DECIBELS and POWER
RATIOS |

The ratio between any two amounts of electrical power is usually expressed in units on a logarithmic scale. The decibel is a logarithmic unit for expressing a power ratio.

Where : PR = power ratio in dB

PR_{(dB)} = 10 log P_{1} = power in (small)

P_{2} = power out (large)

When the output of a circuit is larger than the input, the device is an AMPLIFIER and there is a GAIN. When the output of a circuit is less than the input, the device is an ATTENUATOR and there is a LOSS. In the last example , use the same formula as above and place the larger power over the smaller power, and put a minus sign in front of the PR to indicate a power loss or attenuation.

Basically, the decibel is a measure of the ratio of two powers. Since voltage and current are related to power by impedance, the decibel can be used to express voltage and current ratios, provided the input and output impedance’s are taken in to account.

**Equal Impedance’s :** dB = 20 log dB = 20 log

Where: E_{1} = input voltage I_{1} = input current

E_{2} = output voltage I_{2} = output current

**Unequal Impedance’s:** dB = 20 log dB = 20 log

Where: R_{1} = impedance of the input in ohms R_{2 }= impedance of the
output in ohms

E_{1 }= voltage of the input in volts E_{2 }= voltage of
the output in volts

I_{1 }= current of the input in amperes I_{2 }= current of the output
in amperes

dB, Power, Voltage, Current Ratio
Relationships |

Decrease(-) Voltage and Current Ratio |
Decrease (-) Power Ratio |
Number of dB’s |
Increase(+) Voltage and Current Ratio |
Increase (+) Power Ratio |

1.0000 |
1.0000 |
0 |
1.0000 |
1.0000 |

.9886 |
.9772 |
.1 |
1.0120 |
1.0230 |

.9772 |
.9550 |
.2 |
1.0230 |
1.0470 |

.9661 |
.9330 |
.3 |
1.0350 |
1.0720 |

.9550 |
.9120 |
.4 |
1.0470 |
1.0960 |

.9441 |
.8913 |
.5 |
1.0590 |
1.2220 |

.9333 |
.8710 |
.6 |
1.0720 |
1.1480 |

.9226 |
.8511 |
.7 |
1.0840 |
1.1750 |

.9120 |
.8318 |
.8 |
1.0960 |
1.2020 |

.9016 |
.8128 |
.9 |
1.1090 |
1.2300 |

.8913 |
.7943 |
1 |
1.1220 |
1.2590 |

.7943 |
.6310 |
2 |
1.2590 |
1.5850 |

.7079 |
.5012 |
3 |
1.4130 |
1.9950 |

.6310 |
.3981 |
4 |
1.5850 |
2.5120 |

.5623 |
.3162 |
5 |
1.7780 |
3.1620 |

.5012 |
.2512 |
6 |
1.9950 |
3.9810 |

.4467 |
.1995 |
7 |
2.2390 |
5.0120 |

.3981 |
.1585 |
8 |
2.5120 |
6.3100 |

.3548 |
.1259 |
9 |
2.8180 |
7.9430 |

.3162 |
.1000 |
10 |
3.1620 |
10.0000 |

.1000 |
.01000 |
20 |
10.0000 |
100.000 |

.03162 |
.0010 |
30 |
31.6200 |
1000.00 |

.0100 |
.0001 |
40 |
100.000 |
10000.0 |

.00316 |
.00001 |
50 |
316.20 |
1 x 10 |

.0010 |
1 x 10 |
60 |
1000.0 |
1 x 10 |

.000316 |
1 x 10 |
70 |
3162.0 |
1 x 10 |

dBm

The decibel does not represent actual power, but only a measure of power ratios. It is desirable to have a logarithmic expression that represents actual power. The dBm is such an expression and it represents power levels above and below one milli watt.

The dBm indicates an arbitrary power level with a base of one milli watt and is found by taking 10 times the log of the ratio of actual power to the reference power of one mill watt.

P_{(dBm)} = 10 log

where : P_{(dBm)} = power in dBm

P = actual power

1mw = reference power

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