Upgrade Coils in Crossovers

Not too long ago in Audiogon a user launched a series of personal attacks vaguely based on his misguided and incomplete understanding of inductors and their use in a crossover.  In particular, the user felt that reducing the DC resistance of a coil was always a good thing and that no other considerations mattered.  One of the comments I read was "when we learned about filters we only cared about inductance and capacitance, not resistance."  Well, I'm sorry that their knowledge was incomplete but no reason to get personal because of that.

Here we'll discuss the subtleties of upgrading a coil with particular attention to the issue of DCR. 

DC Resistance

DC resistance is present in every inductor.  If you have only taken a basic AC circuit theory course you may never have even read about it, but it becomes a meaningful topic in more advanced classes.  An inductor is just a wire wrapped into a coil.  All wires have some resistance and all the rules of wire resistance apply to DCR: 

• Larger gauges have lower R per foot/meter
• Smaller gauges have higher R per foot/meter
• Longer wires have more R
• Shorter wires have less R

Further, inductance is proportional to the length of the wire, so higher inductance coils tend to have longer wire lengths and therefore higher R unless we compensate for it with larger wire gauges.  Finally, inductors have a maximum power associated with them.  Just like a resistor or wire they can melt if overheated. 

If you learned about coils in line level circuits your instructor may have skipped discussing DCR because the circuit impedance are often in the tens of kilo ohms.  In those cases the DCR of even a few ohms becomes irrelevant. In speakers with typical woofers having an Re of around 4 Ohms however small values matter.

Sample Crossover

For this practical example we'll use the JBL L82 crossover, provided below.  It's not particularly interesting except that it's a commercial speaker and the inductor DCR is fully documented.

  

For our simulation we'll only use the low pass filter, and we'll assume the speaker is a pure 4 Ohm resistor.  Sadly what we don't have is the speaker impedance data but it doesn't matter as we want to talk about general effects and issues. 

Take a look at the two inductors at the top.  The bar indicates ferrite core inductors.  1.8mH with 0.4 Ohms DCR.  In a crossover, the DCR specification is not a "maximum" but an expected value.  In case of failure a technician should attempt to replace the inductor with the same mH and DCR as specified. To model this AC behavior properly we'd imagine that we have an ideal coil followed by an ideal resistor: 

 

 

It is a simple fact that all inductors have some DCR.  All caps have some equivalent series resistance (ESR), and most resistors may have some parasitic inductance or capacitance unless especially designed not to.   We just ignore them until we are forced to think about them.  

In crossover design the DCR and ESR are important parts of the outcome, but may be more or less important in some places than others. 

In any event, lets take a look at the "transfer function" of the low pass filter with and without any DCR in the two ferrite coils: 

 

The term "transfer function" just means that we are looking at how the crossover affects the voltage that actually reaches the speaker.  The green line, above, represents the original low-pass filter while the blue represents the new "improved" version.   

As you can see the reduced DCR has changed the response of the filter, bumping up the output by about 1.5 dB at 20 Hz.  

The upgrade has now changed the tilt of the bass filter and speaker and altered the tonal balance, starting a domino effect. In order to keep the original speakers tonal balance  we now need to alter the low pass filter so it tilts down less (if possible) and adjust the high pass level.  We've now proven that it's incorrect to assume that cutting the DCR of a coil has no effect on the tonal balance.  This speaker will sound different, because it IS different.  You've now made a very different speaker than you started with and have to grapple with new sets of choices:

• Accept the reduced DCR and new tonal balance (and system impedance, below)
  
• Attempt to adjust the tonal balance and rethink the crossover, which means entirely different inductor values
  
• Add series resistance to maintain the original tonal balance without any more crossover changes. 

 

DCR and System Impedance

For our example this will also affect the system impedance curve, in this case lowering the impedance by almost 1 Ohm: 

Critical DCR

On a practical note, components in series with a driver are less critical than those that shunt to ground.  In those the DCR is a critical value.  In even ordered filter components we often see an actual resistor with a very small value in series with a coil or capacitor, like this: 

 

 

 

In the case of L3, if we were to make significant reductions in the DCR without compensating with additional R in R3 we could accidentally end up with a very low minimum system impedance.  It's not an obvious thing as this change could affect the minimum impedance of the low pass section.   It's also possible that you alter the FR of the high pass filter significantly by making this change.

 

Similar issues can arise when upgrading old speakers with eletrolytic caps and high ESR.  A change here can really alter the system impedance curve in amplifier melting ways.  

Looking at the original schematic we see two coils in the HP filter section as well.  The DCR is specified and these are critical values.  While we may not be able to find exact matches we'd be well served by getting as close as possible OR compensating with additional R values in series.

Baffle Step Compensation

Lastly, advanced speaker designers like Troels Gravesen and others have been known to cheat a little by using the DCR as part of the baffle step compensation.  Reducing DCR can actually point the woofer impedance upwards instead of down. 

Avoiding Surprises 

The best approach is to understand the circuits you are working on. Measure the impedance of the entire speaker, the drivers and the individual components before making major investments in upgrading parts.  For simulation I like to use XSim but VituixCAD is also a free and popular option.  To measure impedance values (including DCR and ESR) I like to use Dayton DATS V3.  

Conclusion

My point is not whether you should/should not reduce the DCR of your speaker inductors but that you should be aware that changing the DCR of a coil has consequences which are material to the frequency and impedance of the final speaker and that you may be much better off doing more research into your existing speaker before proceeding down an upgrade path.