Xenover Ver. 2.0
There is a funny thing about active crossovers. Everyone knows that bi-amping your speakers can bring about marvelous improvements in sound quality, but very few people actually do it. Granted, bi-amping means you've got to buy more equipment, decide on crossover frequencies and slopes, and perhaps even modify your speakers if they're not already wired to accept bi-amplification, but given the benefits, you'd think more people would take the plunge. In an attempt to get at least some of you moving, I'll provide a crossover design that's simple, extremely high performance, and inexpensive.
Let us begin by talking about JFETs for a moment. Your run of the mill JFET has as near infinite impedance as you could ask for, virtually no Gate current, and will self-bias with the addition of a simple resistor. Yes, tube folks have been enjoying these same qualities for years, but you have to admit that, lacking a "P-channel" version of the classic vacuum tube, it does tend to limit topologies a bit. In particular, direct-coupling a push-pull tube output stage (yes, it can be done) is annoyingly difficult, involving all sorts of power supply gymnastics and other annoyances. JFETs allow us to sidestep all that while retaining the benefits.
Back about 40 years ago, John Curl developed a cute little complementary follower circuit utilizing one N-channel and one P-channel device. It has low output impedance and high input impedance. Being a follower, it has unity gain — that is a fancy way of saying that it doesn't amplify the signal. In fact, it'll do an outstanding job of replacing an OpAmps follower, and as a fringe benefit, we can dispense with about ninety of the transistors lurking under the hood of the average OpAmps.
On to the matter of filter topologies. Many are the words that could be spilled on filters; few corners of the audiophile's realm are more filled with buzzwords than filters. Passive/active, first/second/third/fourth order, Butterworth, Bessel, Linkwitz-Riley, and the list goes on.\
The simplest is the first order filter. Each ‘order' represents 6dB per octave of rolloff. A first order crossover has a 6dB/octave slope, meaning that the response drops six decibels for each octave away from the crossover point. It will be down 6dB one octave away (slightly less, actually — it takes a little while for the filter to reach its theoretical slope), then 12dB two octaves away, 18dB three octaves away... each octave representing a doubling or halving of frequency. A first order crossover has one crucial benefit and one deficit. On the plus side, it's the least damaging to the phase relationships between the music above the crossover point and those below. The problem is that 6dB/octave is, well, slow in the rolloff department. It doesn't provide a lot of protection for delicate tweeters. In other words, it's a tradeoff, like everything else.
A second order crossover offers 12dB/octave of attenuation, which is an improvement in terms of protection, but at the price of somewhat more disruption of the phase characteristics. The stereo gods giveth and the stereo gods taketh away — ours is to take what they give us and be happy (or try to find a way to cheat, but that's another story).
The first order crossover is easy to build. A high pass (which passes high frequencies, like you'd want for a tweeter) filter incorporates one capacitor in series with the signal and one resistor to ground. A low pass reverses the order of things—resistor in series, capacitor to ground. Done. Yes, it's really that simple. The second order crossover is a bit more involved. We can skip topologies like Chebyshev and elliptic and go directly to the three that are likely to be of greatest use in audio: Butterworth, Bessel, and Linkwitz-Riley. Just three? Whew! That simplifies things a lot. The Butterworth is the flattest, frequency-wise. The Bessel is the best in terms of phase relationships. The Linkwitz-Riley is an attempt to tame some of the more unruly phase aspects of higher order filters and is very popular among aficionados of fourth order filters.
So how do we achieve these crossover slopes? The first order filter comes pre-packaged with its own topology. For higher order filters, there's only one real contender: Sallen-Key, named after the two fellows who developed it back in the 1950s. Even though we've simplified things by several orders of magnitude, there are still a number of permutations to run through, so with further ado let's start throwing parts together.
Schematic 1 shows the basic JFET buffer building block. I've chosen to run two JFETs in parallel to increase the available output current and lower the output impedance. In most circumstances, you can run just one N-ch and one P-ch and be perfectly happy. The Level control varies the level of the driver. The DC offset pot (V2) sets the output to 0Vdc. We'll come back to that later. For the time being, it's enough to say that this circuit is a non-inverting unity gain buffer and we'll treat it as a unit. (I'd like to note in passing that you can use the circuit as shown as a drop-in replacement for a "passive" preamp. Ta-da! No more high impedance output problems.)
Schematic 2 shows a 6dB/octave high pass filter, based on the buffer shown in schematic 1. The filter is comprised of C1 and R6. Calculate the values by choosing a crossover frequency and a value for C1, then calculate R6 with the following formula:
R6 = 1/(2*П*F*C1)
R6 is the chosen resistor value
F is the desired crossover frequency
If your calculator doesn't have a PI button, 3.14159 will give you more accuracy than you're likely to need.
Let us assume you want a crossover point at 1 kHz. We'll also assume that you want to use a .01uF capacitor. That yields a value of 15915 Ohms for R6. Real world resistor values include 16k in the E-24 (aka 5%) series, and either 15.8k or 16.2k in the E-96 (aka 1%) series. Your choice. And, no, you haven't done anything wrong… electronic engineers face exactly the same sorts of approximations every day. Real parts don't always come in exactly the value that you calculated. Do not worry, the 16k value gives a crossover frequency of 995 Hz. The ‘missing' 5 Hz is not worth losing sleep over as it represents less than a 1% error. Your drivers are more likely to be the problem, here. Rare, indeed is the driver that is manufactured to less than 1% tolerance.
The matching low pass filter is created using the alternate circuit. The value for C2 is the same as for C1 and the value for R5 is the same as R6. R7 ground references the input of the second buffer. It's only needed for the low pass, as R6 performs that function in the high pass version. If you feel like fine tuning things a bit, you can recalculate the value of R5 to reflect the fact that C2 sees it in parallel with R7, but as long as you're working with resistor values on the order of, say, 10k for R5, there will be very little difference.
Should you only need first order crossover slopes, you're done. The only thing left to do is adjust the DC offset pots in the buffers and you're ready to listen. In an ideal world, the Idss of any JFET would match that of others of its kind. Unfortunately, that's not the case. Worse yet, N-ch and P-ch parts are often miles apart. The DC offset pots allow for imbalances between the N devices and the P devices. All you have to do is crank up the circuit the first time, set the output of the buffer to 0Vdc, relative to ground, and walk away. Thirty minutes later, come back and repeat the adjustment and you're done.
If you need a steeper slope, perhaps a second order filter will do the job. This is where the Sallen-Key topology comes in. Schematic 3 shows the same buffer sections with slightly more complicated filters.
Beginning with the high pass, calculate the parts values for a Butterworth filter as follows:
C = C1 = C3
R6 = 0.7071/(2*П*F*C)
R8 = 1.414/(2*П*F*C)
The low pass takes the resistor values as constant and calculates the capacitor values:
R = R5 = R7
C2 = 1.414/(2*П*F*R)
C4 = 0.7071/(2*П*F*R)
The only thing that might appear a little odd is that R6 (if you're using the high pass) and C2 (if you're using the low pass) connect to the output. If you trace the signal through, you'll find that this amounts to a bit of positive feedback. Note that this is true regardless of whether you're using OpAmps, FETs, bipolars, or tubes. It's inherent in the Sallen-Key topology and serves to touch up the response around the crossover point a bit.
Should you choose to use a Bessel function instead of Butterworth, the topology remains the same, but the formulas change slightly.
C = C1 = C3
R6 = 1.1017/(2*П*F*C)
R8 = 1.4688/(2*П*F*C)
R = R5 = R7
C2 = 0.9076/(2*П*F*R)
C4 = 0.6809/(2*П*F*R)
If you want to tri-amp, the tweeter will get a high pass filter and the woofer will get a low pass, just like a bi-amped system. The midrange will require a band pass, however. Don't worry, band pass filters are easy. Just put a low pass and a high pass together and you'll get a band pass. All the formulas are the same and the topologies need not change. You can even save one buffer stage by running the output of the first crossover directly into the second filter section.
Third and fourth order crossovers get more complicated and deserve more space. If there's sufficient interest and if Steven is willing, I'll cover those at another time.
Oh, and the name? Xeno, in Greek, means foreign or strange, and this is an unusual crossover circuit. Pronounce the "X" as "Z" the same way you would xylophone.