Yamaha P-2200, P-2200/2201, P-2201

The Voltage across the Resistor is Less Than the Source

Voltage due to the voltage drop across the output resistor RO:

An "Impedance" is some combination (one, two, three or

more components connected together in a circuit) of Resistors,

Capacitors and Inductors.

Fig. 80 - Elements of an Impedance.

simple ohmic value, so long as only one frequency is

used. However, single frequencies are not representative

of audio sources (except for test tones), so this is a good

place to make a simplifying assumption: the impedances

that we work with in audio can be treated like pure

resistances over the entire audio frequency range. This is

a good assumption, in most cases, and we have used it

throughout this manual. When the occasional exception

shows up, we have treated it separately. If we had to

deal with an actual impedance value (made up of a pure

resistance and a reactance), most of the formulas we use

would

the

same,

but

would

have

deal

with

complex numbers (with a real and imaginary part)

instead of simple ohmic values.

SERIES AND PARALLEL

IMPEDANCE CONNECTIONS

Figure 81 diagrams the differences between series and

parallel connected impedances. The total impedance, ZT,

of a set of series connected impedances is simply their

algebraic sum. The total impedance of a set of parallel

connected impedances is given by the following formula:

NOTE: X is the output resistance (or impedance) of the

source. Y is the voltage drop across the output resistance which

varies depending on other circuit parameters.

Fig. 79 - Voltage Sources.

IMPEDANCE

"pure"

resistance

would

maintain

the

same

value,

in ohms, even if the voltage or current source changed

from a DC source to an AC source at any frequency. On

the other hand, an impedance is made of a pure resistance

connected to a reactance (a capacitor, an inductor, or

some combination of the two). The value, in ohms, of

the magnititude of an impedance changes with frequency,

making it more challenging to manipulate mathematically.

"Pure" circuit components (a perfect voltage source,

perfect current source or pure resistance) do not exist

in the real world, and audio circuits seldom deal with DC

sources, except for occasional batteries and DC power

supplies. However, the P-2200 can be considered to be

a perfect voltage source because it behaves in this

manner within its specified operating limits. Similarly,

a source such as a mixer that is feeding the P-2200 can

be considered to be a perfect voltage source in series

with a pure resistance, the resistance being equal to the

mixer's output impedance. Even a speaker impedance

can be considered to be a pure resistance in some cases,

though in other cases the variation of a speaker's

impedance with frequency must be considered. The

behavior of audio circuits is more easily explained by

making these and other, similar assumptions.

To illustrate a typical assumption, consider that any

impedance can be treated as a pure resistance having a

When there are only two impedances connected in

parallel, the formula can be simplified to:

If the two impedances are the same ohmic value, the

formula further simplifies to:

This final simplified formula is valid for any number

(N) of parallel impedances provided that their ohmic

values are a/I the same:

To calculate the power dissipated in any of the

impedances (any branch) of the circuits of Figure 81,

simply find the voltage across that impedance or the

current through the impedance, (using the voltage

and current division rules that follow). Alternately, find

both the voltage and the current in that branch, and use

the power formulas developed on Page EIGHT 2. Note

that if all the impedances shown in any one of the

circuits in Figure 81 are the same, the power dissipated

in each of those equal impedances is also the same:

one-fourth of the total power dissipated.