Transcript 3336 Lect 10-Frequency response
Han Q Le© ECE 3336 Introduction to Circuits & Electronics
Lecture Set #10 Signal Analysis & Processing – Frequency Response & Filters
Dr. Han Le ECE Dept.
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.
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• • • 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.
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Harmonic function Applications of mathematical techniques Signal and AC circuit problems Fourier transform • RLC or any time-varying linear circuits. Applicable to linear portion of circuits that include nonlinear elements Complex number &analysis Phasors • • • • Signal processing 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).
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Han Q Le© Inductor Example Antenna Variable Capacitor Diode (1N34A) Ground High-Impedance Earphone
Inductor Schematic Carrier wave (sound) signal 20 1.5
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Ante nna 10 Variable Capacitor Diode (1N34A) 30 40 50 Antenna Soundwave Electrical signal (voltage or current) Resonance circuit 1.5
Grou 0.5
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High-Impedance Earphone 10 20 30 40 50 Han Q Le©
Han Q Le© Link to Mathematica file: AM FM
Outline
• • • • Review Signal analysis – Power spectral density Frequency response of a system (circuit) – Transfer function – Bode plot Filters – Analog – Digital Han Q Le©
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Signal Fourier (or harmonic) Analysis
Treat each time-finite signal as if it is composed of many harmonics, using Fourier series
x t a
0
x t n
1
a n
Cos
n m X m t n
1
b n
Sin
n m t t
In complex (or Euler) representation, Fourier series coefficients
X m
are phasor components,
X m X m m
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Signal Fourier (or harmonic) Analysis (cont)
• If the signal is real (all cases involving real physical quantity), then:
X m X m X m X m m X m X m m
Hence, we need to keep only positive frequencies A signal can be represented by a plot of | frequency, or usually |
X m
| 2
X m
| vs. 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 f m frequency vs.
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
Example of Spectra
0.89 s 11 025 Hz 60 80 100 120 140 0 1000 2000 3000 4000 5000 3 2 1 0 1 2 3 0 1000 2000 3000 4000 5000 Han Q Le©
Example of Spectra
0.79 s 11 025 Hz 60 80 100 120 0 1000 2000 3000 4000 5000 3 2 1 0 1 2 3 0 1000 2000 3000 4000 5000 Han Q Le©
Outline
• • • • Review Signal analysis – Power spectral density Frequency response of a circuit – Transfer function – Bode plot Filters – Analog – Digital Han Q Le©
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Example
t
input v in [t] i(t) R C output v out [t] 1 1 Frequency Response or, Frequency Transfer Function C
t
input v in [t] i(t) R output v out [t]
H
1 1 1
t t H
1
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Frequency Transfer Function (Frequency Response Function)
For many linear RLC circuits, the frequency response function usually has the form:
H P Q a
0
b
0
a
1
b
1
a
2
b
2 2 2
a m b n m n
Example: Test 1
H
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2 2
R
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L
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R
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R
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C
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Bode Plot for Vout in Test 1
1 0.1
0.01
0.001
10 4 1000 10 4 10 5 Frequency Hz 10 6 3 2 1 0 1 2 3 1000 10 4 10 5 Frequency Hz 10 6 Han Q Le©
• • •
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.
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R i(t) C output v out [t] 8 6 4 2 0 2 0.0
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1.0
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0.0 0.5 1.0 1.5 2.0 2.5 3.0
Han Q Le© 8 6 4 2 0 0.5
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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
This is a filter This is also filter This is another filter 60 80 100 120 140 0 1000 2000 3000 Frequency Hz 4000 5000 Han Q Le©
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 Han Q Le© plotted.
Low pass
Common Types of Filters
Band pass High pass filter filter Band stop (notch) filter filter 60 80 100 120 140 0 1000 2000 3000 Frequency Hz 4000 5000 Han Q Le©
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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.
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©
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Example: Test 1 Notch Filter
0.100
0.050
0.010
0.005
10 000 15000 20000 30 000 Frequency Hz 50 000 70 000 100 000 1.0
0.5
0.0
0.5
1.0
1.5
2.0
2.5
10 000 15 000 20 000 30 000 Frequency Hz 50 000 70000 100 000
Example: Test 1: Bandpass Filter
1 0.1
0.01
0.001
10 4 1000 10 4 10 5 Frequency Hz 10 6 3 2 1 0 1 2 3 1000 10 4 10 5 Frequency Hz 10 6 Han Q Le©
Digital Filter
• Any filter function can be achieved with digital filter Signal input Micro processor (DSP) Filtered signal output User input Han Q Le©
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Digital Filter
• Digital filter can also be designed with sharp cut-off edge that is difficult with analog filter.
This is another type of filter
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http://www2.renesas.com/linear/en/application/equipment/cd.html
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From TI http://focus.ti.com/docs/solution/folders/print/530.html