# Why loudspeaker impedance varies with frequency

## Basic knowledge: amplifiers

Basically: Amplifiers (often also called power amplifiers) amplify an audio signal in such a way that the desired level is output from the loudspeakers. The audio signal usually comes from a mixer in which it was processed beforehand or from a source such as a CD player or computer.

An amplifier converts power into an audio signal. The audio signal used for control should only be larger but not otherwise changed.

The reason for this is the complexity of the loudspeaker. A loudspeaker consists of a magnet, voice coil and membrane (similar to a dynamic microphone). The voice coil is mounted in the magnetic field and is deflected when the amplifier current flows through it. The membrane, which is firmly connected to the voice coil, then moves the air and thus generates the sound pressure. Due to the weight of the membrane and coil and the electrical resistance of the voice coil, a lot of power is required to generate high sound pressures. In addition, the inertia and interactions of the loudspeaker with the air ensure that the impedance (= frequency-dependent resistance) of the loudspeaker is not constant over the frequency range.

The nominal impedance of a loudspeaker is typically 4 or 8 ohms. With an impedance of 8 ohms (R), an amplifier must generate a voltage (U) of 8 volts so that a current (I) flows from one ampere (U = R * I), which corresponds to a power (P) of 8 watts (P = U * I).

Due to the effects mentioned above, the impedance is unfortunately not constant; with an 8 ohm loudspeaker it can range between about 4 - 20 ohms. Amplifiers must therefore be equipped with ample reserve in order to cope with these fluctuations.

### Output power of an amplifier

The output power of the amplifier determines, among other things, the attainable volume. The sensitivity of the loudspeaker used, given in dB / watt at a distance of 1 meter, also plays an important role, but more on that elsewhere. An amplifier with 200 W on an 8 ohm loudspeaker sends 40 volts of voltage to the loudspeaker, which results in an output current of 5 amps (I = U / R). Conversely, 40 volts times 5 amps result in an output power of 200 watts (P = U * I).

If we now want to double the deflection of the membrane, we must also double the current, i.e. from 5 to 10 amperes. Since the impedance of the speaker is still 8 ohms, we have to apply double the voltage, i.e. 80 volts. If we now calculate the output power of the amplifier, we come to 80 V * 10 A = 800 W, i.e. a quadrupling! It is therefore not surprising that large public address systems require amplifiers with an output of several kW in some cases.

### Performance limits of an amplifier

The power that an amplifier can deliver is limited. For example, the voltage that an amplifier can output can be as high as the voltage that the power supply unit can output. If an attempt is made to exceed this power, the signal is cut off (although amplifiers nowadays have protective circuits that prevent it from being exceeded). This so-called "clipping" leads to the typically distorted sound of an overdriven power amplifier. Power supplies with higher voltages and outputs are technically not a problem, but they increase the costs and weight of the output stages. At some point the maximum power that a socket can deliver (230V / 16A), for example, comes into play.

The minimum permissible impedance is another important characteristic of the amplifier. It should be less than or equal to the impedance of the connected loudspeakers. The lower the impedance of the connected loudspeakers, the higher the current and thus also the power that has to be supplied by the amplifier. You should therefore be particularly careful when connecting several loudspeakers to one amplifier channel. Switching the loudspeakers in parallel reduces the impedance considerably. Two 8 Ohm loudspeakers in parallel correspond to 4 Ohm impedance, 4x 8 Ohm in parallel correspond to 2 Ohm total impedance, which is often the limit that an amplifier can achieve. As we already know, the impedance of an 8 ohm loudspeaker can fluctuate between 4 and 20 ohms depending on the frequency, 4x 4 ohms in parallel then correspond to 1 ohm total impedance! If the total impedance becomes too low, too much current flows in the output and the amplifier overheats and (hopefully) switches off.

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