Just for fun: a superreg with <12 discretes??! ?! ?

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Some RF transistors are certainly good candidates for low-noise jobs, but they are a pain to work with: their DC/LF characteristics generally suck (think Hfe, etc), they want to oscillate as soon as they see something looking like a transmission line in their vicinity, they are fragile and they are expensive.
Transistors like the ZTX series are affordable, robust, have a huge Hfe and an insignificant Rbb.
With a ZTX849 at the input of a nonoiser I managed 0.09µV output noise.
With some care and in the right environment, it is probably possible to duplicate that result with this regulator
 
I have tested the blue LED as a reference:

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This is the (slightly) adapted schematic:

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It results in a 12.24V output voltage.
The dropout is now 1.1V, better than the initial 1.8V but somewhat more than 1*Vbe. The excess voltage is caused by the I*R drop in the BS250.

I have measured the output noise without the LED bypass cap, but with the 6K2 FB resistor bypass: it is thus the <noise of transistor (~negligible here)> + <the noise of the LED> ~= the noise of the LED (due to the quadratic sum): 0.9µV.

Not huge, but bypassing it is certainly beneficial if low-noise performance is important.

When bypassed, all the previously measured dynamic characteristics remain the same.

I also checked the output impedance without the 560µF LED bypass: 400µΩ @1kHz (against 320µΩ with the cap).
 

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I use a home-made X1000 LNA in front of a regular AC millivoltmeter (Levell).
The millivoltmeter has internal filters, and for the values I report (total noise rms), I use the 10Hz to 10kHz one, as it is the most relevant for audio.

The LNA has a 0.8nV/sqrtHz floor, and when I have to make measurements approaching that limit, I use a X10 transformer pushing that down to 0.1nV/sqrtHz.
Most of this is detailed here and in the denoizator thread.

The 10Hz to 10kHz range can be roughly translated to ~100 times the noise density, ignoring the excess noise at low frequencies.

It would of course be nicer to have noise vs. frequency plots, but at the moment I do not have any decent soundcard based setup, so that's the best I can offer.
I can also measure the actual noise density at 1kHz, but it requires some additional efforts
 
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You have chosen FB divider resistor values such that the output voltage should be greater than the 20V input.

In addition, there is no startup mechanism included (in sim, it may sometimes start by itself, but not in reality).

I have changed R8 for 5K6 and added a source and diode for startup:

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V2 is just a simulation ploy, not something meant to be used in the real world.

For a permanent startup, a voltage divider is OK, that's what I used in my LNA supplies:

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It could also be a "kick-start" using a capacitor (the regulator then shuts down automatically if its output is shorted).

Since the regulator is in fact a bistable, it can also double as a button-controlled power switch: one button to switch on, another to switch off.
With some ingenuity, it would probably be possible to use a single button to toggle on and off.

It could also be controlled by a microcontroller port
 
M1 is just a low power PMOS, BS250 is OK, more modern alternatives are better.
Q1 depends on your current requirements: you are not going to achieve the 4A of the BD201 with the BCP53; perhaps 100 to 300mA, depending on the voltage to drop. Its dissipation is limited, and with a higher Vin-Vout you will have to derate the current.

What are your requirements?
 
Mostly the same as for any other regulator: output voltage, current, possibly dropout voltage. The rest, like noise, PSRR, output impedance is essentially part of the design and non-negotiable.
With a discrete reg however, you have the choice of adding bypass caps wherever you like; I showed examples in the measurements.

With this reg, you also need to select a starting method, as it isn't self-starting.

The circuit can be made self-starting with 2 resistors and a diode (the example is my LNA supply), or it can be work as a ON/OFF switch (or rather a ON/STBY switch)
 
M1 is just a low power PMOS, BS250 is OK, more modern alternatives are better.
Q1 depends on your current requirements: you are not going to achieve the 4A of the BD201 with the BCP53; perhaps 100 to 300mA, depending on the voltage to drop. Its dissipation is limited, and with a higher Vin-Vout you will have to derate the current.

What are your requirements?

I will use it to power a headphone amp so just need few hundreds ma. What is the mordern alternatives for BS250 and also the negative side? Thanks!
 
NTR5105P, BSS84 are examples.
For dual polarities, you can also find complementary transistors in a single package.

It also depends on your preferences: SMD or TTH, your favorite supplier, etc

If you state your exact requirements: current, voltage, starting method, I can adapt the schematic for you (in sim, I am not going to test it physically)
 
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