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What is the correct symbol for an ammeter that measures 0..200 mA and generates 0..2 V proportional output?

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That's the same as a current controlled voltage source, a CCVS. The symbol looks like a diamond with an equation next to it. In your case, V=10A.

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We don't normally call that an ammeter, but a current-controlled voltage source. One common symbol is this (courtesy of Wikimedia):

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Text next to the symbol should indicate how it's controlled. For example, "\$I_1\times{}10\Omega\$".

If you want to represent a physical device that has this function, you'd probably just use a rectangular box with pins corresponding to each of the physical pins.

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