Right or wrong!?

Wondering if both of these are correct or not and in that case why?
Question came to me since I have trouble balancing positive/negative sides and want to know if the transformer in the example HAS to be center tapped in this application or you can use a transformer with only single secondary without center tap? (picture borrowed from; https://www.circuitstoday.com/dual-adjustable-power-supply-using-lm-317-lm337 and redrawn by me)

SG should be Star Ground connected directly to main ground and do I need to connect the SG to be able to adjust positive and negative side?

dual-supplyCT.jpg

dual-supply1.jpg
 
NONE of your DC should be flowing back to utility power "ground".

Therefore your lower diagram will not work as expected.

You can use the CT or a voltage doubler.

Or for LOW-current work, a voltage divider.
 
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But if I want to use the upper diagram and don't have a center tapped transformer then I need a transformer with two secondaries if I understand it right. If I want appr. 14-15 volt out on the PSU would it be enough with 2 x 9 volt?? That will give me appr. 3 volt for adjustment over the LM317/337 or is it too little headroom?

dual-supply2T.jpg



And yet another question when I am at it. I have a Aleph J amp that I want to get up running and I have a 300 VA transformer with 2 x 18 volt secondaries. Whould following be an acceptable solution if I don't want to buy another transformer and run the amplifier as double mono?? I already know that I risk humming but 300 VA transformers are not for free so I thought this seemed to be a neat solution using one transformer and in this case I presume it is crucial to separate right/left positive and negative rail using the two different secondaries to avoid humming according to diagram that I found on the web.

amp layout 2.jpg
 
would it be enough with 2 x 9 volt?? That will give me appr. 3 volt for adjustment over the LM317/337 or is it too little headroom?
Do math.

The peak of 9Vrms is 9*1.414= 12.7V. You will lose a Volt in rectifier, 11.7V. You can't really get away with less than 3V drop in the regulator unless the reg is fed from a regulated source. So 11.3-3= 8.7V each side.

BTW: many-many "+/-15V" circuits will run fine on +/-8V. That's enough to support a 3.5V line level which is enough to push almost any line input.
 
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