RC Op-Amp Circuits (5.4)

1
RC Op-Amp Circuits (5.4)

• Prof. Phillips
• March 14, 2003

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
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.

4
A Generic Digital Meter
Input Switching and Ranging
A/D Converter
Amplifier
Processor
Display
5
Voltage Measurements
100V
10V
1V
Hi
Com
6
Model for Meter

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

7
Meter Loading

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

8
Loading

• When measuring the voltage across R, we need to
  make sure that R is much less than 10MW.
• If R is close to 10MW, significant current flows
  through the meter, changing the voltage across R.

9
Loading Example
Ideal Meter
Hi
10MW
2MW
50mA
Com

• Without Meter voltage is 100V
• With Meter measured voltage is 83.3V

10
Current Measurements
100V
10V
1V
Amp
Com
11
Measuring Large Currents (gt 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.

12
Meter Loading
Ideal Meter
Amp
Rs
R
Com

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

13
The Voltage Follower


vin
vout

14
Without a Voltage Follower
Rs

A/D Converter

Sensor
vs
vA/D

• vA/D is not equal to vs

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.

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
With a Voltage Follower




Rs
vs
vA/D

Sensor
A/D Converter

• vA/D is equal to vs

18
An Integrator
C
R




Vin
Vout

19
KCL at the Inverting Input
C
iC(t)
R

iR(t)
i-



vin(t)
vout(t)

20
KCL
21
Solve for vout(t)
22
Class Example

• Learning Extension E5.9