To achieve the textbook filtered curve you expect from generic off-the-shelf or textbook equation calculated passive crossovers, these generic implementations require a constant load impedance/resistance and assume your transducers exhibit a linear frequency response.
That constant load is usually 4 or 8 ohms. A transducer’s impedance varies with frequency. We can compensate for the varying impedance curve using conjugate networks but most builders using these crossovers will not design and build such a network.
Even if the impedance can be flattened, the crossover design works best with a linear driver frequency response. Let’s assume that is true when the transducers is measured on an infinite baffle (2pi environment). Unfortunately the frequency response will change when measuring the transtucers in the speaker cabinet within an anechoic or 4pi environment.
To the left is a computer model of a somewhat linear full-range transducer in 4pi (green curve) and in 2pi (blue curve) on an 8″ wide x 15″ high baffle using a 4th order diffraction model. As you can see, frequency response compensation for the baffle diffraction is a requirement that the generic crossover cannot provide.
Let’s apply a generic 2KHz 2nd order Butterworth Low Pass passive filter to the transducer above. The result is the red curve below along with the textbook expected response in grey. Of course the result is very different than the target response
How do we achieve the target response? That’s the subject of a future post.