Transcript Feature Selection/Extraction for Classification Problems

전자 회로 1
Lecture 1
2009. 03.
임한조
아주대학교 전자공학부
[email protected]
이 강의 노트는 전자공학부 곽노준 교수께서 08.03에 작성한 것으로 노트제공에 감사드림.
Overview
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Review of basic electric circuit
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Introduction to Amplifiers
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Gain
Transfer characteristics
Introduction to Inverters
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Resistor, capacitor, inductor
Current and voltage source (Norton/Thevenin form)
Frequency response (single time constant)
Noise margin
Propagation delay
Some materials in this note are from
•
Lecture notes of Prof. Woodward Yang (Harvard U.)
•
•
March, 2008
http://www.deas.harvard.edu/courses/es154
Lecture notes of Prof. Sang-Bae Kim (Ajou U.)
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Review of Circuit Basics

Some basic circuit elements that will be used
extensively in this class.
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Capacitor

Has memory/hysterisis
Terminal relationship

Stores charges on electrodes (parallel plates)

qc (t )  Cvc (t )
Energy stored in electric field

U (t ) 




t
0
ic vc dt 

t
0
C
dvc (t )
1
2
vc (t ) dt  Cvc (t )
dt
2
Capacitance measured in units of Farads (F)
Range of typical values (1pF ~ 1000uF)
Capacitor types
Remember

Ceramic (pF)
• At LF, C is open circuit
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Mylar (nF)
• At HF, C is closed circuit
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Electrolytic (uF)
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Inductor

Has memory/hysterisis
Terminal relationship

Energy stored in magnetic field

t
t
0
0
U (t )   iL vL dt   LiL (t )


diL (t )
1
2
dt  LiL (t )
dt
2
Inductance measured in units of Henries (H)
Range of typical values (1uH ~ 1H)
Remember
• At LF, L is closed circuit
• At HF, L is open circuit
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Impedance (driven by sinusoidal
source)
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Representation of Signal Source
Thevenin form
Norton form
 s ( t )  Rs is (t )
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The two are equivalent.
However (a) is preferred when Rs is small,  small voltage drop
While (b) is preferred when Rs is large.  small current loss
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Analog vs. Digital Signal
Analog Signal
Analog-to-Digital Converter
Discrete Sampled Signal
111
111
101
Digital Signal
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Time & Frequency Domain
Time and Frequency-Domain Representation of Analog Signals
Amplitude
(power)
f
t
t
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Frequency response (single time constant)
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Bode plots
High pass
Low pass
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Amplifiers (mostly for Analog Circuits)
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Voltage amplifiers
Current amplifiers
Power amplifiers
4 ports
3 ports
(common ground)
The role of DC power supplies
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Gains
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Voltage Gain: Av = vo / vi
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Current Gain: Ai = io / ii
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Power Gain: Ap = Po / Pi = vo io /vi ii = Av Ai
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Gain in dB (decibel)
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Voltage, Current gain = 20 log (Av, Ai)
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Power gain = 10 log (Ap)
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Ap (dB) = ½ [Av (dB) + Ai (dB)]
* For more information, consult App. B.
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Amp. with Power Supplies (How Po > Pi ?)
Pdc  V1 I1 + V2 I 2
Efficiency:
Pdc + PI  PL + Pdissipated
PL
 
 100
Pdc
(1.10)
Because PI is normally very small
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Transfer characteristic w/ Saturation
To operate linearly:
L
L
 I 
A
A
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Nonlinearity and Biasing
 I ( t )  VI +  i ( t )
0 ( t )  V0 + 0 ( t )
 I ( t )  A i ( t )
A =
d 
d 
at Q
Small-signal gain (Av) = slope of the transfer curve at the operation point
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Circuit models for Amps
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Voltage amplifiers
RL
  A oi
RL  R
Ri
 i  s
Ri  Rs

RL
A 
 A o
i
RL  R0
(1.13)
(1.12)
0
Ri
RL
 A o
s
Ri  Rs RL  R0
To make Vo/Vs large (regardless of source and load),
 Ri  should be large
Ro  should be small
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Example: multistage voltage amps.
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Cascade or multi-stage amplifier: input resistance of an
amplifier stage acts as a load to the previous stage.
Typically used for Op-amp.  e.g. 741 type
Desirable characteristics for a voltage amp.
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Large input resistance
Small output resistance
High gain
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Example: BJT (small signal model)
Common emitter amplifier
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Frequency response of an amp.
Vo
T ( ) 
Vi
T ( )  
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Inverter (mostly for Digital Circuits)

Logic inverter symbol
NH H  NM L  VDD /2
Ideal Logic Inverter
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NH H  VOH  VIH
NM L  VIL  VOL
(1.27)
(1.25)
(1.26)
Real Logic Inverter (with linear approx.)
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Implementation of Inverters
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Voltage controlled switch
Vi = low  (b)
Vi = high  (c)
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Inverter with CMOS

CMOS – can be interpreted as a pair of
complementary switches
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Propagation delay of an inverter
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