Chapter 5

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Chapter 5 EGR 260 Circuit Analysis
Reading Assignment Chapter 5 in Electric
Circuits, 9th Edition by Nilsson
Chapter 5 Operational Amplifiers Note We are
temporarily skipping the remaining sections of
Chapter 4. We will cover them after completing
Chapter 5. Operational Amplifier - An
operational amplifier (op amp) is a high gain
differential amplifier with nearly ideal external
characteristics. Internally the op amp is
constructed using many transistors.
Terminology V non-inverting input voltage V-
inverting input voltage Vo output voltage Io
output current I non-inverting input
current I- inverting input current ?VDC
positive and negative DC supply voltages used to
power the op amp (typically ?5V to ?30V) ?V V
- V- difference voltage
Note Sometimes the supply voltage connections
are not shown
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Chapter 5 EGR 260 Circuit Analysis
Operational Amplifiers
8-pin package pinout
8-pin package (3D view)
uA741 symbol in PSPICE
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Chapter 5 EGR 260 Circuit Analysis
Typical Operational Amplifier Schematic
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Chapter 5 EGR 260 Circuit Analysis
Open-loop versus closed-loop operation

• Open-loop
• Relatively rare
• Op amp specifications may be important

• Closed-loop
• Most commonly used
• Some sort of feedback from output to input
  exists
• The input voltage, Vin, is defined according
  to the application

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Chapter 5 EGR 260 Circuit Analysis

• An op amp circuit can be easily analyzed using
  the following ideal
• assumptions.
• Ideal op-amp assumptions
• Assume that ?V 0, so V V-
• Assume the input resistance is infinite, so I
  I- 0
• Realize the all voltages defined above are node
  voltages w.r.t. a common ground (as illustrated
  below)

Illustration Draw an op amp showing a common
negative terminal for all node voltages.
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Chapter 5 EGR 260 Circuit Analysis
Example Determine an expression for Vo in the
inverting amplifier shown below. Illustrate the
results using both DC and AC inputs.
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Chapter 5 EGR 260 Circuit Analysis
Load Connections Vo is typically determined
independent of the load (the circuit connected to
the output). Once Vo has been determined, it
essentially acts like a voltage source to the
load.
Load Current Io is the output current for an op
amp. It can be found using KCL.
Example Find Vo , I1, V2, and Io below.
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Chapter 5 EGR 260 Circuit Analysis
Example Determine an expression for Vo in the
non-inverting amplifier shown below.
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Chapter 5 EGR 260 Circuit Analysis
Example Determine Vo in the inverting summing
amplifier shown below.
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Chapter 5 EGR 260 Circuit Analysis
Example Determine Vo in the non-inverting
summing amplifier shown below.
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Chapter 5 EGR 260 Circuit Analysis
Example Determine VL in the circuit shown below.
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Chapter 5 EGR 260 Circuit Analysis
Example Determine Vo in the circuit shown below.
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Chapter 5 EGR 260 Circuit Analysis
Practical Limitations in op amps Operational
amplifier circuits are generally easy to analyze,
design, and construct and their behavior is
fairly ideal. There are, however, some
limitations to op amps which the engineer should
recognize. There are three primary limitations
as well as some minor limitations that will be
discussed in later courses.
The three primary limitations in op amps are 1)
Limited voltage - In general, the output voltage
is limited by the DC supply voltages. 2) Limited
current - The output current has a maximum limit
set by the manufacturer (check the data
sheet). 3) Frequency limitations - Op amp
performance may deteriorate significantly as
frequency increases (studied in later courses)
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Chapter 5 EGR 260 Circuit Analysis
Voltage Limitations Vo for any op amp circuit is
limited by the supply voltage. In general,
If Vo attempts to exceed these limits, the output
is limited to VDC or -VDC and we say that the
op amp is saturated or is in saturation.
Practically, Vo is often about 2V under the
supply voltage, or
Example Consider the inverting amplifier shown
below (covered earlier). 1) Determine the voltage
gain, ACL Vo/Vin
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Chapter 5 EGR 260 Circuit Analysis
2) Determine Vo for various possible values of
Vin (fill out the table shown below)
3) Graph Vo versus Vin . Identify the saturation
and linear regions of operation.
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Chapter 5 EGR 260 Circuit Analysis

• Example Consider the inverting amplifier shown
  below (covered earlier).
• If R2 4k?, determine range of values for Vin
  such that the op am will operate in the linear
  range
• If Vin 2V, determine R2 (max) such that the op
  am will operate in the linear range

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Chapter 5 EGR 260 Circuit Analysis
Example Sketch Vo (on the same graph) for the
circuit shown below if Vin is a triangle wave as
specified below.
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Chapter 5 EGR 260 Circuit Analysis
Current Limitations The maximum output current,
Io for an op amp is specified by the
manufacturer. Exceeding this limit will
typically destroy the op amp. The output current
can be calculated using KCL at the output node.
An op amp circuit should be designed to insure
that its output current does not exceed the
maximum value, Io (max), specified by the
manufacturer.
Example If Io (max) is specified at 25 mA by
the manufacturer, determine the minimum value of
RL that can safely be used in the circuit shown
below.
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Chapter 5 EGR 260 Circuit Analysis
Using node equations to analyze op amp
circuits As op amp circuits become more complex,
simultaneous equations may be needed to analyze
them. Node equations are a natural choice since
many op amp voltages are expressed as node
voltages. Note Writing a KCL (node) equation
at the output node is not typically helpful
except to find Io since it introduced another
unknown (Io).
Example Determine Vo in the circuit shown below.
Note Writing a KCL equation (node equation) at
the output is only helpful for finding Io since
it introduces another unknown (Io).
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Chapter 5 EGR 260 Circuit Analysis
Example Determine Vo in the circuit shown below.
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Chapter 5 EGR 260 Circuit Analysis
Example The circuit shown below is a current
amplifier. Determine an expression for IL .
Also find the current gain, AI IL/IS.
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Chapter 5 EGR 260 Circuit Analysis
Op amp models So far we have analyzed op amps
using a few ideal assumptions about op amps (such
as V V- and I I- 0) . How would we
convey these assumptions to a circuit analysis
program like PSPICE? Typically, we would
construct a circuit model that acts like the op
amp that we desire. A simple op amp model is
shown below. Also note that PSPICE can be used
to model op amps with specific part numbers (such
as the uA741 in the PSPICE library EVAL.SLB). In
these cases, ORCAD develops very detailed circuit
models that match the characteristics of the
particular op amp. The ORCAD model might look
like the model shown below plus additional
components to more accurately model additional
features.
Typical values for the op amp model shown AOL
100,000 Rin 2M? - 10M?
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Chapter 5 EGR 260 Circuit Analysis
Example Determine Vo in the circuit shown in
two ways 1) by making ideal op amp assumptions
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Chapter 5 EGR 260 Circuit Analysis
Example Determine Vo in the circuit shown in
two ways 2) by using an ideal op amp model with
Rin 2M? and AOL 100,000.
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Chapter 5 EGR 260 Circuit Analysis
Analyzing operational amplifier circuits using
PSPICE There are two ways to analyze op amp
circuits using PSPICE. 1) Use the general op amp
model just introduced (consisting of a resistor
and a voltage-controlled voltage source. 2) Use
one of the op amp models from a PSPICE library
(such as the uA741). Refer to two examples on
the course web site 1) Op Amp Example using a
General Op Amp Model 2) Op Amp Circuit using a
Library Model ( uA741)
Note End of Test 2 material here.