Decibels are the most common way to discuss RF voltage, current and power.
\(dB = 10 \log{\frac{P_1}{P_2}}\)
Also, looking at voltage or current, we have:
\(P = V^2/R = I^2/R\)
Therefore, we get:
\(dB = 20 \log{\frac{V_1}{V_2}}\)
Or:
\(dB = 20 \log{\frac{I_1}{I_{ref}}}\)
When discussing dB it is always an RMS value for voltage or current, since \(P = V^2/R = I^2/R\) assumes RMS values.
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Power
The typical reference power is 1 mW, which gives dBm.
\(dB = 10 \log{\frac{P_1}{1000 mW}}\)
There is also dBW which uses 1 W as the reference.
$$-20 dBm = 0.01 mW$$
$$-10 dBm = 0.1 mW$$
$$0 dBm = 1 mW$$
$$30 dBm = 1 W = 0 dBW$$
Voltage and Current
Typical reference levels are microvolts or microamps in addition to volts and amps.
$$0 dB\mu V = 1 \mu V_{rms}$$
$$60 dB\mu V = 1 mV_{rms}$$
$$120 dB\mu V = 1 V = 0 dBV_{rms}$$
Manipulating Decibels
Decibel arithmetic follows the laws of logarithms, the key one being:
\(\log{A \times B} = \log{A} + \log{B}\)
This means that adding 20 dB to a voltage is equivalent to multiplying by 10, while adding the same to a power is multiplying by 100.
Common values:
$$20 dB = 10$$
$$10 dB = \sqrt{10}=3.16$$
$$6 dB = 2$$
$$3 dB = \sqrt{2} = 0.71$$
$$0 dB = 1$$
$$-20 dB = 0.1$$
To get numbers inbetween you can use the logarithmic rules:
$$26 dB = 20 dB + 6 dB = 20$$
$$4 dB = 10 dB – 6 dB = 3.16/2 = 1.58$$