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ECE 3336 Introduction to Circuits & Electronics Lecture Set #10 Signal Analysis & Processing – Frequency Response & Filters Dr. Han Le ECE Dept. Han Q Le© Outline • Review • Signal analysis – Power spectral density • Frequency response of a system (circuit) – Transfer function – Bode plot • Filters – Analog – Digital Han Q Le© Concept Review: Signal Processing • All electronics around us involve signal processing. • Signal represents information. That information can be something we generate (e.g. texts, sounds, music, images) or from sensors. (discussion: examples of sensors) • Electronics deal with signals: signal processing is to transform the signal and extract the desired information. Han Q Le© Concept Review: Signal Processing (cont.) • Signal processing is a general concept, not a single specific thing. It includes: – signal synthesis or signal acquisition – signal conditioning (transforming): shaping, filtering, amplifying – signal transmitting – signal receiving and analysis: transforming the signal, converting into information • Signal processing is mathematical operation; electronics are simply tools. • Computation is high-level signal processing: dealing directly with information rather than signal. Han Q Le© Applications of mathematical techniques Signal and AC circuit problems Harmonic function Fourier transform • RLC or any time-varying linear circuits. Applicable to linear portion of circuits that include nonlinear elements • Signal processing Complex number &analysis Phasors • signal analysis (spectral decomposition) • filtering, conditioning (inc amplification) • synthesizing Note: The main lecture material is in the Mathematica file – this is only for concept summary Han Q Le© Homework (to be seen in HW 8) Choose an electronic system around you (e. g. a TV, DVD player, phone,…); show a functional block diagram and describe the signal processing sequence (end to end). Han Q Le© Example Antenna Inductor Variable Capacitor Diode (1N34A) High-Impedance Earphone Ground Han Q Le© Schematic Carrier wave (sound) signal Antenna 50 40 30 20 1.5 1 10 0.5 5 -0. -1 5 -1. Ante nna Inductor Variable Capacitor Diode (1N34A) Resonance circuit High-Impedance Earphone 1.5 Grou nd 1 0.5 -0.5 -1 -1.5 Han Q Le© Soundwave 10 20 30 40 50 Electrical signal (voltage or current) Link to Mathematica file: AM FM Han Q Le© Outline • Review • Signal analysis – Power spectral density • Frequency response of a system (circuit) – Transfer function – Bode plot • Filters – Analog – Digital Han Q Le© Signal Fourier (or harmonic) Analysis • Treat each time-finite signal as if it is composed of many harmonics, using Fourier series xt a0 n 1 an Cos n m Xm xt t m n 1 bn Sin n t t In complex (or Euler) representation, Fourier series coefficients Xm are phasor components, Xm Han Q Le© Xm m Signal Fourier (or harmonic) Analysis (cont) • If the signal is real (all cases involving real physical quantity), then: X Xm Xm m m Xm Xm Xm Hence, we need to keep only positive frequencies A signal can be represented by a plot of | Xm | vs. m frequency, or usually | Xm |2 if x(t) is voltage or current, known as the signal magnitude spectrum, or its power spectral density. Equally important is the phase spectrum: plot of fm vs. frequency Han Q Le© Do not be confused between the word “spectrum” in the general English sense vs. specific definition of “spectrum” in power spectral density, or phase spectrum. Han Q Le© The Electromagnetic Spectrum UV & solar blind Visible Han Q Le© Example of Spectra 0.89 s 11 025 Hz 3 60 2 80 1 100 0 1 120 140 0 Han Q Le© 2 3 1000 2000 3000 4000 5000 0 1000 2000 3000 4000 5000 Example of Spectra 0.79 s 11 025 Hz 3 60 2 80 1 100 0 1 120 2 3 0 Han Q Le© 1000 2000 3000 4000 5000 0 1000 2000 3000 4000 5000 Outline • Review • Signal analysis – Power spectral density • Frequency response of a circuit – Transfer function – Bode plot • Filters – Analog – Digital Han Q Le© Example R t input vin[t] C i(t) output vout[t] Frequency Response 1 t 1 1 H 1 or, Frequency Transfer Function C t input vin[t] i(t) t R output vout[t] 1 H Han Q Le© 1 Frequency Transfer Function (Frequency Response Function) For many linear RLC circuits, the frequency response function usually has the form: H Han Q Le© P Q a0 a1 b0 b1 a2 2 b2 2 am m bn n Example: Test 1 H Han Q Le© 1 C2 L2 2 R1 L1 C1 R1 C2 L2 R3 2 R3 1 C1 R1 C2 R1 L1 L2 C1 R1 Bode Plot for Vout in Test 1 3 2 0.1 Phase Shift rad AmplitudeResponse 1 0.01 0.001 1 0 1 2 10 4 1000 Han Q Le© 104 105 Frequency Hz 106 3 1000 104 105 Frequency Hz 106 Applications of Frequency Transfer Function • Any signal can be decomposed as a sum of many phasors (Fourier components) • For a linear system, each component can be multiplied by H[w] to obtain the output phasor • The signal output is simply the sum of all the individual phasor (Fourier component) outputs. Han Q Le© R Example C input vin[t] i(t) 8 8 6 6 4 4 2 output vout[t] 2 0 0 2 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.6 0.4 0.2 0.0 0.2 0.4 0.6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Han Q Le© 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.4 0.2 0.0 0.2 0.4 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Outline • Review • Signal analysis – Power spectral density • Frequency response of a circuit – Transfer function – Bode plot • Filters – Analog – Digital Han Q Le© General Filter Concept Review Power SpectralDensity This is a filter This is also filter 60 80 100 120 140 0 Han Q Le© This is another filter 1000 2000 3000 4000 5000 Frequency Hz General Filter Concept • A system (electronic circuit) can be designed such that its transfer function H[w] has preference (let through) certain ranges of frequencies while attenuating (blocking) other frequencies • Such a circuit is called a filter. Filter is a concept about the function of a circuit, not the circuit itself. • Filter includes both amplitude response and phase shift. Usually, only amplitude is plotted. Han Q Le© Common Types of Filters Band pass filter Power SpectralDensity Low pass filter High pass filter 60 80 100 120 140 0 Han Q Le© Band stop (notch) filter 1000 2000 3000 4000 5000 Frequency Hz Design of Filters • A circuit designed to perform filtering function on an analog signal is called an analog filter. • If a signal is digital (converted into a sequence of number), a filter can be realized as a mathematical operation, this is called digital filter. • Digital filter can be done with any computing device: from a DSP chip to a computer. Han Q Le© Example of Simple Analog Filters RC band stop filter. RC bandpass filters Han Q Le© Example of Simple Analog Filters RLC resonant filter Han Q Le© Example of Simple Analog Filters Notch filter application: rejection line 60-Hz signal Han Q Le© AmplitudeResponse Example: Test 1 Notch Filter 0.100 0.050 0.010 0.005 10 000 15000 20000 30 000 50 000 70 000 100 000 Frequency Hz 1.0 Phase Shift rad 0.5 0.0 0.5 1.0 1.5 2.0 2.5 10 000 Han Q Le© 15 000 20 000 30 000 50 000 70000 100 000 Frequency Hz Example: Test 1: Bandpass Filter AmplitudeResponse 1 0.1 0.01 0.001 10 4 1000 104 105 Frequency Hz 104 105 Frequency Hz 106 3 Phase Shift rad 2 1 0 1 2 3 1000 Han Q Le© 106 Digital Filter • Any filter function can be achieved with digital filter Signal input Microprocessor (DSP) User input Han Q Le© Filtered signal output Digital Filter • Digital filter can also be designed with sharp cut-off edge that is difficult with analog filter. This is another filter This is a filter Han Q Le© This is another type of filter http://www2.renesas.com/linear/en/application/equipment/cd.html Han Q Le© From TI http://focus.ti.com/docs/solution/folders/print/530.html Han Q Le©