Measuring Power with A Logarithmic Amplifier

One of our young engineers asked me why all of us old-timers like to use logarithmic amplifiers when we need to measure input signal power. The answer is simple -- power expressed in dB is a linear function of the logarithm of the voltage. I must admit that the way electrical engineers use dB for everything sometimes makes things seem a bit confusing. In the cable TV market, we assume 75 Ω impedances and use dBmV (decibel millivolt) and dBmW (decibel milliWatt) for units. Anyway, here is a quick derivation and example.

Figure 1: Derivation of dB Relationship between Power an Voltage.

Figure 1: Derivation of dB Relationship between Power and Voltage.

 
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