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routing angle 45 or 90? what is differance and what is better?

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As far as I read no one gave the real answer to the question. The answer is: it depends on the production process.
Hobbyists usually create their homemade circuits using a toner transfer method (or using UV presensitized boards). At the etching process the board is put into ferric chloride to cut out unneeded copper areas. This process is very long and can lead to interrupted traces if the board is left in the ferric chloride solution for too long; but it has no problem etching 90° or 45° angles.
In industrial production however they have to be fast and they cannot risk a high number of interrupted traces. For this reason they use a machine called "Engraver" (or engraving machine, whichever you like the most). This machine uses a very fast iron pointer which "damages" the copper areas that have to be cut out. And the reason of using 45° angles instead of 90° is that the iron pointer has some troubles engraving thin tracks like 0.020 inch traces (and lower). The pointer is not guaranteed to stop right where it's supposed to when switching by a 90° angle, and it may cut out part of the trace that should have been left untouched. When using 45° angles instead, most engraving machines can switch very fast to a 45° direction and this keeps very low the risk of interrupted traces.
If you'll ever consider assigning a board production to any company, they will tell you the minimum trace width and for which thin width traces you must use 45° angles instead of 90°. Next there's a video of an engraving machine at work so you'll better understand how it works and why a 90° angle is an issue.

https://www.youtube.com/watch?v=TYAfNTvgTak

Other than this there are all the electrical characteristics of a PCB that many people already pointed out, and you should consider them if your circuit is going to be very sensitive to them (like circuits dealing with audio and any analog signals).
 

For this reason they use a machine called "Engraver" (or engraving machine, whichever you like the most). This machine uses a very fast iron pointer which "damages" the copper areas that have to be cut out. And the reason of using 45° angles instead of 90° is that the iron pointer has some troubles engraving thin tracks like 0.020 inch traces (and lower). The pointer is not guaranteed to stop right where it's supposed to when switching by a 90° angle, and it may cut out part of the trace that should have been left untouched. When using 45° angles instead, most engraving machines can switch very fast to a 45° direction and this keeps very low the risk of interrupted traces.
If you'll ever consider assigning a board production to any company, they will tell you the minimum trace width and for which thin width traces you must use 45° angles instead of 90°. Next there's a video of an engraving machine at work so you'll better understand how it works and why a 90° angle is an issue.
Sorry but that's a load of bull and as far from reality as I could imagine, professionally made boards are etched not engraved. Engraving boards like that is for small prototype double sided, and not many of them are used, it is to slow a process for the quantities of PCBs made these days.
And analogue and audio do not care whether the corners are 45 90 or any angle in between, neither dose digital, its only when you get into the giga-hertz range of either digital or RF that you have to worry.
 

And only double sided, which are rarer these days, apart from simple stuff. And ever tried machining 0.1mm tracks and gaps.
As the milling tool diameter decreases, the spindle speed has to increase and the feed rate has to generally decrease and be matched to the tool size. Even 0.5mm tools are a nightmare to play with, any lateral force during machining and you have an expensive bit of scrap. Then you have machining time, 1 board per machine, 10 machines, 1hr per board (I am being generous here), 10 hours to produce a batch of 100 providing there are no mishaps. As there are 6 billion passive components placed a day, you would need a lot of milling machines to produce the PCB's.

The reason why to use 45 deg corners has been answered.
1. You can fit more traces into a certain space.
2. It minimises the route length from a to b,
3. Minimises impedance mismatches, while not as critical as thought at normal frequencies, every little bit helps.
4. The layout looks neater.
5. It is common practice, and most engineers will insist on it, so do it.
6. It is easier to etch, no sharp corners to hold etchant, again not as critical today, etching has evolved.
Have Fun:)
 
Without going into excessive detail on the actual shape of a manufactured PCB trace, the fact is you never get a true 90 degree corner, it will always have a radius the same as half the track width...so the ratio is 1.20 not 1.414...or approx. a 20% change in width.
As to simulation this has been done on full 3 D field solvers for various corners on traces and on high speed does not impact until the gigaHz range, and for analogue it is not critical.....
Have Fun
 

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