Dick says, >> A few questions about passive crossovers; >> >>How well do Zobel circuits stabilize the impedence of a driver? >They don't "stabilize" the impedance at all. The objective to so-called >"zobel" networks is provide a resistive termination to a passive network >through the use of a complex conjugate load in parallel with the driver. >There is no "instability" to compensate for. > >In most cases, what's being compnesated for is the effective series >inductance and resistance of the voice coil, thus the correct conjugate >network is a series capacitance and resistance. In rarer instances, the >designer will also attempt to compensate for the reflected motional >impedance of the driver, equivalent to a parallel RLC tank circuit with a >series RLC tank circuit conjugate. > >The assumption is made that the voice coil impedance at high freuqencies >is equivalent to a simple inductor in series with a simple resistor. >Unfortunately, this isn't even approximately the case. Due to eddy current >losses in the metal parts surrounding the voice coil, the impednace is FAR >more comlex than that, and, in fact, looks more like a so-called >"semi-inductor", one whose inductance goes roughly as the inverse square >root of frequency, in series with a "semi-resistor", one whose resistance >goes as the square root of frequency (the terms semi-inductor and >semi-resistor were coined in this application by Vanderkooy). > >Thus, a conjugate constructed out of normal resistors and capacitors can >only approximately compensate for the impedance behavior due to the voice >coil inductance. However, they can get VERY close when done properly. >It's not rocket science. >>Does the addition of the capacitor of the Zobel circuit effect the phase >>shift/order of the crossover? >Well, it depends upon what you mean. It can be shown that it is >impossible to attain a given desired transfer function without a Zobel, >so in a sense the answer is yes, it does. > >On the other hand, if what your are asking is whether a filter properly >compensated by a Zobel conjugate has a different order and transfer >function than a filter properly terminated by a resistor, the answer is >no. The point, again, to the Zobel conjugate is to provide a resistive >termination to the crossover to make the synthesis of a given transfer >function possible. >>I've read about using metal film resitors for the Zobel. How do I >>determine the wattage rating for this resistor? What might be some >>suggestions for a driver powered with, say, 50W? >It depends upon the crossover frequency and order and upon the spectral >distrinution of music. A 50 watt systems with a 4th order high-pass on >the tweeter at 3 kHz could probably survive quite well witha 1 or 2 watt >resistor at the most. Looking at the same system but with a 2nd 1 kHz low >pass is going to require something different. >>What kind of information would I need in order to choose the crossover >>frequency of a driver and how would determine/calculate it once I have >>that information? >That's a VERY complex question. You need to know power handling, axial >and power response of the drivers, impedance, and on and on and on. How >would you design it? Depedns upon what your goals are. >>How do you get this information from Stillwater Design? >>(They even seem reluctant to give me suggestions.) >>What kind of equipment would I need to determine a drivers impedence vs >>frequency curve? How would I do it? >At a minimum, you need an accurate (that is, amplitude stable, reasonably >low distortion, reasonable frequency accuracy) sine wave generator and a >similarily accurate means of measuring AC voltage (flat frequency >response). >>Can it be done with an o-scope and a function generator? How? >It COULD be done, but you'd be FAR better off with a AC voltmeter that >has flat, wide bandwidth. It's just not that easy to inerpolate voltage >readings from an oscilliscope, especially at low frequencies. > >To perform the task, you need to construct something called an >impedometer. This is nothing more than a calibrated AC currnt source with >a voltmeter. The current source you can make by taking your sine wave >generator and feeding it through a resistor whose value is substantially >greate (like at least 20 times for 5% accuracy) the values you are going >to measure. For example, use a 1k resistor for measuring loudspekaer >impedances up to 50 ohms. You may also need a power amp to get enough >voltage into the impedometer for reasonable coltages across the driver. >A rough circuit diagram might look like: > > > +----- 1k ----+ > | | > | +--------+ > | | | > | o | > Sine un- AC volt > Generator known meter > | o | > | | | > | +--------+ > | | > +-------------+ > >"Calibrate" your impednometer by taking an accurate resistor that's in >the range that you're going to measure and put it in place of the driver >(the "unknown" in the diagram) and adjust the level of the sine generator >so you get a convenient reading on the voltmeter. For example, if you >have a 10 ohm resistor in the "unknown" position, adjust the level of the >sine generator until you get, say, 10 mV across it. Now you know that the >impedometer has a calibration constant of 10 mv/ohm. Replace the resistor >with the driver, and measure the impedance at whatever frequency you >desire. >>Could I feed the driver a sine wave from a function generator, vary the >>waves frequency and just plot the impedence? >Using the above method, you got it. >>What amplitude would the waveform have to be? >That's a VERY good question. The amplitude needs to be what you think it >shoudl be. The problem is that the impedance varies with amplitude due to >electrical, magnetic and mechanical non-linearities in the system. WHich >amplitude is best? All of them, unfortunately, because in the variance >lies important information in and of itself. >>How accurate would this method be? >Properly calibrated, it can be as good as your measurement instrument >allow it to be. >>How much will the body/chassis of the vehicle effect the values of the >>inductors? >Potentially, quite a bit. There are two mechanisms at work. First, the >presence of ferromagnetic materials in the magnetic field generated by >the coils can serve to increase the inductance because of the high >permeability of those materials. On the other, the presence of sheet >metal conductors provides a poor secondary to the inductors primary (a >lousy transformer) and the ohmic losses in the metal will dissipate >power. This will tend to lower the inductance, but in a frequency >dependent manner. >>Would a bandpass crossover with two coils and two caps (one pair for hp >>the other for lp) be 2nd or 4th order? >Strictly speaking, it's a forth order function. >>If the aformentioned crossover is 2nd order hp and 2nd order lp (with 360 >>deg phase shift all together) for the mids and the sub's and tweet's >>crossovers are 4th order I can switch the -/+ of the mid to fix the phase >>difference >Its's a 4th order bandpass, meaning that if its a butterworth response, >the phase at the HP crossover point will be -180 deg and at the LP >point it will be +180, as if they were second order low pass and high >pass networks. Thus, you need to act accordingly. >>Now what about the frequency response? How will and how much will the >>varying slopes effect this? >An impossible question to answer generally, because it is so depednet >upon the response of the dricers, the measuring position, and many other >factors. >>What's a good source for low tolerance pots, caps, coils and resistors? >Check the FAQ. >>Are there more exacting equations than those listed in the FAQ? >Yup. >>Are there any books on filter theory and it's application to passive >>crossover design for home and car audio? >Check the AES journals for work by Vanderkooy and Lipshitz, Bullock, and >others. >>Does there exist software explicitly for the purpose of designing filters >>for home and car audio? ie enter a driver T and S parameters and >> output real world values of caps, coils and resistors >No, despite the claims that there are. It's not necessarily the T/S >parameters that affect the design, but the load presented by the driver a >a whole. >>Anything I missed? >| Dick Pierce | >| Loudspeaker and Software Consulting | >| 17 Sartelle Street Pepperell, MA 01463 | >| (508) 433-9183 (Voice and FAX) |