Transcript Document

Today
• Course overview and information
09/16/2010
© 2010 NTUST
Comparators
Comparator
• Op-amps can be used to compare the amplitude of one voltage
with another. Although general-purpose op-amps can be used
as comparators, special op-amps are available to optimize
speed and add features.
+V
• An example of a comparison
circuit is shown. The input is
compared with a reference set by
the voltage-divider. Notice that
there is no feedback; the op-amp
is operated in open-loop, so the
output will be in saturation.
R1
Vin
+
R2
Vout
Examples
Sketch the output of the comparator in relationship to the input;
assume the maximum output is ±13 V.
The threshold is +4.2 V. The output is
in positive saturation when Vin > +4.2
V
V = +15 V
R1
10 kW
Vin
+10 V
+4.2 V
Vin
0V
-10 V
+13 V
+
R2
3.9 kW
Vout
0V
-13 V
Examples
Show the output of the comparator for the last example if the inputs
to the op-amp are reversed.
The threshold is still +4.2 V but now
the output is in negative saturation
+10 V
when Vin > +4.2 V.
+4.2 V
Vin
0V
V = +15 V
R1
10 kW
-10 V
+13 V
+
-
Vin
R2
3.9 kW
Vout
0V
-13 V
Summing Amplifier
• There are a number of useful applications for the basic
inverting amplifier configuration. One is the summing
amplifier that uses two or more inputs and one output.
• The virtual ground isolates
R1
Rf
VIN1
the inputs from each other.
R2
Input current from each input VIN2
R3
is passed to Rf, which
VIN3
+
develops an output voltage
Rn
that is proportional to the
VINn
algebraic sum of the inputs.
Virtual ground
VOUT
Summing Amplifiers
Averaging Amplifier
• An averaging amplifier is a variation of the summing amplifier
in which all input resistors are equal. The feedback resistor is
the reciprocal of the number of inputs times the input resistor
value.
• For example, if there
are three input
resistors, each with a
value of 10 kW, then
Rf = 3.3 kW to form
an averaging amplifier.
VIN1
VIN2
VIN3
R1
Rf
10 kW
R2
3.3 kW
10 kW
R3
10 kW
+
VOUT
Averaging Amplifiers
Scaling Adder
Scalingadder
adder
• A scaling
is another variation of the summing amplifier
in which the input resistors are adjusted to weight inputs
differently. The input “weight” is proportional to the current
from that input.
• Larger resistors will allow
R1
Rf
less current for a given
VIN1
10 kW
10 kW
input voltage, so they
R2
VIN2
have less “weight” than
VOUT
5.0 kW
+
smaller resistors. In the
R3
VIN3
case shown, VIN3 is
2.5 kW
“weighted” 2 times more
than VIN2, which is 2
times more than VIN1.
Scaling Adder
What is VOUT for the scaling adder if all
inputs are + 1.0 V?
By Ohm’s law, the currents into Rf are
I1 = 0.1 mA, I2 = 0.2 mA and I3 = 0.4 mA.
Using the superposition
theorem, the current in
Rf is 0.7 mA. From
Ohm’s law, VOUT = 7 V
VIN1
VIN2
VIN3
R1
Rf
10 kW
R2
10 kW
5.0 kW
R3
2.5 kW
+
VOUT
Integrators
Integratorsintegration is basically a summing process.
• Mathematical
Within certain limitations, an integrator circuit simulates
this process.
• The ideal integrator is
essentially a summing
amplifier with a
capacitor in place of the
feedback resistor.
Vin
Rf
C
In practical circuits, a large
value resistor is usually in
parallel with the capacitor
to prevent the output from
drifting into saturation.
R
+
Vout
Integrators
• ForIntegrators
the ideal integrator, the rate of change of the output is
Vout
Vin
given by
t
Ri C
• The minus sign in the equation is due to the inverting
amplifier. If the input is a square wave centered about 0 V,
the output is a negative triangular wave (provided
saturation is not reached).
C
Vin
Vin
0V
R
+
Vout
0V
Vout
Integrator
Example
A 5 kHz square wave with 10 Vpp is applied to a
practical integrator. Show the output waveform voltages.
During the positive input (½ the period), the change
in the output is
V
5V
Vout  - in t  100 μs = 5.6 V
Ri C
 2.7 kW 33 nF
Rf
270 kW
C
Vin
R
2.7 kW
33 nF
+
Vout
The feedback resistor (Rf) is
large compared to R, so has little
effect on the shape of the
waveform. In a practical circuit,
it will cause the output
waveform to center on zero as
shown on the following slide.
Example
continued…
The results of a computer
simulation on Multisim confirm
the calculated change (5.6 V) in
output voltage (blue line).
Rf
270 kW
C
Vin
R
2.7 kW
33 nF
+
Vout
Example
Examples
Examples
Differentiators
Differentiators
• In mathematics,
differentiation is the process of finding the
rate of change. An idea differentiator circuit is shown. It
produces an inverted output that is proportional to the rate
of change of the input.
In practical circuits, a small value resistor is
added in series with the input to prevent high
frequency ringing.
Vin
Rin Vin
Rf
C
+
Vout
Differentiator
Differentiators
The output
voltage for the ideal differentiator is given by
Vout
 VC
 -
 t

 Rf C

• The minus sign in the equation is due to the inverting
amplifier. If the input is a ramp, the output is a negative dc
level for the positive slope and a positive dc level for the
negative slope.
Rf
Vin
Vin
Vout
C
+
Vout
Differentiator
Examples
A 1.0 kHz, 10 Vpp triangular wave is applied to a
practical differentiator as shown. Show the output in relationship
to the input.
When the input has a positive slope, the output is
V
Vout  -  C
 t

 10 V 
R
C


  2.7 kW 100 nF   -5.4 V
 f
 0.5 ms 

By symmetry, when the input has a negative slope, the
Rf
output will be +5.4 V.
Rin
Vin
+5.0 V
Vin
2.7 kW
C
120 W 100 nF
-
Vout
+
0V
-5.0 V
0
1 ms
2 ms
See next slide for waveforms…
Examples
continued…
The results of a computer
simulation on Multisim confirm
the calculated output voltages
(±5.4 V). The output voltage is
the blue line.
Examples
Examples
Examples
Selected Key Terms
Summing An amplifier with several inputs that
amplifier produces an output voltage proportional to
the algebraic sum of the inputs.
Averaging An amplifier with several inputs that
amplifier produces an output voltage that is the
mathematical average of the input voltages.
Scaling adder A special type of summing amplifier with
weighed inputs.
Selected Key Terms
Integrator A circuit that produces an inverted output that
approaches the mathematical integral of the input.
Differentiator A circuit that produces an inverted output that
approaches the mathematical derivative of the input,
which is the rate of change.
Active filter A frequency selective circuit consisting of active
devices such as transistors or op-amps combined
with reactive (RC) circuits.
Series regulator A type of voltage regulator with the control element
in series between the input and output.
Quiz
1. When an op-amp is configured as a comparator,
the gain is equal to
a. 0.
b. 1.
c. a ratio of two resistors.
d. the open-loop gain.
Quiz
2. The approximate voltage at the inverting input of
the op-amp shown is equal to
a. the average of the input voltages.
b. the sum of the input voltages
c. 0 V
d. VOUT
3
VIN
1
VIN
2
VIN
3
R1
Rf
10 kW
R2
3.3 kW
10 kW
R3
10 kW
-
+
VOUT
Quiz
3. For the scaling adder shown, the input with the
greatest weight is
R1
R
f
VIN
a.
VIN1
b. VIN2
c.
VIN3
1
VIN
2
VIN
3
d. they are all equal
10 kW
R2
5.0 kW
R3
2.5 kW
10 kW
+
VOUT
Quiz
4. In a practical integrator, the purpose of the feedback
resistor (Rf) is to
a. limit the gain.
b. prevent drift.
Rf
c. prevent oscillations.
C
d. all of the above.
Vin
R
+
Vout
Quiz
5. Assume the top waveform represents the input to a
differentiator circuit. Which represents the expected
output?
V
i
n
a.
b.
c.
d.
Quiz
6. The lead-lag network in a Wien bridge with equal
value R’s and C’s attenuates the signal by a factor of
a. 2
b. 3
c. 5
d. 10
Quiz
7. A Wien-bridge is used to produce
a. sine waves.
b. square waves.
c. triangle waves.
d. all of the above.
Quiz
8. For the circuit shown, the two outputs (in red)
produce
a. sine and square waves.
b. triangle and square waves.
c. sine and triangle waves.
C
Vout waves.
d. sawtooth and triangle
+
Comparato
r
R1
Vout
R2
R3
+ Integrator
Quiz
9. The purpose of the op-amp in the series regulator is
a. to sample the output.
b. to establish a reference.
c. as a control element.
d. error detection.
Q1
VIN
VOUT
R1
+
-
R2
R3
Quiz
10. An advantage of a shunt regulator is
a. short circuit protection.
b. efficiency.
c. no need for a reference voltage.
d. all of the above.
Quiz
Answers:
1. d
6. b
2. c
7. a
3. c
8. b
4. b
9. d
5. c
10. a