4 Nepers, Bels and Decibels

Question 1

How are Bels, Decibels and nepers defined?

Answer 1

defined in terms of the ratio of two powers

W₁ = V ² ₁ /R₁ = I ² ₁R₁

and W₂ = V ₂ ² /R₂ = I ₂ ²R₂

Question 2

Equation for ratio is Bels?

Answer 2

Question 3

Equation for ratio in dB?

Answer 3

Question 4

Equation for ratio in Nepers?

Answer 4

Question 5

Neper relationship?

Answer 5

A signal experiences an attenuation of N nepers when its magnitude changes by a factor exp(−N) between two measures.

From the above two ratios it can be determined that 1 neper = 20 log₁₀(e) ≈ 8.686 dB.

Question 6

Decibel ratio when the resistances are equal?

Answer 6

If the resistances are equal, R1 = R2, the ratio in decibels is

Question 7

The equation for decibel watt? dBW

Answer 7

Question 8

Equation for dBm?

Answer 8

Question 9

Relationship between dBm and dBW?

Answer 9

dBm = dBW + 30

Question 10

Equation for dBV?

Answer 10

Question 11

Equation for dBuV (dB-microvolts)

Answer 11

Question 12

Express power in a signal with respect to W_C, the power in the carrier:

Answer 12

Question 13

dBi

Answer 13

dBi Use with antennas to express power from an antenna with respect to Wi , the power from an isotropic antenna (radiates equally at all angles):

Question 14

What is dBd (dB-dipole)?

Answer 14

Use with antennas to express power from an antenna with respect to Wd, the power from a dipole antenna:

Question 15

What is dBsm (dB-square metres)?

Answer 15

Use with areas, such as the reflecting area of an object A:

Question 16

Why are decibels useful?

Answer 16

The decibel scale is useful when a small value is to be compared with a large one.

For example comparing a 0.5 Watt Mobile phone maximum transmit signal level with the minimum signal that can be received, say 5 × 10−14 Watts. On linear scales the received signal looks like zero. On decibel scales the transmit power is -3 dBW and the received signal is -133 dBW. In between the transmitter and receiver it is easy to understand that that the ratio of transmit to received signal is simply 130 dB

Question 17

Gains in cascade?

Answer 17

A very common way of connecting electrical/electronic items together is the cascade connection, where the gains or transmission factor of the elements multiply together. When using decibels the decibel gains of the elements simply add together. For example if there are three devices with linear power gains g1, g2 and g3, their gains in decibels are G₁ = 10 log10(g1), G₂ = 10 log10(g2) and G₃ = 10 log10(g3). The linear gain is:

The linear gain:

gtot = g1 × g2 × g3

Gain in dB:

Gtot = G1 + G2 + G3