Hi grimberg,
Sorry, I missed your question.
The 500 was extremely advanced for its time, and was also very expensive to build. I think that is why when they discontinued it in 1974, no better model followed it up. I was introduced to these while doing warranty and overflow work from Superscope in the 70's and 80's. The first thing you would notice with the covers off are four ginormous filter capacitors, and the equally massive 2.2 KW power transformer. The next thing to grab you might be the buss bars delivering all that power to the output transistors on their own heavy current delivery setup. So, okay. It has serious power capability, more than most actually. However, what makes that amp special is the positive stage has it's own diff pair, as does the negative stage. Then there is the diff pair that controls the entire lot. That amplifier has so much finesse that you forget entirely that it's an animal. I have done exactly one where I built it my way instead of the stock version. So I made some improvements and it transformed a great sounding amplifier into something very special. I couldn't get into my own living room to hear it because the customer and friends picking it up were there. Never heard my PSB Stratus Gold speakers sound as good as that ever. Even my 300DC couldn't create that sound even at lower levels. So a whole pack of guys now want a Marantz 500 and the cost is beyond my reach.
The rebuild takes me about 2 1/2 ~ 3 days including matching all the parts. The end result is more than worth the effort. I already wanted one just done per the factory manual, but this showed me how good they can really be. Yes, it gets a new set of output transistors beta matched pretty closely. Same for the complimentary drivers along with the signal stages. Another aspect of this amplifier is that it uses a buffer input in order to drive the bipolar diff pair. The much more recent Nakamichi receivers called this "HTA" (I forget what it stood for). There was some disbelief when I showed them the Marantz 500 schematic having the same feature.
Now, consider this. That amplifier was probably designed in 1968 for it's release in 1969. So an amplifier designed in 1968 delivers a higher performance than most current products. I think the only reason it wasn't copied was the cost of manufacture. Besides, hand matching is no way to mass produce anything, something other manufacturers have discovered (Counterpoint being a prime example of this).
I am rather fond of this amplifier.
-Chris
Sorry, I missed your question.
Yes, the diagram and manual are freely available in the wild.
The 500 was extremely advanced for its time, and was also very expensive to build. I think that is why when they discontinued it in 1974, no better model followed it up. I was introduced to these while doing warranty and overflow work from Superscope in the 70's and 80's. The first thing you would notice with the covers off are four ginormous filter capacitors, and the equally massive 2.2 KW power transformer. The next thing to grab you might be the buss bars delivering all that power to the output transistors on their own heavy current delivery setup. So, okay. It has serious power capability, more than most actually. However, what makes that amp special is the positive stage has it's own diff pair, as does the negative stage. Then there is the diff pair that controls the entire lot. That amplifier has so much finesse that you forget entirely that it's an animal. I have done exactly one where I built it my way instead of the stock version. So I made some improvements and it transformed a great sounding amplifier into something very special. I couldn't get into my own living room to hear it because the customer and friends picking it up were there. Never heard my PSB Stratus Gold speakers sound as good as that ever. Even my 300DC couldn't create that sound even at lower levels. So a whole pack of guys now want a Marantz 500 and the cost is beyond my reach.
The rebuild takes me about 2 1/2 ~ 3 days including matching all the parts. The end result is more than worth the effort. I already wanted one just done per the factory manual, but this showed me how good they can really be. Yes, it gets a new set of output transistors beta matched pretty closely. Same for the complimentary drivers along with the signal stages. Another aspect of this amplifier is that it uses a buffer input in order to drive the bipolar diff pair. The much more recent Nakamichi receivers called this "HTA" (I forget what it stood for). There was some disbelief when I showed them the Marantz 500 schematic having the same feature.
Now, consider this. That amplifier was probably designed in 1968 for it's release in 1969. So an amplifier designed in 1968 delivers a higher performance than most current products. I think the only reason it wasn't copied was the cost of manufacture. Besides, hand matching is no way to mass produce anything, something other manufacturers have discovered (Counterpoint being a prime example of this).
I am rather fond of this amplifier.
-Chris
I agree with your excellent analysis of transistor load sharing forced by emitter resistors. An analysis showing how it depends of Vbe, Hfe and Re.
You prove that Vbe matching is far more important than Hfe matching and that the actual load sharing is mostly done by the emitter resistors
So, this means that, with adequate emitter resistors, output transistor matching is a myth. Thanks, JMFahey for your debunking.
I say this bluntly: For a well designed amplifier, matching output transistors is non sense.
Hi mchambin,
Really???
Okay, you can believe that if you wish. I've done all this extra work for over 30 years after my own tests showed it was in fact beneficial. On top of that, the top semiconductor producer has found that output transistor matching has concrete benefits through empirical tests. All circuit simulators assume each transistor is identical. You can always experiment by defining a few models of each transistor type in your output stage and play that way.
Also, by extension, this also applies to the diff pair, and there are those who claim that is unimportant.
To each his own I guess, but you would do yourself a service and research this topic. Even the old Marantz service manuals (like the 250 and 500) specify that the outputs must be matched within certain beta ranges. Wide one as they are balancing economics against performance. I used to order those graded parts for Marantz amp repairs. This is what actually started me to look into this idea.
Again, to each his own when you treat the science of this as a religious belief.
-Chris
Really???
Okay, you can believe that if you wish. I've done all this extra work for over 30 years after my own tests showed it was in fact beneficial. On top of that, the top semiconductor producer has found that output transistor matching has concrete benefits through empirical tests. All circuit simulators assume each transistor is identical. You can always experiment by defining a few models of each transistor type in your output stage and play that way.
Also, by extension, this also applies to the diff pair, and there are those who claim that is unimportant.
To each his own I guess, but you would do yourself a service and research this topic. Even the old Marantz service manuals (like the 250 and 500) specify that the outputs must be matched within certain beta ranges. Wide one as they are balancing economics against performance. I used to order those graded parts for Marantz amp repairs. This is what actually started me to look into this idea.
Actually, you say that from a position of ignorance, not meant in a disparaging way. You don't honestly understand this topic and I have to think you haven't done any amount of real research of your own.
Again, to each his own when you treat the science of this as a religious belief.
-Chris
Please enlighten us. Explain the science. I cant find the info from the semi manufacturers you speak of. Firstly a diff pair is nothing like an output pair so dont compare the two.
20db of distortion difference? Did they drive the amp at full power with one transistor taking most of the load so it was clipping? In there tests, did they use emitter resistors? How big? Do they tell you how matched the transistors should be? Not that I dont believe you, but this is the first I hear of this. just wondering how much of an effect this has. Not buying the 20db, ( .01% distortion amp changes to 1% distortion? ). And we are talking about parrallel transistors not complementary, correct?
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Hi mchambin,
0R22 resistors are safe as long as the thermal resistance of the heat sink is low enough. In many really well designed amplifiers, the temperature co-efficient is close to zero or slightly negative (older Marantz products, but higher value of emitter resistors).
Beta match however has more influence over transistor current flow than does a few mV difference in emitter-base voltage. If you look at how much these values vary, beta is far more diverse. The differences in current due to beta variations can easily exceed 50% between transistors in practice. These variations completely swamp out the expected differences in emitter-base voltage, in practice. Indeed several manufactures tell you to measure the difference over the emitter resistors and give limits for these readings.
It is true that at high powers the emitter resistors do a good job of forcing equal current sharing. Not so true at 0R22 though. Unequal beta is still a problem. What is contributing this is that at lower power levels the currents will be more unequal and the higher beta devices will run hotter (increasing beta more). So when you begin hitting higher powers the high beta devices are pre-heated and have even more reason to conduct more than their lower beta brothers.
Measuring current sharing by looking at emitter resistor voltage drops is something I often do (sanity check). When the outputs are not matched, these can vary a lot, but when matched they don't.
I've had a lifetime doing this work and was interested in output beta match early on. My observations over the years proved that Motorola's position on the matter is reinforced. Of course, if the reverse were true I would be looking to see what I did wrong! Their people are a lot smarter than I am.
So, to cbdb who wants to be spoon fed this information, figure out what the normal variations in each parameter are, then apply those variables to some ideal, but mismatched (Vbe) outputs and figure out how much the differences in Vbe can push the current flow in a bank of output transistors. Then perform the same routine assuming variable beta, the range being what you normally see in output transistors.
In the bad old days, beta variations were easily 3:1 - more in fact. Matching output transistors was a depressing job because I had to buy them for the shop and the other techs and I saw first hand how low the yields were. These days the variation is much smaller, 2:1 or less maybe. I haven't paid that much attention but I know I don't need to buy nearly as many today.
I've done all this figuring and jiggering many moons ago and don't really care to dig all that crap out. The end result of that study was that Motorola is absolutely correct. So you aren't trying to prove me wrong at all. You're actually taking On-Semi to task (and their engineering department). So do yourself a favour and read some data sheets and read the conclusions. It's less work on your part.
In the data sheet for the MJ21196 on page 5 there is the test circuit for their distortion test. I'll try to find data sheets that actually make the statement covering THD and beta matching. Ah, it's on page 2 under "DYNAMIC CHARACTERISTICS" under the distortion limits given. https://www.onsemi.com/pub/Collateral/MJL21195-D.PDF
So you don't have to believe me at all. Just believe what the actual experts on power output transistors say.
You know what? I can't believe the lengths I have to go to to help some of you folks. This is all stuff you could have done yourself. Laziness? Religion? For those who didn't accept what I had to say, you must have been invested in some other belief that you were too lazy to actually look into.
So to conclude, Matching beta is necessary to get the best performance out of a given multi-output design. So I'll drop another "secret" that I use. Matching the complimentary drivers and output groups also make a difference. Even in single output per polarity outputs, matching the complimentary gains makes a difference. You can either run with this, or accept less good performance and don't believe me. What I will not do is to waste more time on some of you in an effort to help you.
-Chris
and
Are almost exclusive statements. From experience the cheaper products tend to use values like 0R47 for emitter resistors. Brands that run hotter or at higher power levels tend to 0R22 or even 0R05 (Carver if you don't believe me on this). In our discussion we were using 0R22 as the emitter resistance. Thermal stability tends to be less with smaller values of emitter resistors. Distortion tends to be higher with higher values of emitter resistance. You can't have it both ways. Most consumer products used to use 0R33 resistors. Units using small heat sinks also tend to use higher values of emitter resistors. So we can actually say that cheaper, or less well designed units, tend to higher values of emitter resistance to reduce in field failures. In amplifiers were cost isn't as great a concern and performance heads the effort we will normally see the lower value emitter resistors + large heat sinks and maybe a more aggressive bias control circuit (more complicated than the single Vbe multiplier).
0R22 resistors are safe as long as the thermal resistance of the heat sink is low enough. In many really well designed amplifiers, the temperature co-efficient is close to zero or slightly negative (older Marantz products, but higher value of emitter resistors).
Beta match however has more influence over transistor current flow than does a few mV difference in emitter-base voltage. If you look at how much these values vary, beta is far more diverse. The differences in current due to beta variations can easily exceed 50% between transistors in practice. These variations completely swamp out the expected differences in emitter-base voltage, in practice. Indeed several manufactures tell you to measure the difference over the emitter resistors and give limits for these readings.
It is true that at high powers the emitter resistors do a good job of forcing equal current sharing. Not so true at 0R22 though. Unequal beta is still a problem. What is contributing this is that at lower power levels the currents will be more unequal and the higher beta devices will run hotter (increasing beta more). So when you begin hitting higher powers the high beta devices are pre-heated and have even more reason to conduct more than their lower beta brothers.
Measuring current sharing by looking at emitter resistor voltage drops is something I often do (sanity check). When the outputs are not matched, these can vary a lot, but when matched they don't.
I've had a lifetime doing this work and was interested in output beta match early on. My observations over the years proved that Motorola's position on the matter is reinforced. Of course, if the reverse were true I would be looking to see what I did wrong! Their people are a lot smarter than I am.
So, to cbdb who wants to be spoon fed this information, figure out what the normal variations in each parameter are, then apply those variables to some ideal, but mismatched (Vbe) outputs and figure out how much the differences in Vbe can push the current flow in a bank of output transistors. Then perform the same routine assuming variable beta, the range being what you normally see in output transistors.
In the bad old days, beta variations were easily 3:1 - more in fact. Matching output transistors was a depressing job because I had to buy them for the shop and the other techs and I saw first hand how low the yields were. These days the variation is much smaller, 2:1 or less maybe. I haven't paid that much attention but I know I don't need to buy nearly as many today.
I've done all this figuring and jiggering many moons ago and don't really care to dig all that crap out. The end result of that study was that Motorola is absolutely correct. So you aren't trying to prove me wrong at all. You're actually taking On-Semi to task (and their engineering department). So do yourself a favour and read some data sheets and read the conclusions. It's less work on your part.
In the data sheet for the MJ21196 on page 5 there is the test circuit for their distortion test. I'll try to find data sheets that actually make the statement covering THD and beta matching. Ah, it's on page 2 under "DYNAMIC CHARACTERISTICS" under the distortion limits given. https://www.onsemi.com/pub/Collateral/MJL21195-D.PDF
So you don't have to believe me at all. Just believe what the actual experts on power output transistors say.
You know what? I can't believe the lengths I have to go to to help some of you folks. This is all stuff you could have done yourself. Laziness? Religion? For those who didn't accept what I had to say, you must have been invested in some other belief that you were too lazy to actually look into.
So to conclude, Matching beta is necessary to get the best performance out of a given multi-output design. So I'll drop another "secret" that I use. Matching the complimentary drivers and output groups also make a difference. Even in single output per polarity outputs, matching the complimentary gains makes a difference. You can either run with this, or accept less good performance and don't believe me. What I will not do is to waste more time on some of you in an effort to help you.
-Chris
I agree current sharing is not perfect I dont agree that this affecrs distortion as much as you imply, except at high powers where the amp can no longer supply the current neccesary. Just went thru D Selfs amp book 3rd edition. Start at page 128. Nothing about transistor matching. Actually " No explicit current-sharing components were added when doubling the devices, and this lack seemed to have no effect on LSN reduction. There was no evidence of current hogging, and it appears that the circuit cabling resistances alone were sufficent to prevent this."
Thanks for the link, but that looks like there matching a complementary pair, arent we talking about parrallel transistors? And they dont tell you how unmatched the first test transistors are. And there pushing those transistor to 100 watts. Again, I agree there is an effect, I'm not ready to believe its audible.
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Just read the On-Semi information. My own experience agrees with this, and I have had customers call and ask what I did to make their equipment sound better. The only way you're going to accept what I have said is if you get busy and do some repairs or builds along with equipment to allow you to see this.
I'm not going to debate this any longer. I have given ample proof and information so that you can examine this on your own. Like I said before. Either run with it, or allow yourself to have lower performance. It only matters to you and not me. My customers are believers and can hear it with their own ears. Often they don't expect such a large difference. I'll admit that I do a number of things to improve performance, and the end result can be measured and heard. It's all up to you now.
-Chris
I'm not going to debate this any longer. I have given ample proof and information so that you can examine this on your own. Like I said before. Either run with it, or allow yourself to have lower performance. It only matters to you and not me. My customers are believers and can hear it with their own ears. Often they don't expect such a large difference. I'll admit that I do a number of things to improve performance, and the end result can be measured and heard. It's all up to you now.
-Chris
Agree and add, I´d love to see some Math used, instead of vague assumptions and "Appeal to Authority" (as in: Motorola said so, so it´s true")
No doubt they might have said something similar, but lacking the actual citation and more important taken fully out of context, it loses some of its "convincing power".
I had written a detailed answer but really, have more pressing things to do than try to counter a, so far, "religious belief".
No doubt they might have said something similar, but lacking the actual citation and more important taken fully out of context, it loses some of its "convincing power".
I had written a detailed answer but really, have more pressing things to do than try to counter a, so far, "religious belief".
Hi cbdb,
Yes, I know that. However, I'm not going to dig into this any further. Some folks claim that mismatches work better, but empirical evidence says otherwise. I'll rest on over 30 years of actively looking at this.
No matter what theory says, empirical evidence in real amplifiers trumps. Having over 30 years doing this exactly, measuring before and after matching outputs supports what I have figured out earlier. To let you know how long ago this theory work was done, I was in Ryerson in Toronto, 1981 I think. I can't locate that stuff as it was likely thrown out and no way am I going to recreate it. But, I'm no smarter than most people here, and you guys can do whatever I have done. These days you must have more experience than I had when I did that work.
In the end, it might be a lot easier for you to test what I'm saying. I often do this in repairs and improvement jobs - or new amps I build. Just grab an amplifier using multiple outputs per polarity and measure the distortion. Then measure the emitter currents and remove the outputs and measure beta (marking them). Arrange them in matched sets, or you might have to buy new ones if the ones you have are badly mis-matched. Then repeat the process of measurements.
You don't need to use TO-204 transistors, this holds true using TO-126 or TO-220 parts (cheap). If your THD meter is any good at all, you will see an improvement. On-Semi may have another app note somewhere that covers this as well. I've learned years ago that reading app notes will give you the least expensive education possible.
I'm actually extremely busy normally and I occasionally take the time to help out. But I can't devote time to fight over something I'm trying to help you with.
JMFahey, you are involved in service I think. Try this out. It won't cost you any more than some time, but a lot less than trying to work the math out. In fact, it may give you a tangible edge over your competition. It has for me. Anyway, this is a very real achievable test for you where it may be more costly for other members to attempt.
I used a Leader THD meter at first, then an HP 339A, and now an RTX 6001. ANy of those instruments should allow you to see the difference, depending on how far out the originals were. FOr matching, I used a variety of Heathkit and B&K testers (B&K not so good), as well as jigs to run a set of four to higher currents to prove everything held up over the 1 mA test current tests. Of course the actual numbers were different, but the matches held. You should have this capability and be able to do these tests with minimal hardship.
-Chris
Yes, I know that. However, I'm not going to dig into this any further. Some folks claim that mismatches work better, but empirical evidence says otherwise. I'll rest on over 30 years of actively looking at this.
No matter what theory says, empirical evidence in real amplifiers trumps. Having over 30 years doing this exactly, measuring before and after matching outputs supports what I have figured out earlier. To let you know how long ago this theory work was done, I was in Ryerson in Toronto, 1981 I think. I can't locate that stuff as it was likely thrown out and no way am I going to recreate it. But, I'm no smarter than most people here, and you guys can do whatever I have done. These days you must have more experience than I had when I did that work.
In the end, it might be a lot easier for you to test what I'm saying. I often do this in repairs and improvement jobs - or new amps I build. Just grab an amplifier using multiple outputs per polarity and measure the distortion. Then measure the emitter currents and remove the outputs and measure beta (marking them). Arrange them in matched sets, or you might have to buy new ones if the ones you have are badly mis-matched. Then repeat the process of measurements.
You don't need to use TO-204 transistors, this holds true using TO-126 or TO-220 parts (cheap). If your THD meter is any good at all, you will see an improvement. On-Semi may have another app note somewhere that covers this as well. I've learned years ago that reading app notes will give you the least expensive education possible.
I'm actually extremely busy normally and I occasionally take the time to help out. But I can't devote time to fight over something I'm trying to help you with.
JMFahey, you are involved in service I think. Try this out. It won't cost you any more than some time, but a lot less than trying to work the math out. In fact, it may give you a tangible edge over your competition. It has for me. Anyway, this is a very real achievable test for you where it may be more costly for other members to attempt.
I used a Leader THD meter at first, then an HP 339A, and now an RTX 6001. ANy of those instruments should allow you to see the difference, depending on how far out the originals were. FOr matching, I used a variety of Heathkit and B&K testers (B&K not so good), as well as jigs to run a set of four to higher currents to prove everything held up over the 1 mA test current tests. Of course the actual numbers were different, but the matches held. You should have this capability and be able to do these tests with minimal hardship.
-Chris
Hi cbdb,
Well, you can't. You match compliments in that case. With multiple outputs, you would match each side (polarity), and if you are very lucky they also match as compliments. On-Semi had transistors that were the best I had ever seen like that. They were the MJW0302 and MJW0281 pairs. They all had beta grouped closely around 95. I really wish they had not discontinued them. I would have used them as often as possible. The ones I did get went into Symasym amplifiers (R5.3).
How close you would match outputs depends completely on how touchy current sharing is at your operating levels, and how much distortion you are willing to live with.
Back in time there were outputs with the same specs, but vastly different quality levels. They were the MJ15015/MJ15016 (utter garbage) and the MJ15022/MJ15023 (excellent parts). The only clue was the comment that the first pair were "economy grade". The 015/016 parts had beta all over the place and PNP beta around 200 with NPN beta sitting down near 60. You would see these in cheap amplifiers (Linear Power car amps for example). If you rebuilt some of these using the 022/023 parts, you could really upgrade the performance. Normally with cheap products you have to upgrade a lot more than just the outputs. Going the other way as I have seen some techs do would downgrade an amplifier that originally used 022/023.
So I guess the only answer you can have is "it depends". If you want to know how close I match parts, I try to get them within a couple counts - which is pretty darned close. But I wouldn't be doing that unless I was being paid to improve the performance of a piece of equipment. Normal repairs will get the closest match without going into heroics like ordering a new lot of transistors for that job.
-Chris
Well, you can't. You match compliments in that case. With multiple outputs, you would match each side (polarity), and if you are very lucky they also match as compliments. On-Semi had transistors that were the best I had ever seen like that. They were the MJW0302 and MJW0281 pairs. They all had beta grouped closely around 95. I really wish they had not discontinued them. I would have used them as often as possible. The ones I did get went into Symasym amplifiers (R5.3).
How close you would match outputs depends completely on how touchy current sharing is at your operating levels, and how much distortion you are willing to live with.
Back in time there were outputs with the same specs, but vastly different quality levels. They were the MJ15015/MJ15016 (utter garbage) and the MJ15022/MJ15023 (excellent parts). The only clue was the comment that the first pair were "economy grade". The 015/016 parts had beta all over the place and PNP beta around 200 with NPN beta sitting down near 60. You would see these in cheap amplifiers (Linear Power car amps for example). If you rebuilt some of these using the 022/023 parts, you could really upgrade the performance. Normally with cheap products you have to upgrade a lot more than just the outputs. Going the other way as I have seen some techs do would downgrade an amplifier that originally used 022/023.
So I guess the only answer you can have is "it depends". If you want to know how close I match parts, I try to get them within a couple counts - which is pretty darned close. But I wouldn't be doing that unless I was being paid to improve the performance of a piece of equipment. Normal repairs will get the closest match without going into heroics like ordering a new lot of transistors for that job.
-Chris
Anatech, if you really want a Marantz 500 Why not make up some boards off the schematics and place it all in a DIY case. It won't be an original but it won't cost you 6- 7 grand either.
If there is an attractive amp with power meters and hefty power supply I would be tempted to use that as the case and power supply.
If there is an attractive amp with power meters and hefty power supply I would be tempted to use that as the case and power supply.
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Just found this on the Elliot Sound website.
Matched transistors will rarely give you 'better sound' (whatever that is supposed to mean). In general, distortion will be almost completely unaffected, and there is no influence on frequency response or transient response. What you will get (for paralleled devices) is greater reliability, because the transistors will share the current more equally.
Matched transistors will rarely give you 'better sound' (whatever that is supposed to mean). In general, distortion will be almost completely unaffected, and there is no influence on frequency response or transient response. What you will get (for paralleled devices) is greater reliability, because the transistors will share the current more equally.
Silicon Chip an Australian magazine published a Blameless style of amplifier January - March 2017 using the latest modern transistors throughout.
The output devices were pairs in opposite halves - there was no mention of needing to 'match' those transistors.
The THD result at 100W into 8R at 1kHz measured on an Audio Precision equipment was less than 0.005%.
That suggests a vast improvement in semiconductor design and manufacture between 1973 and 2017.
Hi mjona,
Hi cbdb,
Distortion is lower using matched devices, but the indicated change on a THD meter is very small. This is true for many changes that people report as sounding better. One of the nicest things about having the RTX 6001 is that these things can be seen a little, and it is repeatable - so not noise.
-Chris
Yes, absolutely. However, that just means that obtaining matched sets can be done at a lower cost. If you can, matching is a "tweak" that you can do easily for yourself.
Hi cbdb,
Just about everything on that site is suspect. He designed "by ear" only.
Distortion is lower using matched devices, but the indicated change on a THD meter is very small. This is true for many changes that people report as sounding better. One of the nicest things about having the RTX 6001 is that these things can be seen a little, and it is repeatable - so not noise.
Oh, I don't think so. We have people spending $500 + for cables of various designs and purposes. Surely spending a little extra for parts that can be used elsewhere isn't too much of a hardship. There is a difference between DIY people. Some do it to try and get an amplifier (for example) cheaper while others do this to create something better than you can buy in the store. while also learning. Your viewpoint suggests to me that you would rather build something as cheaply as possible - and that's perfectly okay. Others would like to have improved performance, and this is one of the ways to achieve that goal. As I have said before, I'm just trying to help people out. You don't need to agree with any suggestion I make. But others might and will benefit. I don't have to defend this beyond giving a suggestion I have found to be true in practice. If you are arguing from the position of an armchair thought experiment you'll find that it doesn't compete with real world observations. To each his own ...
-Chris
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