Rc Op Amps Instrumentation Lecture

7/27/2019 Rc Op Amps Instrumentation Lecture

1/22

ECE201 Lect-20 1

RC Op-Amp Circuits (5.4)

Dr. Holbert

November 14, 2002

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2/22

ECE201 Lect-20 2

Digital Meters and Oscilloscopes

Most multimeters and oscilloscopes are now

digital.

A digital multimeter or a digital oscilloscope

has an analog-to-digital (A/D) converter.

Most digital meters and all digital

oscilloscopes have one or more processors.



3/22

ECE201 Lect-20 3

Data Acquisition Systems

In many applications, digital meters and

scopes are being replaced by data

acquisition cards that fit into a computer.

The data acquisition cards have A/D

converters.

The computer provides processing andstorage for the data.



4/22

ECE201 Lect-20 4

A Generic Digital Meter

Input Switching

and Ranging

Amplifier

A/D Converter

ProcessorDisplay



5/22

ECE201 Lect-20 5

Voltage Measurements

Hi Com

10V

1V

100V



6/22

ECE201 Lect-20 6

Model for Meter

The ideal metermeasures the voltage acrossits inputs. No current flows into it; it hasinfinite input resistance.

10M Ideal Meter

Hi

Com



7/22

ECE201 Lect-20 7

10M Ideal Meter

Hi

ComR

Meter Loading

The 10M meter resistance in parallel withRmay change the voltage that you measure.



8/22

ECE201 Lect-20 8

Loading

When measuring the voltage acrossR, we

need to make sure thatR is much less than

10M. IfR is close to 10M, significant current

flows through the meter, changing the

voltage acrossR.



9/22

ECE201 Lect-20 9

Loading Example

Without Meter: voltage is 100V

With Meter: measured voltage is 83.3V

10M Ideal Meter

Hi

Com2M50A



10/22

ECE201 Lect-20 10

Current Measurements

AmpCom

10V

1V

100V



11/22

ECE201 Lect-20 11

Measuring Large Currents

(> 100mA)

The current to be measured is passed

through a small resistor (called ashuntresistor) and the resulting voltage across the

shunt resistor is measured.

From the voltage, the current can be

computed.



12/22

ECE201 Lect-20 12

Rs Ideal Meter

Amp

ComR

Meter Loading

TheRs shunt resistance in series withR maychange the current that you measure.



13/22

ECE201 Lect-20 13

The Voltage Follower

vin

+

vout

+

+



14/22

ECE201 Lect-20 14

Without a Voltage Follower

vA/D

is not equal to vs

vs

Rs

RA/D

+

vA/DSensor A/D

Converter+



15/22

ECE201 Lect-20 15

Op-Amp Review

The idealop-amp model leads to the

following conditions:

i+ = i- = 0

v+ = v-

The op amp will set the output voltage to

whatever value results in the same voltages

at the inputs.



16/22

ECE201 Lect-20 16

Op-Amp Review

To solve an op-amp circuit, we usually

apply KCL (nodal analysis) at one or both

of the inputs.

We then invoke the consequences of the

ideal model.

We solve for the op-amp output voltage.



17/22

ECE201 Lect-20 17

With a Voltage Follower

vA/D

is equal to vs

vsR

s

Sensor

RA/D

+

vA/D

A/DConverter

+

+



18/22

ECE201 Lect-20 18

An Integrator

+Vin

+

Vout

R

C

+



19/22

ECE201 Lect-20 19

KCL at the Inverting Input

+vin

(t)+

R

C

vout

(t)

iR

(t)

iC(t)

i-

+



20/22

ECE201 Lect-20 20

KCL0=i

R

tv

R

vtv

ti ininR)()(

)( =

=

( )

dt

tdvC

dt

vtvdCti

outout

C

)()()( =

=



21/22

ECE201 Lect-20 21

Solve forvout(t)

0)()(=+

dt

tdvC

R

tvoutin

RC

tv

dt

tdvinout

)()(=

dxRC

xv

tv

t

in

out

=)(

)(



22/22

ECE201 Lect-20 22

Class Example

Learning Extension E5.9

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Rc Op Amps Instrumentation Lecture