Amps and Speakers, Living Together
By
Pat Brown
The role of impedance, resistance and reactance in an
audio system 
Click here for Audio power trip Part 1
My column last month (LSI February 2003 issue) provided a look at some
of the basic fundamentals of power generation and consumption. All of
the examples used were not specific to audio. Greater insight into audio
can be gained by looking outside of the traditional ways that we understand
these concepts and learning from things that we experience everyday. This
issue, we will continue in the same form as we explore the complex impedance
and its role in power delivery systems.
In mechanical systems (which include loudspeakers), the frictional component
of the load is accompanied by the very real but less tangible (at least
intellectually) effects of mass and inertia. A body at rest wants to stay
at rest, so the mass of an object must be overcome by the applied force
to get it into motion. Once the body is in motion, it wants to stay in
motion. Some of the applied energy has been stored in the load, and serves
to lessen the amount of applied power that is required to keep the mass
in motion. The mass of the load produces a reactance - an opposition to
the applied force that is frequency-dependent.
Isaac Newton gets much of the credit for quantifying these effects. The
electrical equivalent of this mechanical characteristic is called inductance
- a characteristic that all loudspeakers possess, and one that the amplifier
has to deal with. When the total impedance of a load has both resistive
and reactive components, we say that the load has a complex impedance.
REFLECTED POWER
Reactive elements affect the flow of power from one system to another.
To further understand the complex impedance, let’s take a trip to
Home Depot and consider a mechanical system not unlike a loudspeaker.
Grab a shopping cart and head down the aisle. Shopping carts don’t
have much mass, so they are pretty easy to handle when they are empty.
Let’s visit the construction department and load a half-dozen bags
of ready-mix concrete into the cart. The added weight has made the cart
much harder to push, so we dig in and extend a lot of effort to get it
going. But once it’s in motion, we can let up on the applied pressure.
The shopping cart is now a mass in motion that wants to stay in motion.
Its momentum carries it forward - which is a bad thing for the unwary
consumer that wanders across your path. The mass reactance of the cart
stored some of your early effort to get the cart going, and is now being
reflected (returned to the source), making it easier for you to keep the
cart in motion. The stored energy (which you supplied) must now be overcome
to stop the cart.
Like a moving mass opposes changes in velocity, an electrical inductance
opposes changes in the current flowing through it. This opposition is
called inductive reactance. And because loudspeakers are electro- mechanical
devices, they exhibit this characteristic both mechanically and electrically.
How can one counteract the momentum of the cart? Does a “mechanical
opposite” exist? If we connected a big spring between the cart and
a rigid object (stay with me), the spring would expand as the cart moved
farther from the object. This force would oppose the momentum of the cart,
and could cancel it completely if its value were carefully selected.
Energy stored in a compressed spring, like momentum, is reflected back
to the source - a concept that is sometimes learned the hard way if we
are the source! “Springy” mechanical loads have compliance.
The electrical equivalent is capacitance and the effect is capacitive
reactance - another characteristic that loudspeakers possess. If the tension
of spring and the momentum of the cart exactly compensate each other,
only the resistance remains. The system (or circuit) is said to be in
resonance.
INDUCTIVE AND REACTIVE
Just as mechanical loads have friction, momentum and compliance, electrical
loads have resistance, inductance and capacitance. Acoustical loads (like
the air) have the same properties. The “catch all” term for
the total opposition to current flow into a load is impedance. In many
circuits, the inductive and reactive components may be insignificant and
can be neglected. This is the case for most interfaces in a sound reinforcement
system, at least at audio frequencies.
In loudspeakers, reactance abounds and must be considered. Because all
three are present we say that the loudspeaker has a complex impedance.
A concise mathematical expression for impedance is shown in Figure
1.
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The unit for impedance, resistance and reactance is the ohm. The equation tells us that the reactances are in opposition to each other. At some frequencies one will dominate the other. It is also possible for them to cancel each other, leaving only the resistance. |
The equation also shows that impedance is a pretty complex quantity.
Because reactance is frequencydependent, the impedance will have to be
expressed on a graph.
The shopping cart experience is exactly what happens when we drive a real-world
loudspeaker with an amplifier. The loudspeaker is a mass/spring system
that will both reflect and consume the power that flows into it. At some
frequencies the mass effects will dominate (the load is inductive), at
others the spring effects will dominate (the load is capacitive), and
at others these two effects will cancel and the load will be purely resistive.
It’s becoming easy to see why we can’t accurately describe
the impedance of a loudspeaker with a single number rating.
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The impedance is a complex function of frequency (Figure 2). Manufacturers usually state the nominal impedance on the spec sheet, such as 8 ohms. In reality, there won’t be many frequencies at which the impedance is 8 ohms, a source of great confusion to those that have just obtained their first impedance meter and set out to measure every loudspeaker in the shop. |
The DC resistance of the voice coil wire is the lowest value that the impedance can be, so it is of special interest when determining the maximum power flow into the loudspeaker. Look for the lowest point on the impedance curve when determining how many loudspeakers you can hook to an amplifier.
LOADING THE AMPLIFIER
In last month’s column, we saw that a power source can be rated
in available power. This is simply a measure of how much power is available,
whether from an automobile, a jet engine or you on an exercise bike. Available
power can be stated in watts or horsepower. When a time metric is included,
it can be expressed in watthours, calories, or BTU (British Thermal Units).
Think of available power as how much power a source can supply on a continual
basis. Next, we must consider how much power we can get from the source
- something that is determined by the load.
Physics, like audio (and life) has many ironies. We don’t need knowledge
of the load characteristics to state the available power from a source,
but we do need detailed information about the load to determine how much
power we can get. It is also becoming apparent that putting a power rating
on an amplifier is no easy task. Every loudspeaker’s impedance curve
is different, so which one do we test the amplifier with? One way to do
it is to use a purely resistive load - no reactive component. This levels
the playing field when comparing amplifiers.
But in the real world of loudspeakers and transformers, there may be significant
reflected power back to the amplifier (remember the shopping cart?). Can
the amplifier handle reactive loads? If it can’t, then it will likely
fail in the real world of complex load impedances. Don’t read more
into an amplifier specification than what is there. Specs are great to
get the “big picture,” but they seldom tell the complete story.
POWER TRANSFER
The best way to understand power transfer from the amplifier to the loudspeaker
is to put reactance on the “back burner” for a while and simplify
the complex impedance to a pure resistance. This is not the real-world,
but it’s the next step in understanding what happens in the real
world. Using resistance-only allows us to temporarily ignore the effects
of stored and reflected power.
All of the generated power from the amplifier will simply heat the load
resistor, and none of it will bounce back and slap the amplifier in the
face (which is not an uncommon occurrence in sound systems, as evidenced
by the smell of burnt resistors and semiconductors accompanied by smoke
pouring out of the rack).
The power transfer between a source to a load is determined by the impedance
ratio between the two, which is simply the load impedance divided by the
source impedance. Since we are temporarily ignoring reactance, this becomes
a ratio of the load resistance to the resistance in the amplifier’s
output circuit.
There is also resistance in the wiring, but we will also neglect it for
the present (magic wire). The load resistance is the opposition to current
flowing from the source, resulting in power conversion into heat. For
a loudspeaker, the direct current resistance of a voice coil can be found
with an ohmmeter. In most cases it’s a low number - less than 8
ohms. This accounts for one part of the impedance ratio that determines
the power transfer from the amplifier to the loudspeaker.
The other part is the source impedance of the amplifier. All sources have
internal impedance - an opposition to the flow of current that is inside
the device. The amplifier’s internal wiring, circuit board traces,
and transistors all have inherent resistances (all conductors of electricity
do) and the electrons must fight through this internal opposition as well
as the opposition of the load as they travel around the circuit. The source/load
impedance ratio determines whether the generated power gets dissipated
inside the amplifier, in the interconnecting wiring, or in the load.
In fact, all of these elements will dissipate power, but the idea, obviously,
is to get it to the load. Since power is voltage times current, you need
both to get an appreciable amount of power flow. If the load resistance
is too high, less current flows (there’s more opposition) and power
flow is reduced. If the load resistance is too low, lots of current flows
but the voltage (pressure) is reduced, so again power flow is reduced.
The maximum power transfer takes place when there is a balance between
these two extremes, known as the impedancematched interface (or just matched
interface for short).
This condition exists when the source and load resistances are equal.
Impedance matching has been around as long as time and space - nature
does it all the time. It has been used to interface electrical devices
for about 150 years.
CONSTANT VOLTAGE INTERFACE
Don’t stop reading at this point! If you do, you might walk away
with the idea that impedance matching is the proper way to hook an amplifier
to a loudspeaker. Actually, it’s a terrible way to do it, for several
reasons.
First, in the matched interface, half of the available voltage from the
source is dropped across the output impedance of the source, and only
half of it gets developed across the load. While the matched interface
has good power transfer characteristics, it doesn’t have good voltage
transfer characteristics. The way to get more of the amplifier’s
voltage to develop across the load (loudspeaker) is to make the load impedance
higher than the source impedance.
It’s kind of like sticking your thumb in the end of a garden hose
- the pressure goes up as the flow is reduced, as evidenced by your red
thumb. But because increasing the load resistance produces more opposition
to current flowing from the amplifier (or water through the garden hose),
the power transfer actually goes down. We are sacrificing power transfer
to get better voltage transfer. This seems counterproductive, but this
configuration can still produce plenty of power into the load - just not
as much as is potentially available.
Are you ready for another irony? If you make the load resistance at least
ten times higher than the source resistance, the voltage across the load
is no longer affected by the load resistance’s value. Going back
to the water hose, if you stick your thumb into the end so tightly that
the flow stops, you have realized the maximum pressure available from
the source. From then on, you can’t get any more pressure, even
though you add more opposition. You have constructed a constantpressure
interface.
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The analogous electrical interface is the constant-voltage interface. This mode of operation is nearly universal in audio (I always hate to say always). Output impedances are low relative to the input impedance that they are connected to. See Figure 3 for a schematic representation of the amplifier/ loudspeaker interface. |
TRADING OFF POWER TRANSFER
Why would we deliberately reduce the power transfer between the amplifier
and loudspeaker by using the constant-voltage interface? Why not impedance-match
and get maximum power transfer? There are several really good reasons.
The first is that the constant-voltage interface facilitates the connection
of additional loudspeakers in parallel with the first. If impedance matching
were used, and one loudspeaker were connected across the amplifier, the
connection of a second one in parallel (or series) with the first one
would reduce the power flow to the first loudspeaker. So, every time another
loudspeaker is connected, the loudness of the existing ones would change
(what a mess!). The constant voltage interface maintains the same voltage
(and power flow) to the existing loudspeakers connected to the amplifier
as additional ones are hooked-up.
Now don’t get carried away - if you connect too many you will upset
the conditions that made this a constant voltage interface to start with.
But it is usually possible to connect one, two, or even three loudspeakers
onto a power amplifier and still maintain the constant- voltage condition.
We just have to make sure that the parallel combination of all of the
loudspeakers doesn’t get low enough to make the amplifier’s
voltage drop. This is why amplifier manufacturers specify the minimum
impedance that the amplifier can safely drive. As each additional loudspeaker
is connected in parallel with the first, the total impedance seen by the
amplifier is reduced, so the current flow goes up.
This may seem counterintuitive, but think of a bucket of water with two
holes in it instead of one. More water will flow out of the bucket in
a given span of time. Adding more holes will allow even more flow. When
you hook-up additional loudspeakers to an amplifier, you’re putting
more holes in the bucket! If load impedance seen by the amplifier gets
too low there’s a lot of fallout. The amplifier’s voltage
might drop, its current producing abilities may wane, and the otherwise
relatively small amount of resistance in the interconnecting wires and
plugs can start to become a factor. If operated this way over time, the
amplifier may actually shut down or burn up.
We now have one more piece of the puzzle for discussing meaningful ways
to understand and specify power transfer in audio circuits. Next month
we will discuss some characteristics of audio signals that determine how
much power they are likely generate into the complex impedance of the
loudspeaker.
Pat Brown, with his wife Brenda, heads up Syn-Aud- Con, leading audio
training sessions around the world. For more info, go to www.synaudcon.com.