PSRR and loop gain relation in LDO

[anhnha]

I read somewhere that PSRR is typically the inverse transfer function of the loop gain. However, I can't find any formal proof in books or articles.
Could anyone tell me how to derive that formula?
I am talking about PSRR for LDO.
Thank you.

 

[erikl]

PSRR is not directly connected to the loop gain (Aol/Acl), however a large loop gain enhances the original PSRR, as it enhances the linearity (accuracy) of any circuit. See also this thread.

 

[anhnha]

Thank you.
Could you explain this sentence from the book below.
PSR of an LDO can be approximated by the superposition of the inverse of the loop gain within UGF and the output filtering beyond the UGF.

https://books.google.com.vn/books?id=KFvwyst9SI0C&pg=PA56&lpg=PA56&dq=%E2%80%9Cin-band+PSR%E2%80%9D&source=bl&ots=11TUfuvCVo&sig=IeAHam0JNpOK9sOr-om-JQqzQ0s&hl=en&sa=X&ei=4-5RU4uOFseEkQX3uYGoAQ&ved=0CCgQ6AEwAA#v=onepage&q=%E2%80%9Cin-band%20PSR%E2%80%9D&f=false

 

[erikl]

Both decrease the PSR (as smaller, or more negative in dB, as better!): 1/loop-gain , and PS noise outside of the UGF, because it will be damped additionally. That's why they call it superposition, meaning multiplication of both damping actions.

Regrettably, line frequency noise usually isn't outside of the UGF, so doesn't benefit from additional damping.

 

[anhnha]

My LDO has bad PSRR causing by bad bandgap line regulation.
Is there any way to get a good PSRR with that bad bandgap output voltage?

 

[dick_freebird]

Where PSRR is achieved by feedback, loop gain is the deal.
This is more at the low frequency end. At high frequencies
where individual devices' capacitance serves as an "injection
port" the feedback loop is bypassed or shows up late to the
party.

The bandgap core of course must be solid. You might decide
to put it under its own crude LDO (one that is simple, cuts
the imposed dVIN by some decades, don't care so much
about tempco or absolute accuracy as long as headroom
is maintained).