You didn't need an L-Pad to turn the volume down and balance them with the mains?
Yes, one would normally add an L-pad to balance.
No, an L-pad is not required. With some trial and error selecting the right value cap ( 1.5uF in this case ) makes them blend. The tweets run off the same main amp and it's a simple matter of wiring the cap to it's positive terminal.
The capacitor value merely determines the overlap between the super-tweeter and the existing tweeter. It does not balance the driver efficiencies. Many older adults cannot properly hear above 10k Hz, so the blending is less critical for them and the overall increased volume for higher frequencies may be beneficial, so the L-pad may not be necessary for that audience. Younger listeners will object to the comb artifacts formed as the two drivers, farther apart than 1/4 wavelength, interact.
But that doesn't mean an L-pad isnt' necessary. Here's why.
The capacitor forms a
first-order high-pass filter and determines the filter's corner frequency,
fc, i.e. the lowest frequency passed, at least subject to the 6 dB / Octave roll off. For the example you cited of 1.5 µF that is 8,841 Hz. Choosing a higher frequency crossover point merely reduces the overlap between the cone tweeter and the super-tweeter.
It has nothing whatsover to do with balancing the driver efficiencies.
The tweeter should have an inductor added to create a band-pass filter, and thus prevent overlap between the tweeter (which will distort at higher frequencies) and the super-tweeter. In addition, the super-tweeter itself should have a band-pass to avoid ultrasonic oscillation, which many amplifiers have, as this can destroy a super-tweeter. A normal cone tweeter is mechanically limited, so it tends to be less vulnerable to such oscillation, but it, too, can be destroyed.
An L-pad is a attenuator, either fixed or variable, placed in parallel with a driver, in this case a tweeter, such it presents a constant impedance load, i.e. the impedance will not alter from the driver's nominal impedance, so that the crossover point will not change with attenuation. The L-pad is used to balance the tweeter's output volume to that of the other speakers. It has nothing to do with the crossover point.
As I have many times posted, the math won't lie, unlike the internet. Here's the math from one of my prior postings.
Consider the formulas:
Given:
R is Nominal Speaker Impedance (Ω)
C is Capacitance (Farad)
L is Inductance (Henry)
f is Frequency (Hertz)
Inductor Formulas:
L = R / (2π x f) (Henry)
f = R / (2π x L) (Hertz)
R = 2π x L x f (Ω)
Capacitor Formulas:
C = 1 / (2π x f x R) (Farad)
f = 1 / (2π x C x R) (Hertz)
R = 1 / (2π x C x f) (Ω)
NB:
L is inductance in Henry.
To convert from Henry (H) to milliHenry (mH) multiply by 1,000.
To convert from milliHenry (mH) to Henry (H) divide by 1,000.
C is capacitance in Farad.
To convert from Farad (F)to microFarad (uF) multiply by 1,000,000.
To convert from microFarad (uF) to Farad (F) divide by 1,000,000 or multiply by 0.000001.