EECE312_Ch_04_Analog - EECE312 Electronics EECE312...

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ECE312 Electronics EECE312 Electronics Dr. Walid Kamali Fall 2007 hapter 4: Analog Electronics C apte a og ect o cs
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utline Outline requency Domain Representation of 1. Frequency Domain Representation of Signals 2. Electric Filters 3. Feedback Concepts perational Amplifiers 4. Operational Amplifiers 2
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ignals Signals ignals ontain information about our ± Signals contain information about our physical world, ex: air temperature, wind speed, voice, etc…. ± To process the signals (extract information), electronic systems are used ± A transducer is a device that converts a signal (ex: voice) into an electric signal, that is voltage or current. 3
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Signals are time-varying quantities rbitrary Signal eriodic Signal ± Arbitrary Signal ± Periodic Signal •Frequency f=1/T •The angular frequency ω = 2 π f rad/s. 4
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requency Spectrum Frequency Spectrum useful representation of a signal is in terms of ± A useful representation of a signal is in terms of its frequency spectrum. he Fourier series allows to express a given [ ] t j p e t V t v ω θ V Re ) cos( ) ( = + = ± The Fourier series allows to express a given periodic function of time as the sum of an infinite number of sinusoids whose frequencies integral multiples of the fundamental + + = i i n i t i V V t v ) cos( ) ( 0 5
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eriodic signals Periodic signals he square wave can be expressed as a series of ± The square wave can be expressed as a series of harmonically related components with ω o called the fundamental frequency. ...) 5 sin 5 1 3 sin 3 1 (sin 4 ) ( 0 0 0 + + + = t t t V t v ω π 6
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Time Domain/Frequency Domain Duality ± A signal can be represented by its time-domain presentation v ) or its frequency omain representation v a (t), or its frequency-domain representation V a ( ω ). 7
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oltage and Power Spectra Voltage and Power Spectra he time- verage power in a resistor does ± The time average power in a resistor does not depend on the frequency, or phase of the sinusoidal source. ... 2 ...... 2 2 2 2 2 3 2 2 2 1 2 0 + + + + + + = n V V V V V P ± The Effective value: ... 2 ...... 2 2 2 2 2 3 2 2 2 1 2 0 + + + + + + = n e V V V V V V 8
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pectrum of a series of narrow pulses Spectrum of a series of narrow pulses eriodic pulses of width nd period T have ± Periodic pulses of width τ and period T have Fourier components as follow: ± ( T n V V s n ) / sin( 2 πτ τ = hen and T it becomes a single T n T / ± When τ→ 0 and T , it becomes a single non periodic pulse 9
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on Periodic Signals Non Periodic Signals hen and T it becomes a single non ± When τ→ 0 and T , it becomes a single non periodic pulse ± The Fourier transform of an arbitrary (non- y( periodic) function yields a frequency spectrum that is a continuous function of frequency: 10
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he energy of the pulse The energy of the pulse he spectrum of the single pulse can be ± The spectrum of the single pulse can be written as follow: n( he energy may be compiled either in the Hz V E S V / 2 / ) 2 / sin( ) ( 0 ωτ ω= ± The energy may be compiled either in the time domain or the frequency domain where: second volt 2 4 0 2 2 0 = = τ s s V E R V R E 11
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andwidth and Analog Electronics
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This note was uploaded on 02/07/2011 for the course EECE 312 taught by Professor Walidkamali during the Fall '07 term at American University of Beirut.

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EECE312_Ch_04_Analog - EECE312 Electronics EECE312...

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