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    The Decibel Decibel Math

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    ravindarsingh
    This document provides an overview of decibel measurements in radio frequency applications. It defines the decibel as a logarithmic ratio of power, intensity, or voltage levels. Key points covered include: - Decibels describe a ratio and are calculated using 10log(A1/A2) - Addition and subtraction of dB values corresponds to multiplication and division of linear values - Common dB units of measure include dBm, dBW, dBuV, dBi - Negative dB values indicate attenuation while positive values indicate gain - Examples are provided for calculating output power levels given input levels and device gain specifications.

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    Attribution Non-Commercial (BY-NC)
    Download as PDF, TXT or read online from Scribd

    The Decibel Decibel Math

    Uploaded by

    ravindarsingh
    88 views2 pages
    This document provides an overview of decibel measurements in radio frequency applications. It defines the decibel as a logarithmic ratio of power, intensity, or voltage levels. Key points covered include: - Decibels describe a ratio and are calculated using 10log(A1/A2) - Addition and subtraction of dB values corresponds to multiplication and division of linear values - Common dB units of measure include dBm, dBW, dBuV, dBi - Negative dB values indicate attenuation while positive values indicate gain - Examples are provided for calculating output power levels given input levels and device gain specifications.

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    decible

    Original Title

    Decibel

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    This document provides an overview of decibel measurements in radio frequency applications. It defines the decibel as a logarithmic ratio of power, intensity, or voltage levels. Key points covered include: - Decibels describe a ratio and are calculated using 10log(A1/A2) - Addition and subtraction of dB values corresponds to multiplication and division of linear values - Common dB units of measure include dBm, dBW, dBuV, dBi - Negative dB values indicate attenuation while positive values indicate gain - Examples are provided for calculating output power levels given input levels and device gain specifications.

    Copyright:

    Attribution Non-Commercial (BY-NC)
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    88 views2 pages

    The Decibel Decibel Math

    Uploaded by

    ravindarsingh
    This document provides an overview of decibel measurements in radio frequency applications. It defines the decibel as a logarithmic ratio of power, intensity, or voltage levels. Key points covered include: - Decibels describe a ratio and are calculated using 10log(A1/A2) - Addition and subtraction of dB values corresponds to multiplication and division of linear values - Common dB units of measure include dBm, dBW, dBuV, dBi - Negative dB values indicate attenuation while positive values indicate gain - Examples are provided for calculating output power levels given input levels and device gain specifications.

    Copyright:

    Attribution Non-Commercial (BY-NC)
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 2

    ELE-6106 Basic RF Measurements Tiiti Kellomki 2012

    This material is licensed under a creative commons licence. Use for non-commercial and educational purposes is allowed.

    The Decibel
    Decibel value describes a ratio: Matlab: ratio(dB) = 10 log (A1 / A2). log10(a1/a2) of powers, sound intensities, etc. Gain is 3 dB means that output power is 3 dB more than input. Power is 3 dB makes no sense. Power is 3 dB more than a watt makes sense (what does it mean?).

    Decibel Math
    Addition of dBs corresponds to multiplication: log(a) + log(b) = log(ab). Similarly, subtraction means division. Dont multiply dB values: log(a)log(b) = log(alog(b)) = log(blog(a))? Dont divide dB values:
    one-half of 10 dB is not 5 dB. but what?

    If in doubt, you can always convert to linear


    but then you lose the benefit of dBs!

    Rules of Thumb
    Negative dBs are attenuation, positive are gain. 0 dB means multiplication by one. +10 dB means 10. +3 dB means 2. +7 dB = +10 dB 3 dB means 10 = 5. You will learn the dB values that you need. Train your dB math using the course webpage!

    dB Units of Measure
    Always a reference, e.g.: power is 10 dB above 1 W. Common abbreviations, or units of measure:
    dBm: power above 1 mW, dBW: above 1 W

    P 1 mW dBuV compares to 1 microvolt (check characteristic impedance!), dBuV/m is for field strength dBc is dB above carrier, dBc/Hz for (noise) power density dBi is antenna gain dB more than an isotropic antenna, dBd compares to a half-wave dipole P (dBm) 10 log

    Examples
    Power +13 dBm means 13 dB more than one milliwatt
    So 13 dBm = 10 dBm + 3 dB = 10 mW 2 = 20 mW.

    Intermodulation Measurement
    DUT: gain 14 dB, 1-dB compression point 27 dBm (output power), max input power 25 dBm. Spectrum analyser max input: 30 dBm. Wilkinson splitter with insertion loss: 1 dB. Variable attenuator: max 2 Watts. Fixed attenuators: 6 dB / 1 W.
    L L
    frequency

    Amplifier gain 7 dB, input power +13 dBm


    gives output 20 dBm or 100 mW.

    power

    Sum can include one dB unit of measure (e.g. dBm), but only one. Why? Result is given in the dB unit of measure if one was present in the expression.

    What generator output powers will you use? What will be the input power to SA? Can the DUT handle the power? Can the attenuators handle the power?
    pwr out

    SA

    pwr in

    ELE-6106 Basic RF Measurements Tiiti Kellomki 2012

    This material is licensed under a creative commons licence. Use for non-commercial and educational purposes is allowed.

    Crazy Examples
    Define dB above adulthood limit: age(dBa) = 10 log( age / 18 years ). Lauri is six or 5 dBt. Siiri is half of Lauris age.
    Siiri is 5 dBa 3 dB = 8 dBa. Not like this!: 5 dBa / 2 = 2,5 dBa = 10 years!

    Worth Pondering
    Why do you have 20 log in the voltage decibel instead of 10 log? Is it a different decibel? When the area of a rectangle increases 10000-fold, what happens to the side length? When voltage goes up by 20 dB, how much does the power change?

    Define temperature in dBT 0: temp(dBT 0) = 10 log ( temp (K) / 290 K ).


    Sauna is 80 degrees or +0,85 dBT0. Freezing winter 0,8 dBT0 eli 30 C. Logarithmic scale is not practical, because the dynamic range is quite small.

    A Passive Amplifier?
    Take a 50-ohm coax. 1 watt is propagating along it, giving voltage wave of 7 V rms. Transform the impedance to 300-ohm twin lead using a lossless transformer. The same 1 watt continues, giving now a voltage wave of 17 V rms. What is the gain of the transformer?
    transformer P = U2/Z0, means U = (PZ0)

    Other Things to learn


    Return loss, reflection loss
    and how to calculate these in dB

    VSWR and how to relate it with return loss Why can you use RL = 20 log ( |S11| ) (with a nice 20 and no square), but have Lrefl = 10 log( 1 |S11|2 ) ?

    coaxial cable

    twin lead

    More Material
    Wikipedia: decibel
    more rules of thumb

    Next Lecture
    Tools in all RF tinkering:
    Cables, especially coaxial cables Connectors, different types, how to handle Adapters Attenuators Splitters, couplers, whatnot

    dB or not dB?
    Everything you ever wanted to know about decibels but were afraid to ask... Rohde&Schwarz application note 1MA98 link on course webpage

    Check out:
    Microwaves101.com page on connectors Seminar slides by Agilent (on course webpage, thx!)

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