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The Decibel Explained and Helpful Tips

Op Amp circuit to show voltage gain

We usually see the unit dB when we work with electronic circuits, specifically amplifier circuits. Decibel or dB came from the word bel, in honor of Alexander Graham Bell, the inventor of the telephone. The bel is an inconveniently large quantity to use so the decibel was deviced. It is one-tenth of a bel and is a more practical unit. The Decibel is a relative unit of measurement to describe power or voltage gain, i.e. the logarithmic ratio of an amplifier’s output power or voltage to the corresponding input values. This is shown by the equations below:


Power Gain in dB = 10log (Pout/ Pin)


Voltage Gain in dB = 20log (Vout/ Vin)   if Rout = Rin



The following is a practical circuit we can use as an example to derive voltage gain.

 




If Vin = 0.2VRMS, Vout will be equal to -2.0 VRMS.  The voltage gain will be derived as follows:


Voltage Gain in dB = 20log (2.0V/0.2V) = 20 dB


Aside from describing power or voltage ratios, the decibel can also be used to represent an absolute value that is referenced to a standard value.  The most common used in electronics and communications is dBm, which is a value referenced to 1.0 mW, i.e. 0dBm = 1 mW.  Another common value used is dBW, which is referenced to 1 W meaning 0 dBW = 1 W.  See the list below to check other popular reference values.

dBm – referenced to 1 milliwatt (0 dBm = 1 mW) typically used in measuring audio levels (600 ohms load), video and CATV levels (75 ohms) and in RF systems (50 ohms).

dBu – referenced to 0.775VRMS/ 600 ohms typically used in audio applications.  This is the usual unit of measurement found in audio VU meters.

dBW – referenced to 1 Watt (0 dBW = 1 W) typically used in high power audio amplifiers and RF power amplifiers specifications.

dBuV/m – electric field strength relative to 1 microvolt per meter typically used in RF communications applications.

dBV – referenced to 1 VRMS (0 dbV = 1 VRMS) typically used in electronics in measuring voltage levels.

dBi – this refers to the gain of an antenna referenced to the gain of an isotropic antenna (with omni-directional pattern).

dB/Hz -  this is a measure of relative noise power in a 1-Hz bandwidth.

dBr — refers to the relative difference of a measured value from another set value.  

dBFS  - refers to the amplitude of a digital audio signal compared with the maximum which a device can handle before clipping occur (0 dBFS).

dB SPL - this is a measure of sound pressure level referenced to the threshold of hearing, which is 20 micropascals.  This threshold is defined as the faintest possible sound a person could hear in a quiet room assuming that his hearing is normal and is assigned the value of 0 dB.  It should be noted that the perceptible change in sound level is 3 dB or twice the increase in sound source power.  See the list below for estimated dB SPL levels at different conditions:


dB SPL


Threshold of hearing                         0

Soft whisper                                    30

Average conversation                      60

Busy street                                      80

Rock concert (threshold of pain)    120

Jet engine                                      150


Here are some helpful tips when dealing with the Decibel:


To find the total gain of a series of amplifiers, the gains (expressed in dB) are simply added to each other.  For example, if gain of Amp#1 is +2dB and gain of cascaded Amp#2 is +3dB, the total gain would be equal to +5dB.


Doubling the power (input/ output impedance levels the same) will result to a +3dB power gain.  Increasing the power level by 10 times is equal to a +10dB power gain.  For other power ratios, see the list below:


Power Ratio           Decibel

0.1                         -10

0.25                         -6

0.5                           -3

1                               0

2                             +3

4                             +6

10                         +10

100                       +20

1000                     +30


The following list is also a helpful reference for absolute dB power units:


Power        dBuV        dBm        dBW


1 mW        +30          0        -30

2 mW        +33        +3        -27

10 mW      +40        +10      -20

100 mW    +50        +20      -10

1 W           +60        +30          0

2 W           +63        +33        +3

4 W           +66        +36        +6

10 W        +70        +40        +10

100 W      +80        +50        +20

1 kW        +90        +60        +30

1 MW     +120        +90        +60

 

Insertion loss in RF systems

Thanks for your comments. Yes, you’re right, insertion loss is an important measurement in communication systems. In RF systems, this signal loss is introduced by RF connectors, transmission lines, filters and other passive devices. When doing a link budget calculation, these values are negative so they are simply subtracted from the signal gains introduced by the active devices such as RF amplifiers.

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