Scales and Decibel Scales

8/18/2019 Scales and Decibel Scales

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Notes for EE418x

Project: High Speed Systems Engineering

CISE-EAI

Last Modified: 9/06

Scales and decibel scalesPrepared for EE 418x

Fall 2006

The issues of scaling, in physical sciences is an issue that is more or less learned based on

experience. When the physical scale that one would like to use is not useful and the

graphs and presentation as too hard to be placed, in a page, the new scales come about.

The purpose of this short write up is to provide the students a brief summary of what are

the most important scales, and in particular for the microwave, RF, optical, and high

speed engineers the issues of dB, the form of this scales, the definition and what is calledthe manipulation of the scale is introduced.

A typical student of high speed engineering, are always “shocked” when the see for thefirst time that IL (dB) = Pin (in dBm) - Pout (in dBm). The first question that comes to

mind is how come two dBm units will add to a dB? Please note that dBm and dB are not

units and are scales. The following hopefully clarifies this issue and helps the studentknow other important notes regarding the scaling.

Different Scales

• Linear

•

Logarithmic scale• Decibel scale

Linear scaling:

This is what is what we are regularly used to. The most frequent scale for time and space

is the linear scale. The origin of this scale is zero, and the scale is defined by he smallest

block (mm, sec, days…..)

The most important disadvantage of linear scale is the fact that when trying to have data

with several orders of magnitude all in one scale we have a hard time fitting it to the

linear scale on the same “sheet”.

Logarithmic scaling:

The block of this scales increase or decrease by a factor of 10 (other type of scaling is

also possible but based 10 is the most common in EE). This scale makes numbers of highmagnitude manageable and allows the user to put several orders of magnitude on the

same axis. The 103 is 3 and 10

6 is 6….10

0.2 = 1.58 10

0.5 is 3 10

-2 = 0.01 and so on


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Notes for EE418x


CISE-EAI

Last Modified: 9/06

The most important items about this scaling is that negative numbers and zero cannot be

included in this scale.

Decibel Scaling:

This scaling has its origin in comparison of sound intensity. Originally the intensity was

based on a reference (reference to normal human audible power)

The most common use of this in Electrical Engineering is in also for comparison of

power.

dB = 10 log(P1/P2)

Some examplesP1= 20 W P2 = 5W

dB=10 log(20/5)= 10 log(4) = 10(0.62) = 6.02 dB or about 6 dB

So, all microwave engineers will get use to tables of scale the ratio to the dB

The following is the table for power ratio dB = 10 log(P1/P2)

Ratio dB Ratio dB

1 0 8 9

2 3 9 9.53 5 10 10

4 6 100 20

5 7 103 30

6 8 104 40

7 8.5 105 50

One can also make the voltage ration and current ration of volts and amperes ratio

dBvolt = 20 log(V1/V2) and dBcurr = 20 log(I1/I2)

as one can see these scale for the same ration result in twice the dB compared to the power scale.

Important note:

dB is not a physical quantity. dB is really result of a ration of two physical quantities. So

the dB is really a unit-less quantity. Just like radians, degrees…


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Notes for EE418x


CISE-EAI

Last Modified: 9/06

• Product of two rations is equivalent to the sum of their dBs

• Division of two rations is equivalent to difference of their values in dB

Converting dB values to “pure” numbers:

This is reversing the log also known as anti-logarithm

Steps for power inversion:

Step 1: Divide the given value by 10

Step 2: Use inverse log to get the dB/10 to obtain the number

Steps for Voltage and current inversion

Step 1: Divide the given value by 20Step 2: Use inverse log to get the dB/20 to obtain the number

dBm

This is a scale that a given power is compared to 1mWdBm=10 log ( P1/1mW)

5µW = -23 dBm8 nW = -51 dBm

20 pW = -77 dBm1mW = 0 dBm

3mW = 5 dBm

50 mW = 17 dBm

4kW = 66 dBm2.5 MW = 94 dBm

How can I combine dBm and dBs is it possible?

It is possible to combine the dB and dBm.

For example for the insertion loss we have

IL=Pin/Pout IL (dB) = Pin (in dBm) - Pout (in dBm)

Pout (in dBm) = Pin (in dBm) - IL (dB)

One can extend this to the idea of


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Notes for EE418x


CISE-EAI

Last Modified: 9/06

Gain where G= Pout/Pin or

Return loss RL= Pin/Pref

Important notes when manipulation dB and dBm

Operation Resulting Units Meaning Is it allowed?

dB + dB dB Product of two

numbers

Y

dB - dB dB Ratio of twonumbers

Y

dBm+dBm Not defined Multiplying two

powers

N

dBm-dBm dB Ration of two

powers

Y

dBm+dB dBm Power amplification Y

dBm-dB dBm Power attenuation Y

Reference for the above material: Microwaves Made Simple: Principles and Applications W. Stephen Cheung andFrederic H. Levien, Artech House, Inc. 1985 Unfortunately this book is out of pring

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Scales and Decibel Scales