# Active crossover circuit

Posted on Jan 6, 2013

A simple 3-way crossover, intended for triamping Hi-Fi systems. This is a conventional 12dB / Octave unit, and cannot be expected to have the same performance as a Linkwitz-Riley aligned filter network. It will still be a vast improvement over nearly any passive crossover, and is ideal for beginners or those who want to experiment further with multi-amping, but without the complexity of a major project. The retuning (to (sub)-Bessel / Linkwitz-Riley alignment) is recommended, as the performance will be more in line with modern standards - see information below.

The crossover is based on the 2nd order Butterworth filters. The resistors Ra and Rf set the gain of each filter to 1.582, which is slightly less than the required value of 1.586. This value of gain (Ao) follows from the formula ... k = 3 - Ao where k = 1 / (Q-factor of the filter). For a 2nd order filter, the value of k can be obtained from the butterworth circle for n = 2. It turns out that k = 1 / cos(x), where x = ? / (2 * n) which is ? / 4 in this case. Thus for a butterworth response, the Q-factor turns out to be 0.707. Please see references (1) for more details. Note that the mid-range filter is preceded by an inverting amplifier. This is needed for 2 reasons - Firstly, the gain of the mid-range is (1.582 * 1.582) which must be brought back to the level of the low-mid & mid-high ranges (1.582). Secondly (and more importantly), the 2nd order butterworth filter has an inherent property of shifting the phase of any signal passing through it depending on the signal's frequency so that at cut-off the signal is 90° out of phase with the input (direction of shift depends on whether the filter is high-pass or low-pass). Thus at 300 Hz the low-mid range filter has shifted the signal by 90° and the mid range has also done the same (but in an opposite direction). Hence, at 300 Hz, the signals appearing at the low-mid range & mid range outputs are going to be 180° out of phase with each other & will cancel out...

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