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To calculate a specific impedance curve the resulting impedance would have to be calculated for each frequency. Resistance is calculated just like impedance (in fact we could say that the resistance is the impedance at a frequency of 0 Hz). The calculation is valid for any type of impedance, be it from electronic equipment or loudspeakers. At the bottom of this document you will find a link to an in-depth article on speaker impedance.
Since impedance is different for each frequency, what is calculated is the nominal, or the minimum impedance, or the impedance at a given frequency.
There are two basic ways of connecting loads (loudspeakers are often referred to as "loads" when dealing with power delivery and impedance calculations), series and parallel, with their respective calculation methods. We can also combine both types of connections in a "series-parallel" connection.
Series connection
The illustration below shows the series connection of a group of speakers to a power amplifier channel:Z_{1 } represents the first load and Z_{n} the last (nth) load in a group of n speakers. The suspension points indicate that the connection can be made with any number of boxes. The current passing through each speaker is the same.
Serial connections have some disadvantages. The main one is that if one of the loads fails (the speaker voice coil gets burnt and becomes an open circuit, or simply a connector becomes loose), all the elements in the series are left without a signal. The other relates to a more diffuse concept: the damping factor (a link to an educational document on this subject is provided at the bottom of this document). The series connection makes the damping factor tend to 1, since speakers in series with a given speaker work as a series impedance, and therefore as if they were a cable that provides a large amount of impedance. Therefore series connections are usually limited to industrial public address or commercial background music applications when it comes to full range signals, since low frequencies lack "tightness". In mid and high frequencies, series connections are accepted since in these frequency ranges the damping factor does not affect the sound quality, and therefore we find commercial loudspeakers where several components within the same mid or high frequency section are connected in series. From a practical point of view, series connections are cumbersome to make when using loudspeakers with input connectors in portable applications, since loop-through cables cannot be used to carry the signal from one loudspeaker to another, and are therefore easier to implement when used in applications with fixed connections and bare wire connectors.
The calculation of a series impedance is extremely simple, since we only have to add up the impedances (or resistances, if we want to calculate the value of the total resistance):
Z_{total} = | Z_{1} + Z_{2} + Z_{3} ... + Z_{n} |
For example, if we had four 2-ohm speakers connected in series, the total impedance would be 8 Ohms (2+2+2+2). In this example the amplifier would deliver its specified power per channel at 8 ohms, which would be equally distributed to each speaker. For example, if the amplifier specifies 1000W per channel at 8 ohms, each of the four components receives 250W. The power distribution is equal in this example because all the elements in series have the same impedance.
(NOTE: If the impedances were different, the calculation of the received power would be more complicated, being the received power for each speaker is proportional to its impedance, and we would therefore be using an impractical connection).
Go to part 2: Parallel connection