• Parallel and series connections: description and calculations

    Series-parallel connection

    If we combine series connections with parallel ones we have the so-called "series-parallel" connections. They are normally used for public address systems or background music when we have a number of speakers that we want to connect to an amplifier and neither the serial nor the parallel connection gives us a total impedance that matches our needs. To calculate the resulting impedance, the speakers connected in series are grouped together, and then the parallel sum of all these impedances is calculated.

    The illustration shows it more simply. We have pairs of 8Ω (eight-ohm) speakers connected in series. The pairs are connected to each other in parallel. We calculate the total impedances of each pair of speakers, which, since they are in series, is only 8+8 ohms, giving a total of 16 ohms per pair. Then we only have to calculate three 16-ohm impedances in parallel, which is simply 16/3 (that is, 5.33 ohms) following the formula given above.

    This type of connection shares the disadvantages of series connections, with the particularity that if a speaker is disconnected or burnt (open circuit), only the elements connected in series to it would also lose their signal. For applications where series-parallel speaker connections would be used, a speaker system with an input transformer (70 or 100V line) is an alternative that delivers high practical parallel connections.

    Addendum: Impedances summing in multi-way passive loudspeakers

    In a speaker with a passive crossover filter, although the different frequency sections are in parallel, the impedance summing formula should not be used to calculate the total impedance of the speakers. This happens because there is impedance separation, so we can consider that each band's impedance is independent from the others. This happens because what the crossover filter does is to increase the impedance outside the passband of the component. For example, at low frequencies the impedance of the combination HF driver+filter makes the value of the impedance in those frequencies very high, and therefore negligible.