I had thought that, but I may now go with the LM3886 due to it having short circuit protection and simplicity. I have a P3A built already which I use for its original purpose (an audio amplifier), and if the leads touch, it instantly toasts all output transistors.
That suggests that you need to use a real AC to RMS converter. If you are going up to 1KHz and need to read RMS, you need a meter that correctly processes frequencies in the many KHz range. Low cost meters digital meters are not likely to be able to do this. The more expensive ones may.
Some of the old "moving iron" meters did amazing stuff with the design of the magnetics. Today RMS conversion is done with methods that involve PWM or sampling tricks, the nonlinearity of diode junctions or thermal methods.
Each of these methods has its drawbacks that tend to limit the frequencies it is good for.
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