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Gain Bandwidth Product. Op-Amp. P in. P out. P DC. Gain Bandwidth Product. Think in terms of Energy Conservation. P out – P in ≤ P DC. Gain Bandwidth Product. P out – P in ≤ P DC.

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slide2

Op-Amp

Pin

Pout

PDC

Gain Bandwidth Product

Think in terms of Energy Conservation

Pout – Pin≤ PDC

slide3

Gain Bandwidth Product

Pout – Pin≤ PDC

Now consider Power expressed in the Frequency Domain as the Power Spectral Density Function, S(ω), and the Gain of the Op-Amp expressed as a function of Frequency, G(ω).

∫ G(ω) S(ω) dω - ∫ S(ω) dω≤ PDC

Pout – Pin≤ PDC

slide4

Gain Bandwidth Product

Next, the expression

∫ G(ω) S(ω) dω - ∫ S(ω) dω≤ PDC

simplifies to

∫ [G(ω) – 1] S(ω) dω≤ PDC

and for large G(ω)

∫ G(ω) S(ω) dω≤ PDC

slide5

Gain Bandwidth Product

∫ G(ω) S(ω) dω≤ PDC

  • Next assume:
  • amplifier bandwidth is BW
  • amplifier Gain (G) is constant over BW
  • signal spectra (S) is constant over BW

G(ω) S(ω) = G x S x BW

G x BW ≤ PDC / S

slide6

Gain Bandwidth Product

G x BW ≤ PDC / S

constant term

 Gain Bandwidth Product

  • Therefore if
  • G increases, BW must decrease, or
  • BW increases, G must decrease.
slide7

Gain Bandwidth Product

G x BW ≤ PDC / S

constant term

 Gain Bandwidth Product

If G = 1, then

BW = “Unity-gain Bandwidth”

slide8

If G = 1, then

BW = “Unity-gain Bandwidth”

slide9

TL084

Unity-gain

Unity-gain Bandwidth

slide10

TL084

Open loop gain

Unity gain

Unity-gain Bandwidth

slide12

VE = VIN+ - VIN-

VOUT = a * VE

VIN-

VIN+

slide13

The available DC power to the amplifier can either be put to use as

high signal gain over a limited bandwidth

or

limited gain over a wide bandwidth.

slide14

For fixed DC input power, the greatest signal gains are achieved with weak input signals.

To get high gains in already amplified signals (as in output stages), increased amounts of DC power must be used.

slide16

a (V+ - V-)

Differential Amplifier Circuit Analysis

slide17

a (V+ - V-)

Differential Amplifier Circuit Analysis

slide18

a (V+ - V-)

Differential Amplifier Circuit Analysis

slide19

a (V+ - V-)

Differential Amplifier Circuit Analysis

slide20

a (V+ - V-)

Differential Amplifier Circuit Analysis

 ZF/ ZG

common mode rejection ratio

v1

v1

vid / 2

v2

vid / 2

vicm

v2

Model of inputs with common-mode and differential-mode components

Original Inputs

vi1

vi2

Common Mode Rejection Ratio
slide24

Common Mode Rejection RatioCMRR

whereAis the differential mode gain andAcmis the common mode gain

Ideally:CMRR Typically: 60 dB  CMRR  120 dB

input and output impedances of noninverting op amp configuration

-

Ro

vo

Rd

vd

ii

+

io

Avd

-

vi

RL

+

CL

Input and Output Impedances of Noninverting Op-amp Configuration

The unity gain buffer input impedance is much higher than the op-amp input impedance Rd. The amplifier output impedance is much smaller than the op-amp output impedance Ro.

slide30

The available DC power to the amplifier can either be put to use as

high signal gain over a limited bandwidth

or

limited gain over a wide bandwidth.

slide31

high signal gain over a limited bandwidth

or

limited gain over a wide bandwidth.

G=10,000

G=10

G=10

G=10

G=10

instrumentation amplifier

R2

R2

vref

R3

R3

R4

R4

v1

v2

vout

R1

Instrumentation Amplifier
instrumentation amplifier example

R2

R2

vref

R3

R3

R4

R4

v1

v2

vout

R1

Instrumentation Amplifier Example

Burr-Brown INA118

Parameters:

Gain:

slide36

ECG Amplifier System

Multiple Subsystems

slide37

ECG Amplifier System

Input Instrumentation Amplifier

instrumentation amplifier38

R2

R2

vref

R3

R3

R4

R4

v1

v2

vout

R1

Instrumentation Amplifier
slide39

ECG Amplifier System

Intermediate Filter and Amplifier

slide40

Low-Pass

with

G=200

High-Pass

ECG Amplifier System

Intermediate Filter and Amplifier

slide41

ECG Amplifier System

Analog-to-Digital Converter

slide43

ECG Amplifier System

Zero Reference Bias Circuit

slide44

ECG Amplifier System

High-pass Filter for Autozeroing of DC Offset

slide45

ECG Amplifier System

CMRR Boost Circuit

(Negative Common Mode Signal Injection on Subject’s Right Leg)

slide46

ECG Amplifier System

CMRR Boost Circuit

(Negative Common Mode Signal Injection on Subject’s Right Leg)

slide47

Common Mode Rejection RatioCMRR

whereAis the differential mode gain andAcmis the common mode gain

Ideally:CMRR Typically: 60 dB  CMRR  120 dB

instrumentation amp

R2

R2

C

R3

R3

R4

R4

R

v1

v2

vout

2R1

Instrumentation Amp

A feedback network may also be included with the instrumentation amplifier.

vdiff = v2 - v1