Should I replace the crossover capacitors in my vintage AR 3a speakers?

Interesting conversation. Have restored a few sets of vintage speakers. Always replace the XO caps. most of the time, don't even test them, just replace. 

Every time it has been a night and day difference for the better! It always opens the speaker up, more bass, cleaner midrange, highs star to sing. 

If you are worried about ESR, try to get caps that don't have a low ESR. Even a cap that might register correct value might have a super high ESR, telling you it needs to be replaced. My last set of speakers a couple caps were in spec, but ESR was about 1ohm. 

From my experience, new caps always read on the low side, old caps are either on the high side, or just at value. If you have a 100uf old cap reading at 100uf or over, it's most likely about done. 

If you are unsure, just do one speaker, compare to the old. if you don't like it, swap it back. 

Good info here from @erik_squires ​​​​​​

Only two things I would add to it:

- The ESR-as-part-of-the-design consideration is most likely to create an issue when a person decides to replace electrolytics with film caps, which have low ESR. As long as you replace same with same you should be OK

- If you’re going to get a Dayton Audio DATS, you’re likely to get the best price from Parts Express since Parts Express owns Dayton Audio

Personally I lean more to the side of leaving well enough alone when appropriate, which is when the factory used high quality components, and those components still test well within spec (of course you always test caps out of circuit). A crossover is not like a Class A amp in which caps are literally being baked to a crisp.

Indeed, specifically old elctrolytics. Film to film is usually OK.

What I find amusing is when modders replace old electrolytics wiht film caps, removing 0.5 Ohms of ESR or more in the process and then proclaim what a difference it makes. Well, yeah, it kind of has to at that point, for good or ill. Same with changint DCR in coils without understanding the whole circuit.  When I make speaker crossovers I specifically pick among the various gauge coils to get a specific final sound.  I don't get small gauge coils for cost savings.

Not saying good caps don’t make a difference. Just saying it’s good to know what’s changing.

I've recapped similar speakers, most recently, my AR58S speakers.  As in the 3a, it's a 12" 3-way, using dome mids and tweeters.  My 58S's used Unicon branded electrolytic caps, which still sounded very good.  Though, I didn't measure their capacitance or ESR, as both can drift after decades of use.

When recapping, I always mod 1 speaker, and then compare it to the stock speaker.  That allows me to hear any initial differences, and if a balance adjustment needs to be made, I can add small value resistors in series with the capacitors, to compensate.

I do like boutique caps.  Most often using Mundorf and or ClarityCap films.  With this recap, I used Mundorf EVO Oils for the tweeters and ClarityCap CSA's on the mids.  Bypassed NPE's on the woofers.  After the recap, the treble sounded great, both open and airy, but the mids were very recessed and opaque on it's upper end. I let the CSA caps play for weeks, without much improvement.  In the end, I added bypass caps to them, which helped restore midrange balance.  I haven't used ClarityCaps on the mids since.  While good with a bypass cap, I found them too rolled off without.  Now, I typically use all Mundorf caps.  Jantzen and Audyn caps are said to be very good as well, though I haven't personally used those.

Good luck.