Fundamentals of Audio and Acoustics 33Direct current (dc) flows in one direction only. In ac
(alternating current) the direction of current flow is
alternating at the frequency of the waveform. Voltage
and current are not always in sync so the phase relation-
ship between them must be considered. Power flow is
reduced when they are not in relative phase (synchroni-
zation). Voltage and current are in phase in resistive
circuits. Phase shifts between voltage and current are
produced by reactive elements in a circuit. Reactance
reduces the power transferred to the load by storing
energy and reflecting it back to the source. Loud-
speakers and transformers are examples of sound
system components that can have significant reactive
characteristics. The combined opposition to current
flow caused by resistance and reactance is termed the
impedance (Z) of the circuit. The unit for impedance is
also the ohm (: . An impedance can be purely resistive,
purely reactive, or most often some combination of the
two. This is referred to as a complex impedance. Imped-
ance is a function of frequency, and impedance
measurements must state the frequency at which the
measurement was made. Sound system technicians
should be able to measure impedance to verify proper
component loading, such as at the amplifier/loudspeaker
interface.
(2-12)where,
Z is the impedance in ohms,
R is the resistance in ohms,
XT is the total reactance in ohms.
Reactance comes is two forms. Capacitive reactance
causes the voltage to lag the current in phase. Inductive
reactance causes the current to lag the voltage in phase.
The total reactance is the sum of the inductive and
capacitive reactance. Since they are different in sign one
can cancel the other, and the resultant phase angle
between voltage and current will be determined by the
dominant reactance.
In mechanics, a spring is a good analogy for capaci-
tive reactance. It stores energy when it is compressed
and returns it to the source. In an electrical circuit, a
capacitor opposes changes in the applied voltage.
Capacitors are often used as filters for passing or
rejecting certain frequencies or smoothing ripples in
power supply voltages. Parasitic capacitances can occur
when conductors are placed in close proximity.(2-13)where,
f is frequency in hertz,
C is capacitance in farads,
XC is the capacitive reactance in ohms.In mechanics, a moving mass is analogous to an
inductive reactance in an electrical circuit. The mass
tends to keep moving when the driving force is
removed. It has therefore stored some of the applied
energy. In electrical circuits, an inductor opposes a
change in the current flowing through it. As with capac-
itors, this property can be used to create useful filters in
audio systems. Parasitic inductances can occur due to
the ways that wires are constructed and routed.(2-14)
where,
XL is the inductive reactance in ohms.Inductive and capacitive reactance produce the oppo-
site effect, so one can be used to compensate for the
other. The total reactance XT is the sum of the inductive
and capacitive reactance.(2-15)Note that the equations for capacitive and inductive
reactance both include a frequency term. Impedance is
therefore frequency dependent, meaning that it changes
with frequency. Loudspeaker manufacturers often
publish impedance plots of their loudspeakers. The
impedance of interest from this plot is usually the
nominal or rated impedance. Several standards exist for
determining the rated impedance from the impedance
plot, Fig. 2-16.ZR^2 += XT^2XC^1
2 SfC-------------=Figure 2-16. An impedance magnitude plot displays imped-
ance as a function of the applied frequency. Courtesy
Syn-Aud-Con.XL= 2 SfLXT XLā= XC0102020 200 2K 20K
FrequencyImpedanceZmin