Chapter 8
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Ideal Amplifier
Characteristics
A voltage amplifier
Simple voltage amplifier model
2
• If the input resistance of the amplifier Rin
were very large, the source voltage vS and
the input voltage vin would be
approximately equal:
3
• By an analogous argument, it can also be
seen that the desired output resistance for
the amplifier Rout should be very small,
since for an amplifier with Rout = 0, the
load voltage would be
4
• We can see that as Rin approaches infinity
and Rout approaches zero, the ideal
amplifier magnifies the source voltage by a
factor A
vL = AvS
• Thus, two desirable characteristics for a
general-purpose voltage amplifier are a
very large input impedance and a very
small output impedance.
5
The Open-Loop Model
• The ideal operational amplifier behaves very
much as an ideal difference amplifier, that is, a
device that amplifies the difference between two
input voltages. Operational amplifiers are
characterized by near-infinite input resistance and
very small output resistance. As shown in Figure
8.4, the output of the op-amp is an amplified
version of the difference between the voltages
present at the two inputs.
6
The input denoted by a plus sign is called the
noninverting input (or terminal), while that
represented with a minus sign is termed the
inverting input (or terminal).
The current flowing into the input circuit of the
amplifier is zero, or:
7
The Inverting Amplifier
• The input signal to be amplified is
connected to the inverting terminal, while
the non-inverting terminal is grounded.
Inverting amplifier
8
The voltage at the noninverting input v+ is easily identified
as zero, since it is directly connected to ground: v+ = 0.
The effect of the feedback connection from output to inverting
input is to force the voltage at the inverting input to be equal to
that at the non-inverting input.
9
Example 8.1 Inverting
Amplifier Circuit
• Determine the voltage gain and output
voltage for the inverting ampilfier circuit of
figure 8.5. What will the uncertainty in the
gain be if 5 and 10 percent tolerance
resistors are used, respectively?
Figure 8.5
10
Figure 8.5
Figure 8.6
11
Check your understand
• Calculate the uncertainty in the gain if 1
percent “precision” resistors are used.
12
The Summing Amplifier
Noninverting amplifier
Summing amplifier
13
Example 8.2 Voltage
Follower
14
Check your understand
• Derive an expression for the closed-loop
gain of the voltage follower that includes
the value of the open-loop voltage gain as a
parameter. How large should the open-loop
gain be if we desire to achieve the intended
closed-loop gain with less than 0.1 percent
error?
15
The Differential amplifier
16
• The analysis of the differential amplifier may be
approached by various methods; the one we select
to use at this stage consists of
1. Computing the noninverting- and invertingterminal voltages v+ and v−.
2. Equating the inverting and noninverting input
voltages: v− = v+.
3. Applying KCL at the inverting node, where i2 =
−i1.
17
• The differential amplifier provides the ability to
reject common-mode signal components (such as
noise or undesired DC offsets) while amplifying
the differential-mode components. To provide
impedance isolation between bridge transducers
and the differential amplifier stage, the signals v1
and v2 are amplified separately.
18
19
Check your understand
• Derive the result given above for the
differential amplifier, using the principle of
superposition. Think of the differntial
amplifier as the combination of an inverting
amplifier with input equal to ύ1 and a noninverting amplifier with input equal to ύ1.
20
21
Example 8.3 Electrocardigram
(EKG) Amplifier
Figure8.12 EKG waveform
Figure 8.11 Two-lead
electrocardiogram
22
Figure 8.13 EKG amplifier
23
Instrumentation Amplifier
Instrumentation amplifier
24
Example 8.14
Instrumentation Amplifier
• Determine the closed-loop voltage gain of
the instrumentation amplifier circuit of
figure 8.14.
25
Figure 8.15 Input (a) and output (b) stages of
instrumentation amplifier
26
27
Example 8.5 Level Shifter
• The level shifter of figure 8.16 has the
ability to add or subtract a DC offset to or
from a signal. Analyze the circuit and
design it so that it can remove a 1.8-V DC
offset from a sensor output signal.
28
Figure 8.17
Figure 8.16 level
shifter
29
Check your understand
• With reference to Example 8.5, find ∆R if the
supply voltages are symmetric at +or- 15V and a
10-kΏ resistors.
• With reference to Example 8.5, find the range of
value of Vref if the supply voltages are symmetric
at +or- 15V and a 1-kΏ potentiometer id tied to
the two 10-k Ώ resistors.
30
31
Example 8.6 Temperature
Control Using Op- Amps
32
33
Check your understand
• How much steady-state power, in Watts,
will be input to the thermal system of
Example 8.6 to maintain its temperature in
the face of a 10ºC ambient temperature
drop for values of Kp of 1, 5, and 10.
34
Active Filters
• The class of filters one can obtain by means
of op-amp designs is called active filters.
Figure 8.19 op-amp circuit
employing complex impedances
35
Active low-pass filter
Normalized response of active low-pass filter
36
Active high-pass filter
Normalized response of active high-pass filter
37
Active bandpass filter
Normalized amplitude response of active bandpass filter
38
Example 8.7 Second- Order
Low-Pass Fiter
• Determine the closed-loop voltage gain as a
function of frequency for the op-amp
circuit of Figure 8.27.
39
40
Check your understand
41
The Ideal Integrator
Op-amp integrator
42
Example 8.8 Integrator a
square Wave
• Determine the output voltage for the
integrator circuit of Figure 8.30 if the input
is a square wave of amplifier +or- A and
period T.
43
44
Check your understand
• Plot the frequency response of the ideal
integrator in the form of a Bode Plot.
Determine the slope of the straight-line
segments in decibels per decade. You may
assume RsCF = 10.
45
The Ideal Differentiator
Op-amp differentiator
46
Voltage Supply Limits
• The effect of limiting supply voltages is
that amplifiers are capable of amplifying
signals only within the range of their supply
voltages.
47
Example 8.9 Voltage Supply
Limits in an Inverting Amplifier
• Compute and sketch the output voltage of
the inverting amplifier of Figure 8.33.
48
Figure 8.34 Op-amp output with voltage
supply limit
49
Example 8.10 Voltage Supply
Limits in an Op-Amp Integrator
• Compute and sketch the voltage of the
integrator of Figure 8.35.
50
Figure 8.36 Effect of DC
offset on integrator
51
Check your understand
• How long will it take for the integrator of
Example 8.10 to saturate if the input signal
has a 0.1-V DC bias [that is, ύs(t) = 0.1 +
0.3 cos(10t)]?
52
Frequency Response Limit
Another property of all amplifiers that may pose
severe limitations to the op-amp is their finite
bandwidth.
53
Open-loop gain of practical op-amp
The finite bandwidth of the practical op-amp
results in a fixed gain-bandwidth product for
any given amplifier.
54
• Another limitation of practical op-amps
results because even in the absence of any
external inputs, it is possible that an offset
voltage will be present at the input of an
op-amp.
55
Example 8.11 Gain-Bandwidth
Product Limit in an Op-Amp
• Determine the maximum allowable closedloop voltage gain of an op-amp if the
amplifier is required to have an audio-range
bandwidth of 20 kHz.
56
57
Check your understand
• What is the maximum gain that could be
achieved by the op-amp of Example 8.11 if
the desired bandwidth is 100kHz?
58
Example 8.12 Increasing the
Gain-Bandwidth Product Means
of Amplifier in Cascade
• Determine the overall 3-dB bandwidth of
the cascade amplifier of Figure 8.39.
59
60
Check your understand
• What is the actual gain in decidals at the
cutoff frequency ω0 for the cascade
amplifier?
• What is the 3-dB bandwidth of the cascade
amplifier of Example 8.12?
61
62
Example 8.13 Effect of input
Offset Voltage on an Amplifier
• Determine the effect of the input offset
voltage Vos on the output of the amplifier of
Figure 8.40.
63
64
Check your understand
• What is the maximum gain that can be
accepted in the op-amp circuit of Example
8.13 if the offset is not to exceed 50 mV?
65
Input Bias Current
• Another nonideal characteristic of op-amps
results from the presence of small input
bias currents at the inverting and
noninverting terminals.
Figure 8.14
66
Example 8.15 Effect of slew
Rate Limit on an Amplifier
• Determine the effect of the slew rate limit
S0 on the output of an inverting amplifier
for a sinusoidal input voltage of known
amplifier and frequency.
67
Figure 8.46 Distortion introduced by
slew rate limit
68
Check your understand
• Given the desired peak output
amplifier(10V), What is the maximum
frequency that will not result in violating
the slew rate limit for the op-amp of
Example 8.15?
69
Example 8.16 Effect of Short
Circuit Current Limit on an
Amplifier
• Determine the effect of short circuit limit Isc
on the output of an inverting amplifier for a
sinusoidal input voltage of known
amplitude.
70
Figure 8.48 Distortion introduced by
short-circuit current limit
71