- Negative dB

What happens if P₂ > P₁ in the formula

Let's try an example with P₂ = 1 W and P₂ = 20 W.

10·log₁₀(P₁ / P₂)
= 10·log₁₀(1 W / 20 W)
= 10·log₁₀(0.05)
= 10·log₁₀(5·10^-2)
= 10·log₁₀(0.69897-2)
= 10·(-1.30103)
= -13 dB

In general, when the denominator is larger than the numerator, we get a negative decibel value. It's worth trying a few problems involving negative dB.

1. P₁ = 1 W and P₂ = 100 W. How many decibels is P₁ relative to P₂?
2. P₁ = 15 W and P₂ = 30 W. How many decibels is P₁ relative to P₂?
3. P₁ = 1 W and P₂ = 100 mW. How many decibels is P₁ relative to P₂?
4. P₁ = 4.3 mW and P₂ = 9.5 mW. How many decibels is P₁ relative to P₂?
5. For an attenuator, P_out = 15 mW and P_in = 1 W. What is the gain of the attenuator?
6. Two parts in a radar system have a gain of x and -x, respectively. What can you say about the relationship between the power ratios of the two parts?