#### Table of Contents:

- Circuit Design: How to Measure Impedance of a Loudspeaker
- Variable frequency sine wave generator
- Impedance Calculation

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.

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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.