Dissimilar parallel speaker impedance calc? Vintage Magnatone M15 3x8 content

[Carlsoti]

TL;DR: How do I calculate the total impedance of dissimilar speakers in parallel when one of them has a capacitor for a 1st order HPF?

      I thought I was all set on Magnatone amps with the M10 I repaired a while back, but I recently found an amp I considered to be something of a White Whale. An Estey-built 3 hole Magnatone M15 in generally good condition popped up on my local FB marketplace, with the note that the reverb and FM Vibrato didn't work, but otherwise it seemed to work and sound OK. "With original cover!" too.
     I took the gamble and feel that I've gotten pretty lucky, so far. It's got all original glass with nothing in bad enough condition to raise any concerns on the Mighty Mite II. One shorted filter cap killed the 2.5k dropping resistor for the reverb amp. I replaced all the caps and the dead resistor in that filter string and the reverb came to life. It's a bit LESS deep and ambient than the reverb in my M10, but a completely different circuit, so I can live with that. The stereo F.M. Vibrato seems to work as intended now, too.
     There is the tiniest, faintest distortion under the signal that's only apparent at the very tail end of a sustained note. It's so quiet that a small desk fan on "low" can completely mask the sound of it. It's a ratty, raspy, clipping diode sort of distortion that will need to be addressed in the future. In addition to adding an IEC connector with the appropriate grounding mods, I plan on re-capping the 60+ year old PSU and bias supply, as well as replacing the rectifier and bias diodes before addressing the underlying distortion.
     As some might expect, the circuit doesn't conform to the schematic in the cab, but it does seem to match the attached schematic, though I have yet to trace the entire circuit.
    I REALLY want to hear this stereo F.M. vibrato with some wide-set extension speakers, which is where the original "TL;DR" question comes in. When I look up crossover calculators online, most have HP/LP configurations for a two driver set.

     How do I calculate the configuration shown in the attached schematic? Maybe the easier and more appropriate question to ask is, what would be the appropriate ohms for the extension cabinets if I take the HF driver and cap out of the equation? Those accordion players must like REALLY bright tones, but it's WAY overkill for an over-driven strat.

Any insights you could provide would be greatly appreciated.

P.S. I had asked about mods to the M10 a while back and talked about using the anti-hum positions of the power switch for things like NFB defeat + cathode bypass cap, etc. I was spouting from memory and there aren't enough positions on the switch for all that.  Those mods are still being contemplated, particularly now that I have this M15 which is considerably more original than the M10. 

[shooter]

R1 * R2 * R3 / R1 + R2 + R3 = speaker impedance

[Carlsoti]

Thanks for the quick reply, Shooter.
Does the capacitor not come into play in that calculation at all? Maybe the info on the schem is throwing me for a loop. It lists the OTs as 10k:16ohm, or about 625:1, but the internal load present is closer to 5.3 ohms, giving a reflected impedance closer to 3,300. IDK what to do with that info. I would guess that the "appropriate" external load would be a 16ohm speaker for each side, but I should be able to safely use an 8 ohm, as well. That is IF I have calculated the original internal load correctly.
   The glass in this amp isn't cheap and I want to make sure I'm not abusing it or the transformers.

P.S. As a follow up, it seems to me the external speaker switching is kinda weird. When is the "ON" position, the external speakers are in parallel with the internal. When the switch is "OFF", but an external load is present, it takes the internal load out of the circuit. Is that correct? 

[sluckey]

P.S. As a follow up, it seems to me the external speaker switching is kinda weird. When is the "ON" position, the external speakers are in parallel with the internal. When the switch is "OFF", but an external load is present, it takes the internal load out of the circuit. Is that correct?

Yes. Also notice that with no ext. spkr. plugged in, the internal speaker switch does nothing.

[WimWalther]

A loudspeaker is a complex impedance, moreso when you start adding crossover components. And in either case, it's very much frequency-dependent.

So either use the standard (simple) math to calculate a rough value.. and if that doesn't suit your needs, you'd be best off just measuring the impedance - it's really not that difficult.

[Dave]

If you measure a speaker for DC resistance with a meter, that resistance will usually be around 80 to 90 percent if nominal impedance. So, an 8r speaker will usually read 6 or 7 ohms DC resistance. With that in mind, if you measure your paralleled ,  series , crossovered , over whatever speaker network, you can use the same idea. If it all comes in at say ... 7.3 or something like that, you could use it on an 8 ohm tap. You get the idea.


Dave

[sluckey]

If you measure a speaker for DC resistance with a meter, that resistance will usually be around 80 to 90 percent if nominal impedance. So, an 8r speaker will usually read 6 or 7 ohms DC resistance. With that in mind, if you measure your paralleled ,  series , crossovered , over whatever speaker network, you can use the same idea.

That won't work in this case. Your dc ohm meter cannot measure the tweeter because of the capacitor. Your meter will only see the DCR of the 8" speaker.

BTW, the schematic has an error in the labeling for channel 1 internal speakers. See attached correction. (CH2 speaker is correct)

[Carlsoti]

A loudspeaker is a complex impedance, moreso when you start adding crossover components. .... it's really not that difficult.

I have a tendency of wanting to learn more than I already know. It's often useless in the face of typical guitar amp repairs, but I still like to learn stuff. I recall from working at Rockford Fosgate/Hafler 20+ years ago that the finite calculations of passive crossovers and drivers as a circuit can get complex, to say the least. I received similar info as you've given from Jim Strickland back then. I was hoping someone here was of the same nearly maniacal mindset that might be able to push me towards the math, as I may find it applicable to other scenarios in the future.

Also, it seems that the engineers at Magnatone were on a completely different water supply than those at Fender, Marshall, Ampeg, etc. I'm trying to get a better feel for what their intentions were.

For example, the 10k:16ohm OTs listed on the schematic would be right in the "ideal" range for the 7189A tubes used, but the quick-math shows the actual load closer to 5.3 ohms, which changes the reflected impedance on the tubes significantly. It's simple enough to try various impedance drivers and take measurements, hoping I don't kill any tubes or transformers, but I don't have a lot of extra speakers around, nor am I equipped to run the tests with high wattage resistors. I've already had to make a few sacrifices in order to purchase this amp, and can't justify the possible cost of replacement parts in a scenario where applying myself to learn more is a reasonable alternative.

[Dave]

If you run a 4r speaker on an 8r tap or a 16r speaker on an 8 ohm tap, you are very unlikely to blow anything up. If you want to do some experimenting, as long as you don't go over a 100 percent mismatch, you should be fine.


Dave

[66Strat]

A loudspeaker is a complex impedance, moreso when you start adding crossover components. .... it's really not that difficult.

I have a tendency of wanting to learn more than I already know. It's often useless in the face of typical guitar amp repairs, but I still like to learn stuff. I recall from working at Rockford Fosgate/Hafler 20+ years ago that the finite calculations of passive crossovers and drivers as a circuit can get complex, to say the least. I received similar info as you've given from Jim Strickland back then. I was hoping someone here was of the same nearly maniacal mindset that might be able to push me towards the math, as I may find it applicable to other scenarios in the future.

Also, it seems that the engineers at Magnatone were on a completely different water supply than those at Fender, Marshall, Ampeg, etc. I'm trying to get a better feel for what their intentions were.

For example, the 10k:16ohm OTs listed on the schematic would be right in the "ideal" range for the 7189A tubes used, but the quick-math shows the actual load closer to 5.3 ohms, which changes the reflected impedance on the tubes significantly. It's simple enough to try various impedance drivers and take measurements, hoping I don't kill any tubes or transformers, but I don't have a lot of extra speakers around, nor am I equipped to run the tests with high wattage resistors. I've already had to make a few sacrifices in order to purchase this amp, and can't justify the possible cost of replacement parts in a scenario where applying myself to learn more is a reasonable alternative.

At what frequency? The reflected impedance is frequency dependent based upon the response curve of the speaker. For example, the impedance of the attached 8 inch Jensen response curve, is about 8 ohms at 200 hertz. At 3,000 hertz the impedance is about 10 ohms. For a 16 ohm speaker, these numbers are approximately twice as much, (16 ohms and 20 ohms). Notice also that as the frequency is increased, the sensitivity of the speaker is diminished. Hence the need for the tweeter (3 inch speaker). The capacitor works in combination with the rising response curve of the 8 inch speaker to pass higher frequencies to the 3 inch speaker. The size for the capacitor is chosen based upon the tweeter used, and the desired crossover region of the response curve. Tweeters don't like low frequencies. Too low of a frequency can/will damage/destroy a tweeter. At 8 ohms of impedance, the frequency begins to cross over at about 2,000 hertz. The capacitor increasingly allows higher frequencies to pass to the 3 inch speaker.

https://www.jensentone.com/specification-sheet/44