Here's a good introductory video on linear regulators. It uses the LM317 but almost all linear regulators operate the same way:
LM317 Adjustable Voltage Regulator Tutorial -- Afrotechmods
https://youtu.be/IjJWWGPjc-wWhen it comes to linear regulators there are a lot of choices out there with different specs. If you were to use the LM317 here's what you'd have to worry about:
- your circuit appears to draw a max of 1A and that's within the LM317 limits
- to get a regulated output of 9.5V you'll need an input voltage of around 12V
- the lowest voltage attainable by the LM317 is 1.25V so we're good there
- if your circuit draws 1A even at 2V you're looking at having the LM317 dissipate 10W. That's going to require a good size heat sink and perhaps also active cooling (i.e. a fan). If your circuit draws less current at lower voltages then your cooling needs will be less.
There are a bunch of LM317 modules available on Amazon and they implement basically the same design in the Afrotechmods video. Most come with rather puny heat sinks but they would probably work if you just replaced the heat sink with something more substantial.