ECE201 Lect-18 1

RC Op-Amp Circuits (6.4)

Dr. Holbert

April 10, 2006

ECE201 Lect-18 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.

ECE201 Lect-18 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 and storage for the data.

ECE201 Lect-18 4

A Generic Digital Meter

Input Switchingand Ranging

Amplifier

A/D Converter

ProcessorDisplay

ECE201 Lect-18 5

Voltage Measurements

Hi Com

10V

1V

100V

ECE201 Lect-18 6

Model for Meter

The ideal meter measures the voltage across its inputs. No current flows into it; it has infinite input resistance.

10M Ideal MeterHi

Com

ECE201 Lect-18 7

10M Ideal MeterHi

ComR

Meter Loading

The 10M meter resistance in parallel with R may change the voltage that you measure.

ECE201 Lect-18 8

Loading

• When measuring the voltage across R, we need to make sure that R is much less than 10M

• If R is close to 10M, significant current flows through the meter, changing the voltage across R.

ECE201 Lect-18 9

Loading Example

• Without Meter: voltage is 100V

• With Meter: measured voltage is 83.3V

10M Ideal MeterHi

Com2M50A

ECE201 Lect-18 10

Current Measurements

AmpCom

10V

1V

100V

ECE201 Lect-18 11

Measuring Large Currents (> 100mA)

• The current to be measured is passed through a small resistor (called a shunt resistor) and the resulting voltage across the shunt resistor is measured.

• From the voltage, the current can be computed.

ECE201 Lect-18 12

RsIdeal Meter

Amp

ComR

Meter Loading

The Rs shunt resistance in series with R may change the current that you measure.

ECE201 Lect-18 13

The Voltage Follower

vin

+

–

vout

+

–

+–

ECE201 Lect-18 14

Without a Voltage Follower

vA/D is not equal to vs

vs

Rs

RA/D

+

–

vA/DSensor A/D

Converter+–

ECE201 Lect-18 15

Op-Amp Review

• The ideal op-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.

ECE201 Lect-18 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.

ECE201 Lect-18 17

With a Voltage Follower

vA/D is equal to vs

vsRs

Sensor

RA/D

+

–

vA/D

A/D Converter

+

–+–

ECE201 Lect-18 18

An Integrator

–

+Vin+

–Vout

R

C

+–

ECE201 Lect-18 19

KCL at the Inverting Input

–

+vin(t)+

–

R

C

vout(t)

iR(t)

iC(t)

i-

+–

ECE201 Lect-18 20

KCL

0i

R

tv

R

vtvti inin

R

)()()(

dt

tdvC

dt

vtvdCti outout

C

)()()(

ECE201 Lect-18 21

Solve for vout(t)

0)()(

dt

tdvC

R

tv outin

RC

tv

dt

tdv inout )()(

dxRC

xvtv

tin

out

)(

)(

ECE201 Lect-18 22

Class Example

• Learning Extension E6.9