Non-Foster Networks
Not all networks obey Foster's theorem, those that do may be referred to as Foster networks and those that do not are non-Foster networks. In particular, an active circuit, containing an amplifier, may well not be a Foster network. For example, it is possible to create negative capacitors and inductors with negative impedance converter circuits. These circuits will have an immittance function with a phase of ±π/2 like a positive reactance but a frequency with a negative slope.
Read more about this topic: Foster's Reactance Theorem
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