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ELE-6106 Basic RF MeasurementsTiiti Kellomäki 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:ratio(dB) = 10 log (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?).

Matlab: log10(a1/a2)

Decibel Math• Addition of dB’s corresponds to multiplication:

log(a) + log(b) = log(ab).• Similarly, subtraction means division.• Don’t multiply dB values:

log(a)log(b) = log(alog(b)) = log(blog(a))?• Don’t 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 ×½×10 = ×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

– 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

mW 1log10(dBm) PP

Examples

• Power +13 dBm means ”13 dB more than one milliwatt”– So 13 dBm = 10 dBm + 3 dB = 10 mW · 2 = 20 mW.

• Amplifier gain 7 dB, input power +13 dBm– gives output 20 dBm or 100 mW.

• 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.

Intermodulation Measurement• 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?

SALL

L

• 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.

pwr out

pwr in

frequency

powe

r

2

ELE-6106 Basic RF MeasurementsTiiti Kellomäki 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 Lauri’s age.

– Siiri is –5 dBa – 3 dB = –8 dBa.– Not like this!: –5 dBa / 2 = –2,5 dBa = 10 years!

• Define temperature in dBT0: temp(dBT0) = 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.

Worth Pondering

• Why do you have ”20 log” in the ”voltagedecibel” instead of ”10 log”? Is it a differentdecibel?

• When the area of a rectangle increases10000-fold, what happens to the side length?

• When voltage goes up by 20 dB, how muchdoes the power change?

”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?

P = U2/Z0,means

U = (PZ0)

trans-formercoaxial cable twin lead

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 ) ?

More Material

• Wikipedia: decibel– more rules of thumb

• “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

Next Lecture

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

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