What determines where a center tap should be placed on an inductor or does it not matter?
Inductors generally do not have taps, at least not in any circuit technologies that I work with.
You may be thinking of taps on transformers? Input taps on AC Mains transformers are meant to allow you to use them in different source voltage circuits (like 110Vrms and 240Vrms). Output taps are meant to let you generate multiple output voltages with a single transformer, including balanced +/- outputs.
Center taps can be common on inductors used in oscillators and some matching networks. For instance, certain types of antennas will have a coil at the bottom of the antenna with a tap. The transmission line attaches at this tap. Where the tap is determines the impedance that the transmission line 'sees'. In general, I'd say the main significance of where a tap is on an inductor is for impedance.
Tempted to say in the centre otherwise it wouldn't be a centre tap.
You tap to enable an impedance transformation..
An RF amplifier using a dual gate Mosfet which has a hi-z input to the gate would require the incoming 50 or 75 Ohm to be tapped near the bottom of the coil.
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