But you have to go very low, to make the bias current negligible. For example, you want 10V, so use 470R resistors with the LM7805, for R1 & R2, the output voltage will be nearly 12V, an error of 20%, because the typical bias current is 4.3mA, according to the data sheet, but it could be as high as 8mA, giving just over 13V out.
This equation might work for LM317, but I don't think the bias current of 8mA will make that effect on the LM7805. It's been awhile since I did this, but I have a feeling even 5%
error offset (which is fixable) with 470R R1 at double Vref is wayyyy too much. I think this is case of applying wrong equation correctly? Using values like this, I seem to recall ignoring bias current and getting output I wanted. Maybe I am wrong.
anyhow, I agree fundamentally with what you said Hero, I just don't think it's significant as you think.
I shall have to break out the breadboard and try it. If I have any 78xx.
* edit: Well, color me wrong. Your application of the equation seems to be spot on. Using 500R resistors for R1 and R2, I got output voltage of 13V, lol. With this large of an offset contributed by the bias current, I suspect the diode/zener trick could be more temp stable when increasing output voltage by more than a couple volts.
For small bump in voltage within a few diode drops, any effect would be proportionally less, of course. So I'm still conflicted if this isn't still better than diode trick for small increase in output voltage.
I understand what Wraper is saying, now. Yeah, 78XX are technically not as good as LM317 in any way, except when they're good enough. 2 extra resistors is more cost of manufacture. Or more complex BOM and inventory if you are the manufacturer.