to the air in a manner in which the efficiency of the loudspeaker as a system is increased (i.e., with one watt of power going to the loudspeaker, the sound pressure on-axis with the horn will be greater, because all of the acoustic energy radiated from the loudspeaker is focused by the horn). Since the acoustic signal produced by the loudspeaker is now restricted within the walls of the horn, the speaker is said to be loaded by the horn. The horn offers an acoustical impedance to the loudspeaker and, like a transformer, the horn changes the impedance that the source amplifier sees. In this case our amplifier actually sees a somewhat higher impedance or opposition to current flow than the speaker would offer if it were directly coupled to the air itself.

WHEN FOUR OHMS IS NOT FOUR OHMS
There is an enclosure in our product line that we have been making for twenty years called, the FH-1 low frequency enclosure. We use a four ohm loudspeaker in this enclosure; however, as long as the enclosure is operated above its cut-off frequency of 60 Hz, the actual load impedance that the power amplifier sees is nominally eight ohms. Likewise, we use a four ohm loudspeaker in the Mid bass horn of HDH-4 and HDH-1 speaker enclosures. As long as these horns are operated above their cut-off frequency of 300 Hz, the midbass of the enclosure will exhibit an eight ohm load to the amplifier.

The mechanical loading of the loudspeaker by the horn makes an impedance transformation so the amplifier sees a load impedance of 8 ohms within the horns operating bandpass. I mention the horn's operating bandpass because if you operate any horn below its cut-off (-3 dB down point on the low frequency portion of its response curve), the driver reverts back to its original lower impedance. As long as you send horn loaded enclosure frequencies that are above the cut-off, the system will offer a higher load impedance to the power amplifier.

The DC resistance of the loudspeakers discussed above is 3.2 to 3.8 ohms. Mounting the loudspeaker on a horn doesn't change the DC resistance, but a power amplifier driving that horn will see a load impedance that is more than twice that of the nominal four ohm impedance of the individual speaker. Hopefully some of us now understand how a four ohm loudspeaker can become an 8 ohm loudspeaker system when mounted on a properly designed horn.

I had mentioned earlier a situation I discovered in Africa where a technician had a basic understanding of impedance, but he didn't understand how horn loading can change the impedance of a loudspeaker. We used to have a low frequency enclosure called the FH-2. This enclosure had two four ohm loudspeakers wired in parallel within a folded horn. Since each of the loudspeakers was loaded by the horn, the individual loudspeakers were mechanically raised to eight ohms. Therefore, in parallel the two equivalent eight ohm speakers offered a four ohm load to the amplifier when operated in its designated bandpass 60 Hz - 400 Hz.

The technician thought he was correct and that perhaps the manufacturer had goofed. So he wired what he thought were two four ohm loudspeakers in series, thinking that he then had an eight ohm load for the power amplifier. However, since these were horn-loaded speakers, he actually changed a four ohm enclosure into a sixteen ohm enclosure. He changed them from two horn-loaded eight ohm speakers that were mixed in parallel to two eight ohm loudspeakers wired in series that now offered a sixteen ohm load for his CS-800 amplifier. So instead of the CS-800 producing 400 watts into 4 ohms (200 to each speaker), it produced only 100 Watts (50 watts to each speaker). Now not only did he have a 6 dB loss in SPL, he totally destroyed the damping or control capability of the power amplifier by reducing his potential damping factor from a rating of 200 to that of 0.5. More on Damping Factor later.

Perhaps now that you have further insight into complex impedance, you may also agree that when misinformed people try to "out think" the manufacturer of a loudspeaker system, they more often than not have their own foot crushed by the wheel that they are trying to reinvent.

I mentioned that loudspeakers should not be wired in series for sound reinforcement applications. And it was all right to wire them in parallel, but that they should each have their own pair of speaker cable leads and be wired in parallel at the output terminals of the power amplifier. This is the professional way of wiring loudspeakers in parallel. All loudspeakers generate a back voltage due to the motion of the voice coil within the magnetic field of the voice coil gap. This is referred to as a Back-EMF or backward-electro-motive-force.

Sir Issac Newton said that for every action there is an equal and opposite reaction. If you would take a fifteen inch Black Widow loudspeaker and hook its terminal up to the input of an oscilloscope and slap the cone abruptly with the palm of your hand, you could cause a voltage to be displayed on the scope greater that 80 volts peak to peak, 40 volts peak, or about 28 volts RMS.

If two loudspeakers are wired in parallel within an enclosure at a distance from the power amplifier, each speaker creates a back-EMF that causes low frequency cancellation as these voltages are out of phase with the incoming signal. When the two loudspeakers are wired in parallel at the output terminals of the power amplifier, the very low internal output impedance (source impedance) of the amplifier (typically 0.02 ohms) acts as a shunt or near short circuit to the back-EMF voltages.

ARE YOU READY FOR MORE?
I mentioned Damping Factor earlier and I wanted to wait until I discussed Source Impedance before I covered it more thoroughly.

SOURCE IMPEDANCE
Up until now I have been talking about the impedances offered by the loudspeaker load on the amplifier. The loudspeaker load impedance is often referred to as the output impedance of the amplifier; however, it is more correct to call this the amplifier load impedance. This is because amplifiers have an internal output or "source impedance."

The ratio of the source impedance to the load impedance is the amplifier's Damping Factor rating number. The damping Factor number can be obtained by dividing the loudspeaker load impedance by the internal output or source impedance of the power amp. A typical power amplifier source impedance is 0.02 ohms. If I were to divide an 8 ohm speaker load by 0.02 ohms, I would have a Damping Factor number of 400.

As you can see the impedance of the load affects the damping factor of the amplifier. The same amplifier would have a damping factor of 200 into a four ohm load (4 / 0.02 = 200).

The damping factor is the ability of the amplifier to control the loudspeaker load. Another word for control is regulation. The control of the load is a function of the ability of the power amplifier's regulation of the load. If you have a precise millivolt scale on a digital voltmeter, you can calculate the percentage of regulation by measuring the output voltage of the amplifier without a load (open circuit), then place the load resistance value on the amplifiers output and measure the voltage. It will have dropped a very small amount.

If you then take the No Load Voltage and subtract the Full Load Voltage from it, and then divide that number by the Full Load Voltage, you will have calculated that amplifier's percentage of regulation. If you now take the reciprocal of that percentage of regulation, you will have the Damping Factor rating number of that amplifier into that load value.

NLv - FLv / FLv = % Regulation

1 / % Regulation = Damping Factor

or DF = 1 / (NLv - FLv / Flv)

Note: You can't really measure Damping Factor at full power because that amplifier will not be able to maintain its regulation, but as an example let's say you are measuring a CS-800X into an eight ohm load with 6 dB of head room. Your open circuit (NL) voltage is measured at 20 volts, you place an eight ohm load in the circuit (you better use a dummy load or a speaker will be awfully loud), then you measure a (FL) voltage of 19.95 volts, your math would now be:

20 - 19.95 = 0.05 / 19.95 = 0.0025

% of Regulation would be .25%

The reciprocal of 0.0025 = 1 / 0.0025 = 400

DF = 400

Source Impedance (Z source) would then be calculated from an inversion of the previous formula for damping factor (DF = Z Load / Z Source) would now become:

Z Load / DF = Z Source or

8 / 400 = 0.02 ohm Source Impedance

This, ladies and gentlemen is what damping factor is all about. Remember the resistance of the load affects the amplifier's ability to control its load. We have all heard that the professional method of loudspeaker cable connections in audio is use to a heavy gauge cable and the shortest possible cable run. Losses in loudspeaker cable runs are due to the friction, or heat, caused by the high level of electron current flow. Most manufacturers provide an American Wire Gauge (AWG) ## 18 in a 25 foot length as a standard loudspeaker cord. But the electrons flow back and forth in a 50 foot circuit. The speaker wire itself opposes current flow because it has a resistance value.

Let's use an example of an 8 ohm loudspeaker connected directly to the output terminals of a power amplifier:

102 ÷ 8 = 100 ÷ 8 = 12.5 watts

Now let us suppose we are practicing very poor audio and have a loudspeaker connected at the end of 153.6 ft of ## 18 gauge copper wire. AWG ## 18 wire has a resistance of 6.51 ohms per 1000 ft (1000 / 6.51 = 153.60), which means that 153.6 ft of ## 18 copper wire will have a resistance of 1 ohm. Since a loudspeaker wire has two conductors, there would actually be 2 ohms of resistance in series with an 8 ohm speaker connected via 153.6 ft of two conductor AWG ## 18 copper wire. Now our power amplifier looks out at the load and sees the 2 ohms of wire resistance, in series with 8 ohm loudspeaker impedances. So the load is now actually 10 ohms instead of 8 ohms.


102 ÷ 10 = 100 ÷ 10 = 10 watts

At first glance you may say that you are only losing 2.5 watts (which is a 20 percent power loss). However, you are actually losing 36% power. Of the 10 watts now produced by the amplifier, 2 watts is dissipated in the wire, while only 8 watts gets to the loudspeaker.

If you think this is not cool, let's examine what this would do to the amplifier's ability to control or dampen the loudspeaker load. The loudspeaker actually sees the 2 ohms of wire resistance in series with the amplifier's internal output or source impedance. So instead of a Damping Factor of 400, you would have:

DF = Load Z / Source Z

DF = 8 ohm / (.02 + 2 ohm) = 8 / 2.02 = 3.96 DF

We started out with a potential damping factor of 400 and because of our poor choice of 153.6 ft of wire, we have destroyed the amplifier's ability to dampen or control the loudspeaker load. Can you see now why those who know, employ the professional method of putting the power amplifier as close to the loudspeaker system as possible and then use the heaviest gauge wire that will fit the loudspeaker connector. If you haven't been doing this, you need to start, as you are no longer ignorant regarding the importance of damping factor.

Before I give up on damping factor, I would like to make one more point. In the above example I stated that the source impedance of a CS-800X was .02 ohms; therefore, the DF was 400 when driving an 8 ohm load. Well, I don't usually promote products in a paper intended to educate the customer, but I just must make an exception. Beginning with our recently introduced power amplifier model CS-800S, we have included circuitry (patent applied for) that automatically maintains a high damping factor. This is really an ingenious and simple circuit that our chief of analog engineering, Jack Sondermeyer, came up with.

There is a circuit that measures the small change in output voltage when the load impedance changes, and through a feedback network, the circuitry maintains a constant output voltage as the voltage neither increases or decreases with a change in load impedance. You can almost think of it as a negative source impedance so the Damping Factor remains high. It is still affected by the resistance in the wire, so you still would be wise to practice the professional method of short runs and heavy duty loudspeaker wire. The CS-800S amplifiers coming off of our production line at Peavey consistently spec out at greater than 2000 DF, and that is only because that is the highest number our system can measure.

WE ARE NOT DONE YET!
This paper is on Impedance, and in the course of this paper's unfolding I segued into source impedance and used it as a means of explaining damping factor. Source impedance also applies when you are interfacing components within the audio system. With loudspeakers, we are trying to match the loudspeaker load impedance to the output of the power amplifier to obtain maximum power. When we are only trying to transfer signal from one device to another within the audio chain, we are not trying to accomplish any work, so we are not trying to produce significant levels of current. We are just trying to pass or transfer the audio signal. There is, of course, current flow, of course, current flow, as electrons are moving back and forth, but the intention is to pass the signal as a voltage and not produce high levels of current and power. However, each signal processor in front of the power amplifier sees the input impedance of the next device as a load on its output.

Years ago, during the Jurassic period of audio, they attempted to transfer audio signal into 600 ohm loads. This is no longer valid today. The typical input impedance of a modern power amplifier is 20,000 ohm or 20 k. However, the internal output impedance (Source Z) of audio devices can be anywhere from 50 ohms to 2,000 ohms. In order to transfer the signal without introducing major deviations in level and frequency response, the Source Z to Load Z should have a ratio of 10:1; some people accept 7:1, but I hold to the 10:1 ratio.

The source impedance is often overlooked by the non-technician sound system operator. Ignorance may be bliss, but getting bitten on the behind is not pleasant. There are many signal processors, equalizers, and crossovers that do an adequate job in certain applications, but these same devices can cause many problems when the source-to-load impedance becomes reduced.

The best and first example I am going to use is in interfacing a number of power amplifiers in larger systems. There is a limit to how many power amplifier inputs can be paralleled. The limit is determined by the source impedance of the mixer output, the equalizer, or the electronic crossover.

Using the math associated with Ohm's Law, we can calculate what the load impedance will be when we parallel power amplifier inputs. Two 20,000 ohm inputs in parallel becomes a 10,000 ohm load to the signal source. Dividing the input Z by the number of amplifiers whose inputs are in parallel will give the resultant load Z that the signal source sees. Thus ten power amplifiers with their inputs in parallel would be 20,000 ohms divided by 10, or 2,000 ohms.

This means that if the internal output or source impedance of the signal source were 200 ohms, we could successfully transfer the electrical audio signal with no problems. But if the Source Z were 330 ohms we would be below the stated 10:1 Z ratio.

In large scale professional audio it is very important to consider the capability of products to drive long lines and/or loads that represent multiple impedances in parallel. There are many mixers, equalizers, and crossovers that are priced economically, and they work fine in certain simple applications. These products can present problems in large systems, however.

If you want to know how many power amplifiers can be driven by a signal source, multiply the internal output impedance of the source by 10, and divide the result into the source impedance of the power amplifiers. For instance, in our product line we have two series of graphic equalizers, the EQ series and the Q series. The EQ series exhibits a 75 ohm source impedance while the less expensive Q series has a 330 ohm source impedance.

75 x 10 = 75020,000 / 750 = 26

330 x 10 = 3,33020,000 / 3,330 = 6

You can now see that a Peavey EQ-31 can drive 26 CS amplifiers with their inputs in parallel, while the Q series could only drive 6. Thus, in applications such as small systems, the Q series could do a fine job, but there is a limit and now you know the boundaries.

I know of one mixer manufacturer that has a source impedance in their mixer's channel inserts of 1,000 ohms. This is not a real problem if you come out of the mixer with a five to eight foot shielded signal patch cable to interface some processor. But there are many users of this product that have them in studios where the inserts are permanently wired through lengthy cable that is run beneath the floor across the studio to a patch bay. They don't realize that the mixer channel is now rolling off the high frequencies significantly because of the capacitance of the cables and the high source impedance.

The cable itself becomes a low pass filter. The amount of high frequency roll-off is determined by the value of the source impedance. You can find the point where the frequency begins to roll off by taking reciprocal (1/X) of the source impedance (R) times the capacitance (C) in the cables, 1 / (R x C). Let's say, for example, that the cable is long enough to offer 0.2 mfd of capacitance (a microfarad is mathematically 0.000,001 farad).

1 / 100 x 0.000,000,2 = 1 / 0.000,02 = 50,000 Hz or 50 kHz

1 / 1,000 x 0.000,000,2 = 1 / 0.000,2 = 5,000 Hz

The signal processor hooked up to the mixer with an insert with a 100 ohm source impedance would pass signals out to 50 kHz, while the mixer with the 1,000 ohm source impedance in its insert would have significant roll-off above 5 kHz.

We have come to the end of this lengthy paper on Impedance. I believe we have pretty much thoroughly covered the subject. Some of the things I just shared with you took me fifteen years or more to understand as I now do. I don't know about you, but I am still learning. If you are learning, you are growing. When you stop growing you cease to produce quality.

Below, you'll find a chart relating source-to-load impedances and the number of amplifiers that can be driven with the inputs wired in parallel. There is also a chart on loudspeaker wire.

SOURCE Z LOAD IMPEDANCE
(in ohms) 1 K ohm 2 K ohm 10 K ohm 20 K ohm
75 1 2 13 26
100 1 2 10 20
330 0 0 3 6
1000 0 0 1 2
2000 0 0 0 1

Copper Wire Guage
AWG## Dia
mils
Dia
mm
Cir
mils
Square
inches
Sq
mm
Meter/
ohm
Feet/
ohm
Audio
amps
Max
pwr
Length
DF<50
22 25.35 0.6438 642.4 0.000504 0.33 18.52 60.75 3    
18 40.30 1.024 1624 0.001276 0.82 46.8 153.6 5 150W 10 Ft
16 50.82 1.291 2583 0.002028 1.31 74.47 244.26 7 280W 15 Ft
14 64.08 1.628 4107 0.003226 2.08 118.4 388.35 9 400W 25 Ft
12 80.81 2.053 6530 0.005129 3.31 188.3 617.7 12 800W 40 Ft
0 101.9 2.588 10380 0.008155 5.26 299.5 982.32 17 2,000W 65 Ft

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