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Let's consider a lock-in measurement of a resistive device. One may do a DC sweep with an added AC component to get a differential conductance measurement. The AC reference component for a typical low frequency (kHz or below) LI measurement is typically described by some voltage amplitude, frequency, and phase. However, for measurements which use higher frequency signals, say an RF signal to a qubit, the signal is often described by its power in dBm, frequency, and phase. Maybe my scenario and question is too vague or unclear, but can someone explain try to clear this up for me? And wouldn't power depend on the circuit details?

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Real circuits are almost never entirely resistive (i.e. have a real-valued impedance) at RF frequencies. Since real power is given by $P=VIcos\theta$, and $\theta$ is unknown, being a complex function of the circuit and wiring and frequency, it is easier to talk about signal power in dBm, where it's usually understood that we mean "real" power.

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