C.3 VOLTAGE RATIOS IN DECIBELS

Although the decibel is fundamentally defined in terms of power, it can also be applied to voltage or current ratios when the impedance of the circuit is constant. Power in resistive circuits is given by:

p o w e r r a t i o = 10 \log_{10} (\frac{P_{2}}{P_{1}}) a n d P_{2} = \frac{V_{2}}{R} a n d P_{1} = \frac{V_{2}}{R}

(C.9)

so the ratio of powers is:

p o w e r r a t i o = 10 \log_{10} (\frac{V_{2}^{2}}{V_{1}^{2}}) = 10 \log_{10} {(\frac{V_{2}}{V_{1}})}^{2} = 20 \log_{10} (\frac{V_{2}}{V_{1}})

(C.10)

The use of 20 rather than 10 in Equation (C.10) arises from the square relationship between voltage and power. The same relationship applies for current ratios when the circuit impedance is constant.

This convention allows engineers to describe voltage gains, signal amplitudes, or transmission losses directly in decibels, provided the impedance is unchanged—an assumption valid in most RF and baseband signal chains.