Let's say we want to build a dipole bass system using four 12" drivers with the following specifications: Vas: 164 litres., Fs=30Hz, Qts=1.10, Qes=1.30, Qms=7.0, R=8 ohms, Xmax=8mm, Sd=0.0547m^2 .
To maximize efficiency, the drivers will be wired in parallel, giving an effective Re of 2 ohms. We also want to know what SPL levels we can expect if we drive the system with 100W of power.
To increase the Qts to the target value, we can use a series resistor Rs, and calculate its value as follows:
Qes' = 1.75*7/(7-1.75)
Qes' = 12.25/5.25
Qes' = 2.33
Rs = Re*(Qes'-Qes)/Qes
Rs = 2*(2.33-1.30)/1.30
Rs = 2*1.03/1.30
Rs = 1.6 ohms
As we plan to drive the system with 100W of power, assuming 10:1 differences between average and peak levels, we can use a 10W or greater resistor for Rs.
As the total resistance, Rs+Re, will be 3.6 ohms, the amplifier will have to be capable of driving at least a 3.6 ohm load.