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in my system, there are only two input power rail: +12V,20A and -12V,-20A, (they come from an isolated DC-DC brick modules).
now I want to use a -7V, -6A voltage to supply the power amplifiers, can I convert it from -12V voltage? How?
TI does not offer an integrated FET negative input / negative output (also called Quadrant 3) converter, you would need to make one using a controller and external power FETs. The circuit works like an inverted BUCK, but the controller drives the power FETs like a BOOST converter.
See this earlier E2E thread - https://e2e.ti.com/support/power-management-group/power-management/f/power-management-forum/1058496/negative-input-negative-output-with-buck-converter/3920025#3920025
1184.The Parallel Universe of Negative Input Voltages.pdf
Alternately, you could use a BUCK converter between the +12V input and the -7V output, with the normal output of the BUCK connected to ground, and the normal "ground" of the BUCK converter connected to the negative VOUT. Since the converter will span +12V to -7V, it will need to support more than 19V input, but here are some resources to help you:
Create an Inverting Power Supply Using Peak Current Mode Buck Converter: https://www.ti.com/lit/an/slvae10/slvae10.pdf
Basic Calculation of an Inverting Buck-Boost Power Stage: https://www.ti.com/lit/an/slva721a/slva721a.pdf
Creating an Inverting Power Supply Using a Synchronous Step-Down Regulator: https://www.ti.com/lit/an/slva458b/slva458b.pdf
Using the TPS5430 as an Inverting Buck-Boost Converter: https://www.ti.com/lit/an/slva257a/slva257a.pd (TPS5430 is only rated for 3A, but the process is the same for higher currents)
Minimizing Buck-Boost (Inverting) Converter High-Frequency Switching Noise: https://www.ti.com/lit/an/slva219a/slva219a.pdf
Inverting Application for the LMZM33604/6: https://www.ti.com/lit/an/snva835b/snva835b.pdf (This is a 6A integrated FET and inductor module with an input range upto 36V
Which ever solution you pick you may need to level shift control signals, such as Enable and Power Good, between the System Ground and either the -7V output or -12V input. Here is a useful applications note about circuits for that:
Level-Shifting Control for an Inverting Buck-Boost: https://www.ti.com/lit/an/slva540/slva540.pdf
thank you Peter, your integrated and prolific answer really helps me. Merry Christmas!