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