Most
of the people have noticed a change in the voice of others when they
speak through the telephone. Most of the people might have experienced
difficulty in hearing other sound in the environment where the person at
the other end of the telephone calls from. It happens mostly for high
frequency sound like instrument music, sound from video game etc. People
who are interested in electronics and who have done some audio circuits
with loudspeakers might have experienced an exactly opposite phenomenon
in which the sound reproduced by the loudspeaker is more clear and loud
for higher frequencies. Also those who have experienced quality of
music played through the home theater system know how far better it is
from a single speaker which can create the same loudness.The explanation
for all the above mentioned phenomenon is simply due to the fact that a
simple sound generating device cannot produce all the audible
frequencies with the same loudness.

The
audible range for human being starts from 20Hz to 20 KHz and it varies
from person to person and significantly with the increasing age of each
one. The voiced speech of a typical adult male will have a fundamental
frequency from 85 to 180 Hz, and that of a typical adult female from 165
to 255 Hz. The telephone can reproduce the sound which falls in the
range of 300 Hz to 3 KHz only. It is only due to the presence of higher
harmonics of the human voice in that range makes the telephone useful.
Since the maximum frequency is only 3 KHz the higher frequency sounds
are little audible through the telephone.

The
telephone system is only an example which has been optimized to perform
at a certain range of frequency. Such a kind of optimization is
required in most of systems because when it comes to the electronic
devices like filters, amplifiers, loudspeakers etc. their
characteristics vary with frequency of operation. This change in
characteristics with the frequency explains why the home theaters with
different kind of loudspeakers are able to produce high quality sound
including all the high frequency and low frequency sounds which are not
at all possible with a single loudspeaker.

The
mechanical construction of the loudspeaker plays a significant role in
deciding its performance at different frequency range but those who are
designing circuit for the loudspeaker are more interested in an
important electrical characteristic of the loudspeaker called impedance.
This article discusses how to measure the impedance of a loudspeaker at
a required frequency of operation.

__DESCRIPTION:__
Every electronic component including resistors, capacitors
and inductors produce a resistance to the current flowing through it
and it is generally called impedance irrespective of the component. This
impedance value for a particular device may or may not vary with the
frequency of the current flowing through it. A good quality resistor has
almost the same impedance value from 0 Hz (DC) frequency to infinite
hertz, but the impedance of a capacitor decreases with frequency and an
inductor increases with frequency. Thus in case of a resistor the
resistance and the impedance has the same value. Simply the impedance is
the resistance of any component at a given frequency and hence
impedance value of a component isalso represented in Ohms. Like the
resistance is denoted with letter ‘R’, the impedance is denoted with the
letter ‘Z’.

The
impedance of a loudspeaker has very high variations with the frequency
of operation and it is significant in the design of audio devices like
amplifiers, speaker drivers etc. Consider the case of an amplifier with a
loudspeaker at its output.

The
amplifier is a device which can source a current to the loudspeaker and
every current sourcing device has an internal resistance and here it is
represented as a resistance R

_{int}. Since the resistor has the same value for its resistance and impedance it is also marked as Z_{int}. This internal resistance of the amplifier is also referred to as the output resistance and hence it is marked as Z_{out}. The impedance of the loudspeaker is represented as Z_{ls}.
In the above system both the Z

_{out}and Z_{ls}comes in series with each other and the same current flows through both of them. As in the case of a two resistors connected in series with each other, the same current flowing through two impedances connected in series will generate different voltages across both the impedances. In the above figure V_{fs}is the voltage of the fictional source inside the amplifier which is generating the frequency and the V_{fint}is the voltage drop across the internal resistance and the V_{fls}is the drop across the loudspeaker.
From the above figure it can be understood that even though the amplifier generates a voltage V

_{fs}the loudspeaker receives only a voltage of V_{fls}and the rest will get dropped across the internal resistance as given by the following equation:**V**

_{fint}= V_{fs}–V_{fls}
The
value of the voltage drop by the same current across the impedances
depends upon the value of the impedance and the value of the current
flowing through them. If the voltage at the operating frequency is
represented by ‘V

_{f}’ and the current by ‘I_{f}’and the impedance by ‘Z’, the V_{f}is directly proportional to the Z as given by the following equation:**V**

_{f}= I_{f}* Z
Applying this knowledge in the above equation it can be re-written as the following:

**V**

_{fint}= V_{fs}– I_{f }* Z_{ls}
From the above equation it is clear that the loudspeaker with low impedance ‘Z

_{ls}’will produce large internal voltage drop ‘V_{fint}’ in the amplifier and vice versa. Since the impedance is frequency dependent one should find the loudspeaker which provides the highest impedance at the operating frequency. The variation of the impedance of a common loudspeaker can be plotted as shown in the following figure:
The
direct method to calculate the impedance of a loudspeaker at the
required operating frequency is to connect it with a pure sine wave
generator having the frequency same as the required operating frequency
and measure the voltage drop across the loudspeaker. The details of the
sine wave generating circuit used to calculate the impedance of a
loudspeaker is discussed below. Since in audio applications the
impedance should be calculated for a range of frequencies and hence a
variable frequency sine wave generator has been designed based of Wien
Bridge oscillator.

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