In this article i will present a way to model the impedance of a speaker driver and how to use that in crossover design. Most crossover calculators on the internet assume a linear fixed impedance as the load of the filter but as you will see this is not the case. For this purpose I created a spreadsheet that will calculate the parameters for you.
The spreadsheet uses Electrical and Mechanical parameters of the loudspeaker driver and calculates the equivalent electrical component value to be used with any circuit simulation software (e.q. SPICE).
Re and Le are electrical components and describe the voice coil properties. Lces, Cmes and Res are mechanical components that are shifted via the BL coupling factor to the electrical side of the impedance model.
It is important to take this fact into consideration because more often than not the mechanical part of the impedance has an influence on the way the filter will respond.
In the below example you can see a standard L-R lowpass filter with a corner frequency of 1kHz. You can see the filter applied to a 8 ohm resistor in the way the most online calculators are being used and you can also see the filter applied to a complex load which represents the electrical model of the loudspeaker (without a box).
Now lets look at the filters response ( dashed line represent the 8 ohm resistor load and the solid line represents the advanced electrical model load )
As you can see the differences cannot be negligible. Below you can find the attached spreadsheet that you can use to build the model. Also it can calculate the box influence for a closed box or bass reflex. The tree elements are connected in series and form a branch that is connected in parallel to the mechanical equivalent components.
Electric Model of Loudspeakers