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.
Next
page
|
|
 |
| |
|
