chapter 11 amplifiers - seoul national...
TRANSCRIPT
Chapter 11Amplifiers
- Specifications and External Characteristics -
1. Various Amplifier models to calculate Amplifier performance 2. Amplifier efficiency.3. Input and output impedances of Amplifiers.4. Determination of Ideal Amplifier for various applications.5. Frequency-response requirements for Amplifier applications.6. Linear and nonlinear distortion in Amplifiers.7. Pulse-Response parameters of Amplifiers.8. Differential Amplifiers and Common-mode rejection requirements.9. Various sources of dc offsets and design balancing circuits.
Goal
Basic Amplifier ConceptsIdeal Amplifier : Production of an output signal with identical waveshape as the input signal, but with a larger amplitude.
( ) ( )tvAtv ivo =
Inverting vs Noninverting Amplifiers
Inverting Amplifiers : Negative Voltage GainNoninverting Amplifiers : Positive Voltage Gain.
InputNoninverting
Inverting
Common Ground Node
Ground : - Reference Voltage Level- Returning Path Current
Power : - 60Hz Power Reference - Not always connected to Chassis
Sometimes Chassis can be 120V ac with Power System Ground
Current Gain
( )L
iviv
i
o
RRAAA
PPG 2===
L
iv
i
oi R
RAiiA ==
Power Gain
Loading Characteristics
oL
Lvo
i
ov RR
RAvvA
+==Voltage Gain
mVvRR
Rv ssi
ii 3
2=
+= VvvA iivo 67.6104 == V
RRRvAv
oL
Livoo 33.5=
+=
8000=+
==oL
Lvo
o
iv RR
RAvvA
5333=++
==oL
L
si
ivo
s
iv RR
RRR
RAvvsA
9102×==L
ivi R
RAA
121016×== iv AAG
Voltage Gain << Current Gain << Power Gain
410=voA
8000, 104 109 1012
Cascaded Amplifiers
2
2
1
1
1
2
1
1
1
2
i
o
i
o
o
o
i
o
i
ov v
vvv
vv
vv
vvA ×=×==
21 vvv AAA =Current & Power Gain : Product of Individual Stages
21 iii AAA = 21GGG =
Example of Cascaded Amplifiers
15012
21
1
11 =
+==
oi
ivo
i
ov RR
RAvvA
750021 == vvv AAA50
22
2
22 =
+==
oL
Lvo
i
ov RR
RAvvA
5
2
111 10==
i
ivi R
RAA 750222 ==
L
ivi R
RAA6
21 1075×== iii AAA
7111 105.1 ×== iv AAG 4
222 1075.3 ×== iv AAG 1121 10625.5 ×== GGG
Simplified Models for Cascaded Amplifier - Determine Voltage Gain with loading by the Next stage - Overall voltage gain : Product of the gains of the separate stages - Input impedance : that of the first stage- Output impedance : that of the last stage.
15012
21
1
11 =
+==
oi
ivo
i
ov RR
RAvvA 10022 == vov AA
Power Supplies & Efficiency
BBBAAAs IVIVP +=
dosi PPPP +=+
%100×=s
o
PPη
rmsVRR
RvAvoL
Livoo 8=
+=
WRvP
L
oo 8
2
==
WIVIVP BBBAAAs 5.22=+=
WPPPP osid 5.14=−+=
%6.35%100 =×=s
o
PPηA
RvI
L
oo 1==
rmsmVvi 1=
ARvI
i
ii 1==
Current-Amplifier Model
Aisc : Current Gain with Output Short Circuited.
o
ivo
i
oi R
RAi
iA == scsc : Short Circuit Current Gain
o
ivoosc
i
ii R
vAiRvi == &
Transconductance-Amplifier Model
o
vo
i
om R
AviG == sc
sc
Gmsc : Conductance Gain with Output Short Circuit
: Short Circuit Transconductance Gain
o
ivoosc
i
ii R
vAiRvi == &
Transresistance-Amplifier Model
ivoi
om RA
ivR == oc
oc
Rmoc : Conductance Gain with Output Short Circuit
: Open Circuit Transresistance Gain
o
ivoosc
i
ii R
vAiRvi == &
Example of Various Amplifier Models
100=voA
3scsc 10===
o
ivo
i
oi R
RAi
iA
SviG
i
om 0.1sc
sc ==
Ω=== kRAi
vR ivoi
om 100oc
oc
Amplifier Input ImpedancesHigh Input Impedance : ElectroCardioGraph
- Small Voltage Measurement- Impedance varies with Person & Contact Condition
Low Input Impedance : Ammeter- Small Current Measurement- Keep Total Circuit Impedance Constant
ElectroCardioGraph Ammeter
Amplifier Output Impedances
Low Output Impedance : Parallel Speaker (Varying Impedance)- If High Amp Impedance, Voltage depends on Load Impedance
Intensity of Speaker varies with Number of Live Speaker- Low Amp Impedance, Voltage is almost Constant
Better Choice
Impedance depends on Highly Diverse Requirement based on Purpose
Low Output Impedance can force a Desired Voltage Waveformto appear across variable Load Impedance
High Output Impedance : Signal to LED LED is proportional to Current Not Voltage
Force Current Proportional to Signal Waveform (Voltage)High Impedance is BetterHigh Output Impedance can force a Desired Current Waveformto appear across variable Load Impedance
Special Output Impedance Transmission LineCharacteristic Impedance Zo such as 75Ω, 300Ω
If Impedance Ri is not Zo, Ghost Image appearsSpecific Impedance is necessary
The proper classification of a given amplifier depends on the ranges of source and load impedances with which the amplifier is used.
Ideal Amplifier
Usually 1Ω ~100Ω 1KΩ ~100kΩ >1MΩSmall Medium High
Frequency Response
i
ovA
VV
=
( ) ( )o302000cos1.0 −= ttvi π ( ) ( )o152000cos10 += ttvo π
o
o
o
45100301.0
1510∠=
−∠∠
==i
ovA
VV
Amplifier affects Phase & Amplitude of Sinusoidal WaveformComplex Gain with Phasor
For Example
dBAA vdBv 40log20 ==
Amplitude : x100 Phase : 45o Shift
Gain as a Function of Frequency AC Coupled
DC Coupled
Video Amp : DC component Brightness
Electrocardiograph : 1mV Signal with Electrode Voltage 1VAudio Amp : 20Hz ~15kHz signal is necessary
Filter Application
DC component High Pass Filter Reduction of DC
AC component Low Pass Filter Cut High Frequency
Low Pass Filter
High Pass Filter
Amplitude DistortionAmplitude Distortion : Gain of an amplifier has a different magnitude for the various frequency Components of Input Signal
( ) tttvi ππ 6000cos22000cos3 −=
( ) tttvo ππ 6000cos52000cos30 −=
Phase DistortionPhase Distortion : Phase shift of an amplifier is not proportional to frequency
( ) )6000cos(10)2000cos(30 tttvoA ππ −=
( ) )1356000cos(10)452000cos(30 oo −−−= tttvoB ππ
( ) )456000cos(10)452000cos(30 oo −−−= tttvoC ππ
No Phase Shift
Time Delay Wave Distortion
Distortionless AmplificationTo avoid Linear Waveform Distortion- Constant Gain Magnitude - Phase Response is Linear versus Frequency
for the range of frequencies contained in the input signal.
Pulse Response
Waveform Difference:- Rise Time : Leading & Trailing Edge Distortion - Overshooting- Ringing- Tilt
Rise Time
Btr
35.0≅ B : Bandwidth
Overshoot & Ringing
Specific Amplification at Special frequency such as fr (Ringing frequency)
Related to Gibbs Phenomenon
Gibbs Phenomenon
Gibbs phenomenon is an overshoot (or "ringing") of Fourier Series and other eigenfunction series occurring at simple discontinuities. It can be removed with the Lanczos Sigma Factor
m : Last term, removes the Gibbs Phenomenon. sinc(x) : the Lanczos σ factors.
The sinc function : “Sampling function," in signal processing and the theory of Fourier Transform. Full name is "sine cardinal
Tilt
%100 tiltpercentage ×∆
=PP
TfLπ200 tiltpercentage tilt,of amounts smallFor ≅
Transfer Characteristic & Nonlinear Distortion
Transfer Characteristic : a plot of instantaneous output amplitude versus instantaneous input amplitude.
Curvature in Transfer Characteristic : Nonlinear Distortion.
Av=10000
Harmonic Distortion( ) ( )tVtv aai ωcos=
( ) ( ) ( ) ( ) L++++= tVtVtVVtv aaao ωωω 3cos2coscos 3210
1
22 V
VD =1
33 V
VD =1
44 V
VD =
L++++= 25
24
23
22 DDDDD
Total Harmonic Distortion (THD)
( ) 44
33
221 )()()( iiiio vAvAvAvAtv +++=For Nonlinear Amp,
With
Fundamental Component Harmonic Distortion
Differential Amplifiers- Two input terminals: an Inverting input & a Noninverting input. - Output is proportional to the difference between two input signals.
21 iiid vvv −= iddo vAv =Ad : Differential Gainvid : Differential Signal
Differential & Common-mode Signal
( )21cm 2/1 iii vvv +=21 iiid vvv −=
21 & ii vv
Two Input Signal to the Differential Amp can be analyzed byA Small Differential Input (v1 , v2) & Common Mode Signal
Many Technically Important Signals : ECG, T,P,x,Length,,,,,
Common-Mode Rejection Ratio
cmcm iiddo vAvAv +=
cm
log 20CMRRAAd=
Real Amp :
Good Differential Amp= High CMRR
Common Mode Gain Measurement
cm
log 20CMRRAAd=
Differential Gain Measurement
ECG (ElectroCardioGram) with 60Hz Common Mode Signal
Offset Voltage, Bias Current & Offset Current
Modeled by several dc sources:- Two Bias-Current Sources : IB- An Offset Current Source : Ioff- An Offset Voltage Source : Voff
Real Differential Amp : vo is NOT ZERO even if vi is Zero.(The effect of these sources is to add a (usually undesirable) dc term to the ideal output.)
Minimization of Bias Current
Norton/Thevenin Theorem
Rs1 = Rs2 Bias Current Effect can be Zeroed.
Current Source Volatge Source
Example of Balancing Network
Various Offset CompensationVarious Offset Compensation
- Parallel Resistor- Offset terminal set V
- Parallel Resistor- Offset Compensation
at Input terminal