Handbook for Sound Engineers

Fundamentals and Units of Measurement 1657

(48-41)

Example: The dBm for a 32 : load is

This can also be determined by using the graph in
Fig. 48-5.
To find the logarithm of a number to some other
base than the base 10 and 2.718, use

(48-42)

A number is equal to a base raised to its logarithm,

(48-43)

therefore,

(48-44)

The natural log is a number divided by the natural

log of the base equals the logarithm.

Example: Find the logarithm of the number 2 to the

base 10:

In information theory work, logarithms to the base 2

are quite commonly employed. To find the log 2 of 26

To prove this, raise 2 to the 4.70 power

48.4 Sound Pressure Level

The sound pressure level (SPL) is related to acoustic

pressure as seen in Fig. 48-6.

0.4 0.6026 1.660 0.20 0.4 0.3388 2.951 0.70 0.4 0.1905 5.248 0.20 0.4 0.1072 9.333 0.70

0.5 0. 5957 1. 679 0.25 0.5 0.3350 2.985 0.75 0.5 0.1884 5.309 0.25 0.5 0.1059 9.441 0.75

0.6 0.5888 1.698 0.30 0.6 0.3311 3.020 0.80 0.6 0.1862 5.370 0.30 0.6 0.1047 9.550 0.80

0.7 0. 5821 1.718 0.35 0.7 0.3273 3.055 0.85 0.7 0.1841 5.433 0.35 0.7 0.1035 9.661 0.85

0.8 0. 5754 1.738 0.40 0.8 0.3236 3.090 0.90 0.8 0.1820 5.495 0.40 0.8 0.1023 9.772 0.90

0.9 0.5689 1.758 0.45 0.9 0.3199 3.126 0.95 0.9 0.1799 5.559 0.45 0.9 0.1012 9.886 0.95

dB

Voltage

Loss Gain dB

Power

dB

Voltage

Loss Gain dB

Power

20.0 0.1000 10.00 10.00 60.0 0.001 1,000 30.00

Use the same num-

ber as 0–20 dB but

shift decimal point

one step to the left.

Thus since

10 dB = 0.3162

30 dB = 0.03162

Use the same num-

ber as 0–20 dB but

shift decimal point

one step to the

right. Thus since

10 dB = 3.162

30 dB = 31.62

This column

repeats every

10 dB instead

of 20 dB

Use the same num-

bers as 0–20 dB but

shift point three

steps to the left.

Thus since

10 dB = 0.3162

70 dB = 0.0003162

Use the same num-

ber as 0–20 dB col-

umn but shift point

three steps to the

right. Thus since

10 dB = 3.162

70 dB = 3162

This column

repeats every

10 dB instead

of 20 dB

40.0 0.01 100 20 80 0.0001 10,000 40.00

Use the same num-

ber as 0–20 dB but

shift point two steps

to the left. Thus

since

10 dB = 0 3162

50 dB = 0.003162

Use the same num-

ber as 0–20 dB but

shift point two steps

to the right. Thus

since

10 dB = 3162

50 dB = 316.2

This column

repeats every

10 dB instead

of 20 dB

Use the same num-

bers as 0–20 dB but

shift point four steps

to the left. Thus

since

10 dB = 0.3162

90 dB = 0.00003162

Use the same num-

ber as 0–20 dB but

shift point four

steps to the right.

Thus since

10 dB = 3.162

90 dB = 31620

This column

repeats every

10 dB instead

of 20 dB

100 0.00001 100,000 50.00

Table 48-3. Relationships between Decibel, Current, Voltage, and Power Ratios (Continued)

dB dB dB dB dB dB dB dB

Voltage Loss Gain PowerVoltage Loss Gain PowerVoltage Loss Gain PowerVoltage Loss Gain Power

dBm at new Z dBm 600 : 10 600 :

Znew

= + log---------------

dBm 32 4 dBm 10 600 :

32 :

+= log---------------

=16.75 dBm

nb

L

=

ln n =ln bL

ln n

ln b

-------------=L

ln 2

ln 10

----------- 0.693147

2.302585

=----------------------

=0.301030

ln 26

ln 2

----------- =4. 7 0

2

4.70

26=