series crossovers

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   Hi
I wonder if anyone can work this out.

First order series crossovers use the same capacitor and inductor values as the equivalent parallel network with the same crossover frequency.

If you have a higher impedance tweeter than woofer (16ohm tweeter, 8ohm woofer for example) you simply calculate the capacitor value for the higher impedance but keep the inductor value the same. This isn't obviously true to me but is confirmed by simming using akabak script below.

Second order series uses capacitor values that are double and inductor values that are half the equivalent parallel network. seems to make sense and again this is confirmed using akabak.

I can't figure out how to make the second order series work with different tweeter and woofer impedances. Would be interested if anyone knows the answer or if they can prove it is either possible or impossible.

cheers
Phil

System  'S first 8 8'

Coil 'L1' Node=1=2 L=0.001274H
Capacitor 'C1' Node=2=0 C=0.000019875F
Resistor 'T1' Node=1=2 R=8ohm
Resistor 'W1' Node=2=0 R=8ohm

System  'S first 16 8'

Coil 'L1' Node=1=2 L=0.001274H
Capacitor 'C1' Node=2=0 C=0.000009938F
Resistor 'T1' Node=1=2 R=16ohm
Resistor 'W1' Node=2=0 R=8ohm

System  'S second 8 8'

Coil 'L1' Node=1=2 L=0.0009H
Capacitor 'C1' Node=2=0 C=0.000028126F
Capacitor 'C2' Node=1=3 C=0.000028126F
Coil 'L2' Node=4=0 L=0.0009H
Resistor 'T1' Node=3=2 R=8ohm
Resistor 'W1' Node=2=4 R=8ohm

System  'S second 16 8'

Coil 'L1' Node=1=2 L=0.0009H
Capacitor 'C1' Node=2=0 C=0.000028126F
Capacitor 'C2' Node=1=3 C=0.000028126F
Coil 'L2' Node=4=0 L=0.0009H
Resistor 'T1' Node=3=2 R=16ohm
Resistor 'W1' Node=2=4 R=8ohm

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snowflake Members Profile Send Private Message Find Members Posts Add to Buddy List Old Croc Joined: 29 December 2004 Location: Bristol Status: Offline Points: 3122	Post Options Post Reply Quote snowflake Report Post Thanks(0) Quote Reply Topic: series crossovers Posted: 05 March 2016 at 8:11pm
	Hi I wonder if anyone can work this out. First order series crossovers use the same capacitor and inductor values as the equivalent parallel network with the same crossover frequency. If you have a higher impedance tweeter than woofer (16ohm tweeter, 8ohm woofer for example) you simply calculate the capacitor value for the higher impedance but keep the inductor value the same. This isn't obviously true to me but is confirmed by simming using akabak script below. Second order series uses capacitor values that are double and inductor values that are half the equivalent parallel network. seems to make sense and again this is confirmed using akabak. I can't figure out how to make the second order series work with different tweeter and woofer impedances. Would be interested if anyone knows the answer or if they can prove it is either possible or impossible. cheers Phil System 'S first 8 8' Coil 'L1' Node=1=2 L=0.001274H Capacitor 'C1' Node=2=0 C=0.000019875F Resistor 'T1' Node=1=2 R=8ohm Resistor 'W1' Node=2=0 R=8ohm System 'S first 16 8' Coil 'L1' Node=1=2 L=0.001274H Capacitor 'C1' Node=2=0 C=0.000009938F Resistor 'T1' Node=1=2 R=16ohm Resistor 'W1' Node=2=0 R=8ohm System 'S second 8 8' Coil 'L1' Node=1=2 L=0.0009H Capacitor 'C1' Node=2=0 C=0.000028126F Capacitor 'C2' Node=1=3 C=0.000028126F Coil 'L2' Node=4=0 L=0.0009H Resistor 'T1' Node=3=2 R=8ohm Resistor 'W1' Node=2=4 R=8ohm System 'S second 16 8' Coil 'L1' Node=1=2 L=0.0009H Capacitor 'C1' Node=2=0 C=0.000028126F Capacitor 'C2' Node=1=3 C=0.000028126F Coil 'L2' Node=4=0 L=0.0009H Resistor 'T1' Node=3=2 R=16ohm Resistor 'W1' Node=2=4 R=8ohm

odc04r Members Profile Send Private Message Find Members Posts Add to Buddy List Old Croc Joined: 12 July 2006 Location: Sarfampton Status: Offline Points: 5482	Post Options Post Reply Quote odc04r Report Post Thanks(0) Quote Reply Posted: 06 March 2016 at 10:51am
	Hey Phil, I will try and draw out the maths for it sometime this week. Probably at work when I am bored.

snowflake Members Profile Send Private Message Find Members Posts Add to Buddy List Old Croc Joined: 29 December 2004 Location: Bristol Status: Offline Points: 3122	Post Options Post Reply Quote snowflake Report Post Thanks(0) Quote Reply Posted: 08 March 2016 at 1:51pm
	that would be great, it's got me stumped

odc04r Members Profile Send Private Message Find Members Posts Add to Buddy List Old Croc Joined: 12 July 2006 Location: Sarfampton Status: Offline Points: 5482	Post Options Post Reply Quote odc04r Report Post Thanks(0) Quote Reply Posted: 08 March 2016 at 2:08pm
	Totally forgot about this! I'll have a poke now. Only sitting around waiting for polymer to dry anyway. Like paint but smellier.

odc04r Members Profile Send Private Message Find Members Posts Add to Buddy List Old Croc Joined: 12 July 2006 Location: Sarfampton Status: Offline Points: 5482	Post Options Post Reply Quote odc04r Report Post Thanks(0) Quote Reply Posted: 10 March 2016 at 12:31pm
	I think I know how to do it, but I need to check the maths with LTspice or similar. Had flu for the last few days so not been able to do much on it

snowflake Members Profile Send Private Message Find Members Posts Add to Buddy List Old Croc Joined: 29 December 2004 Location: Bristol Status: Offline Points: 3122	Post Options Post Reply Quote snowflake Report Post Thanks(0) Quote Reply Posted: 11 March 2016 at 11:38am
	I will be impressed if you do this whilst struggling with flu and high on solvents

audiomik Members Profile Send Private Message Find Members Posts Add to Buddy List Old Croc Joined: 06 April 2010 Location: Bath, UK Status: Offline Points: 2962	Post Options Post Reply Quote audiomik Report Post Thanks(0) Quote Reply Posted: 11 March 2016 at 12:40pm
	Phil you will find an answer to this in Horowitz and Hill, I have an Electronic copy of this useful book here as well as a printed version! Mik
	Warning! May contain Nuts plus springs, washers, screws, etc, etc.

odc04r Members Profile Send Private Message Find Members Posts Add to Buddy List Old Croc Joined: 12 July 2006 Location: Sarfampton Status: Offline Points: 5482	Post Options Post Reply Quote odc04r Report Post Thanks(0) Quote Reply Posted: 11 March 2016 at 12:44pm
	I pretty much managed it. I started by analyzing the impedance network of the upper and lower half. Then I calculated the series capacitor shift needed to put the crossover point back to where it was if its series resistance load changed, and then from that reverse engineered the inductor to make sure the total network impedance did not change at Fc. This seemed to work ok. And then I noticed that the formulae for what I had worked out are on the ESP website :) Doh. Tested with LTspice and they work fine substituting a 12 Ohm resistance for the original 8. I was using the examples there for initial LTSpice testing figures. C = 1 / (2 * Pi * f * (Z / √2)) L = (Z / √2) / (2 * Pi * f) I noticed when I was reverse engineering the series cap Fc when changing R that the calculated Fc was actually 1/sqrt(2) that of the planned. For instance if you design a 1KHz series second order crossover then work out the RC and LC series constants they will evaluate to 707hz (1/sqrt(2) * 1KHz) Over the flu now thankfully, not much fun. For a while I was wondering if I had damaged my throat with solvents... Don't think so though, just bad timing

snowflake Members Profile Send Private Message Find Members Posts Add to Buddy List Old Croc Joined: 29 December 2004 Location: Bristol Status: Offline Points: 3122	Post Options Post Reply Quote snowflake Report Post Thanks(0) Quote Reply Posted: 11 March 2016 at 12:50pm
	found it online: http://iate.oac.uncor.edu/~manuel/libros/ElectroMagnetism/The%20Art%20of%20Electronics%20-%20Horowitz%20&%20Hill.pdf

odc04r Members Profile Send Private Message Find Members Posts Add to Buddy List Old Croc Joined: 12 July 2006 Location: Sarfampton Status: Offline Points: 5482	Post Options Post Reply Quote odc04r Report Post Thanks(0) Quote Reply Posted: 11 March 2016 at 12:53pm
	I'd highly recommend buying a second hand copy, it's a fantastic reference. I probably use it the most out of any textbook for general electronics when I've forgotten something. Didn't think to check it this time.

snowflake Members Profile Send Private Message Find Members Posts Add to Buddy List Old Croc Joined: 29 December 2004 Location: Bristol Status: Offline Points: 3122	Post Options Post Reply Quote snowflake Report Post Thanks(0) Quote Reply Posted: 11 March 2016 at 2:36pm
	okay got it now, thanks for the help. the formulas should be C=1/(2PifZ) L=Z/(4Pi*f) use the Z of the tweeter to find the cap in series and the coil in parallel with the tweeter use the Z of the woofer to find the coil in series and the cap in parallel with the woofer this is different to the first order circuit where changing the tweeter alters the cap in parallel with the woofer and leaves the coil unaltered.

snowflake Members Profile Send Private Message Find Members Posts Add to Buddy List Old Croc Joined: 29 December 2004 Location: Bristol Status: Offline Points: 3122	Post Options Post Reply Quote snowflake Report Post Thanks(0) Quote Reply Posted: 11 March 2016 at 6:45pm
	actually haven't got it - the above gives approx the right values for a 16R/8R setup (although the normalized voltages at crossover are slightly less than 0.707) but doesn't work for other impedances