The decibel (dB) is widely used in electronics to describe ratios. Many people find this logarithmic unit difficult to understand, but in fact, it was designed for mental calculation and should not be perceived as overly complicated.

dB is suitable for situations where the dynamic range is large but the requirement for significant digits is not high. For example, whether the exact value of ripple rejection ratio is ten thousand times (80 dB) or fifteen thousand times (83 dB) is not particularly important; it is sufficient to know that it is not one thousand times (60 dB).

One common point of confusion is why the decibel value for power (energy) ratio is calculated as \(10 \log(\mathrm{ratio})\), while for voltage ratio it becomes \(20 \log(\mathrm{ratio})\)? This is because \(P=U²/R\), i.e., a voltage ratio of \(10\) times is a power ratio of \(100\) times. Keeping this in mind will prevent confusion.

For mental calculation, it is essential to know the relationships between common dB values and ratios. At a minimum, remember that 3 dB is \(2\) times, and 10 dB is \(10\) times:

Additionally, understand that adding and subtracting dB is equivalent to multiplying and dividing ratios, and negative dB values correspond to fractions. By breaking down dB values into sums of numbers in the table and using interpolation, mental calculation becomes possible.

For example:

• 27 dB = (10 + 10 + 7) dB → \(10 \times 10 \times 5=500\) times
  • When calculating voltage ratio：
    27 dB ≈ (14 + 14 ) dB → \( 5 \times 5 = 25\) times (the exact value is 22.4 times)
• -34 dB = -(10 + 10 + 10 + 3 + 1) dB → \(1/2500\)
  • Voltage ratio:-34 dB =-(20 + 14) dB → \(1/50\)