MEASUREMENTS IN FREQUENCY DOMAIN: GENERAL ASPECTS.

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Presentation transcript:

MEASUREMENTS IN FREQUENCY DOMAIN: GENERAL ASPECTS

TOPICS Going beyond time Foundations of Fourier Theory Importance and usage of Decibel

GOING BEYOND TIME (frequency domain)

Any real signal can be obtained through the sum of sinusoidal components. Going beyond time…...

Mathematical model of a sinusoidal component c(t) : c(t) = A cos(2πf t + φ) A : amplitude f : frequency φ : phase (constant)

Tridimensional representation: time, frequency, amplitude

Why frequency domain measurements ? Time: problem Frequency: solution

Some fields of application Telecommunications, Telematics Analog and Power Electronics Electromagnetics Electrical Systems and Machines Bioengineering

Measurement examples Modulation Distorsion Noise

FOUNDATIONS OF FOURIER THEORY Jean Baptiste Joseph Fourier, , French mathematician and physicist.

Fourier Series Periodic and time-continuous signal Expansion in series of sinusoidal functions

Fourier Series c n = spectrum of s(t) amplitude = │c n │; phase = arg(c n ) period

Fourier Transform Aperiodic and time-continuous signal Analysis S(f) = spectrum of s(t) Synthesis

Spectrum examples (periodic signals) Time T Sinusoidal wave Frequency f = 1/T T Time Square wave Frequency 1/T3/T5/T

Spectrum examples (aperiodic signals) Frequency Time Transient signal Frequency Time Ideal impulse

IMPORTANCE AND USAGE OF DECIBEL

Decibel definition Ratio between two power values: P 2 is expressed in relative terms with respect to P 1 Swapping P 2 and P 1 changes the sign of A (dB)

Role of resistances If the powers refer to a couple of voltages applied to two resistances: V 2 is the rms voltage applied to R 2 V 1 is the rms voltage applied to R 1

Role of resistances If R 2 = R 1

Fundamentals rules  Inversion  Addition  Subtraction

Absolute values in Decibel : dBm Choosing 1mW as reference power value P (mW) is expressed in milliwatt P (dBm) is independent of R

V REF is the rms voltage producing 1mW power: Absolute values in Decibel : dBm

For R = 50 Ω, V REF = For R = 75 Ω, V REF =

Absolute values in Decibel : dBV Choosing 1V rms as reference voltage value V (dBV) is indipendent of R

dBm/dBV conversion R = 50 Ω R = 75 Ω

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