Resistor puzzle - Page 1
Forum section: electronics / general

author: Mike Warren
author_rank: Unknown
timestamp: March 11, 2013, 03:56:06 am
content: I have four 8 Ohm resistors. I want to be able to switch them to any one of the following values, using at least 2 resistors in each mode and as few SPDT relays as possible: 2 Ohms, 4 Ohms, 8 Ohms, 16 Ohms, 32 Ohms.The best I've been able to come up with is 5 relays. Can anyone do better?In case it isn't obvious, this is for an audio dummy load. I'd hate to build it and then discover I could have done it with fewer relays.I'll post my solution later. Don't want to put preconceptions in anyone's head.And the relays need to be SPDT. I can't use DPDT as the other pole will be used for the other channel.

author: IanB
author_rank: Super Contributor
timestamp: March 11, 2013, 04:09:29 am
content: For 2 ohms you need four 8 ohm resistors in parallel. If you can do that with fewer than 8 relays you are doing bloody well. Congratulations on your ingenuity!

author: NiHaoMike
author_rank: Super Contributor
timestamp: March 11, 2013, 04:15:19 am
content: Is it allowed to add resistors of other values? 16 ohms and 32 ohms are typically headphone loads, which are very low power. (Or is that for emulating series strings of speakers?)

author: Mike Warren
author_rank: Unknown
timestamp: March 11, 2013, 04:31:36 am
content: Quote from: IanB on March 11, 2013, 04:09:29 amNot really. A resistor does not need to be disconnected at both ends to take it out of circuit.I want to give others a chance to play before I post my solution. There are plenty of people smarter than me here. I'm hoping someone will see a way I didn't.

author: Mike Warren
author_rank: Unknown
timestamp: March 11, 2013, 04:32:54 am
content: Quote from: NiHaoMike on March 11, 2013, 04:15:19 amNo. Only the 4 resistors, relays and wire.QuoteYes.

author: Rufus
author_rank: Super Contributor
timestamp: March 11, 2013, 04:44:22 am
content: I get 5 as well

author: Mike Warren
author_rank: Unknown
timestamp: March 11, 2013, 04:59:57 am
content: Quote from: Rufus on March 11, 2013, 04:44:22 amThat's slightly different to mine.

author: Gall
author_rank: Frequent Contributor
timestamp: March 11, 2013, 08:04:11 am
content: I think I can prove mathematically that it requires exactly 5 SPDT relays or 3 DPDT relays. I'm sure about 3 but i'm not sure about 5.

author: jcook1979
author_rank: Newbie
timestamp: March 11, 2013, 08:10:24 am
content: 5 is the best that I can come up with, given the conditions.

author: nuhamind2
author_rank: Regular Contributor
timestamp: March 11, 2013, 03:12:19 pm
content: For only 4 switch (normal switch) I can only make 4 combination ,except the 4 ohm.

author: Mike Warren
author_rank: Unknown
timestamp: March 11, 2013, 10:55:18 pm
content: Quote from: nuhamind2 on March 11, 2013, 03:12:19 pmUnfortunately, 4 Ohm and 8 Ohm are the 2 most used settings.

author: Mike Warren
author_rank: Unknown
timestamp: March 11, 2013, 10:57:09 pm
content: Well, it looks like it's going to have to be 5. I like Rufus's idea best because it also includes an open circuit state when power is removed.Thanks everyone.

author: grumpydoc
author_rank: Super Contributor
timestamp: March 11, 2013, 11:18:19 pm
content: I, also, can only manage a 5 relay solution.If you drop the 2ohm requirement you can get by with three relays and if you have 2, 4, 8 and 16 ohm resistors available there's an obvious 4 relay 5 resistor solution which gets you 2-32 ohms in 2 ohm increments.I can't see how nuhamind2's solution gets 2 ohms, I can only get 8, 16 and 32 out of it.

author: Frollard
author_rank: Newbie
timestamp: March 11, 2013, 11:31:38 pm
content: This must be a problem suggested by a manager...Where you would part-swap tens-of-dollars relays for tens-of-cents resistors?!

author: Mike Warren
author_rank: Unknown
timestamp: March 11, 2013, 11:37:35 pm
content: Quote from: grumpydoc on March 11, 2013, 11:18:19 pmExcept power is an important factor. The resistors are 100W 8 Ohm types.

author: Mike Warren
author_rank: Unknown
timestamp: March 11, 2013, 11:38:21 pm
content: Quote from: Frollard on March 11, 2013, 11:31:38 pmNot at all. The power resistors cost more than the relays.

author: grumpydoc
author_rank: Super Contributor
timestamp: March 11, 2013, 11:38:46 pm
content: QuoteAs this is intended for a loudspeaker dummy load I presume that handling a decent amount of power is part of the spec, so the price trade off between the relay and resistor is probably not "tens-of-dollars relays for tens-of-cents".In fact I suspect that an unstated requirement is that the 2ohm combinationisachieved by having the four resistors in parallel to increase power handling.Edit: Ah, I see Mike makes the same point

author: Mike Warren
author_rank: Unknown
timestamp: March 11, 2013, 11:47:31 pm
content: Quote from: grumpydoc on March 11, 2013, 11:38:46 pmYes, I don't see any other way of getting 2 Ohms from four 8 Ohm resistors.

author: NiHaoMike
author_rank: Super Contributor
timestamp: March 12, 2013, 01:21:17 am
content: If 5 relays is the minimum, would there be extra credit for wiring them such that going between steps requires only one relay to toggle? (Assuming that's possible, of course.)Also note that to accurately emulate a speaker, it takes series inductance and (if you really want to be accurate) shunt capacitance. (Some digital amplifiers expect the series inductance of the speaker to be part of the output filter and might not operate as intended with a plain resistive load.) Also note that you'll definitely need snubbers on the relays to suppress arcing - full power on the 32 ohm position is 113V RMS.

author: Mike Warren
author_rank: Unknown
timestamp: March 12, 2013, 01:47:58 am
content: Quote from: NiHaoMike on March 12, 2013, 01:21:17 amNo, but the fewer contacts it needs to go through, the better.

author: nuhamind2
author_rank: Regular Contributor
timestamp: March 12, 2013, 02:41:57 am
content: oopps, got my answer wrong. Can't see clear through my crowded skecthbook. This is the best I can manage. The left one can't make 2 Ohm, the right one can't make 32 ohm

author: grumpydoc
author_rank: Super Contributor
timestamp: March 12, 2013, 08:14:58 am
content: QuoteWell, umm, yes - obviously. But you mentioned that the solution you were after had to use 4x8ohm and no other values. So I assumed you wanted the 2ohm load to be 4 in parallel and not, say, a single 2ohm resistor. That plus the fact that if you have an amp capable of driving 2ohms it's usually a fairly beefy one so it would be an advantage to have multiple resistors making up the load.

author: Mike Warren
author_rank: Unknown
timestamp: March 12, 2013, 09:03:37 am
content: Right on all counts.This dummy load will make up part of a larger audio test unit to replace one I made 20 years ago that's pretty much worn out. This one may even have a microcontroller in it. I'm still considering the spec and features. One thing requirement is that it will be at least 90% made from stuff I already have lying around, and I happen to have a bunch of electronic volume ICs from an out of production device. And plenty of AVRs.If I'm happy with how it turns out I'll publish the design.

author: Mike Warren
author_rank: Unknown
timestamp: March 12, 2013, 09:07:05 am
content: Quote from: nuhamind2 on March 12, 2013, 02:41:57 amI'm thinking about simplifying it. 16 and 32 Ohms will be very rarely needed. But I do need a lot of power, particularly at 2 and 4 Ohms.

author: Gall
author_rank: Frequent Contributor
timestamp: March 12, 2013, 11:52:53 am
content: This means you could use high power 4 ohm resistors to get 2, 4 and 8 ohms. Or just something like a R-2R ladder DAC to get any resistance.6 Ohm is used sometimes too.

author: Mike Warren
author_rank: Unknown
timestamp: March 12, 2013, 12:00:47 pm
content: Quote from: Gall on March 12, 2013, 11:52:53 amExactly what I was thinking. It means a different type of resistors, but I have an idea there too.QuoteI would never need 6 Ohms.

author: NiHaoMike
author_rank: Super Contributor
timestamp: March 12, 2013, 03:32:18 pm
content: Quote from: Mike Warren on March 12, 2013, 09:07:05 amGiven that IGBTs are becoming fast enough to make good audio amplifiers, there would likely be a trend towards higher voltages with series (and series-parallel) connected speakers for large room audio systems.

author: Mike Warren
author_rank: Unknown
timestamp: March 13, 2013, 01:30:06 am
content: Quote from: NiHaoMike on March 12, 2013, 03:32:18 pmYou could be right, but that's not what I'm seeing at the moment. The trend is either multiple amps or for larger distributed systems using 100V line.Still trying to decide, but maybe if I can delete at least one relay I could omit the 32 Ohm setting. I hate relays and will avoid using them whenever I can.