Chapter 5 – Operational Amplifiers

Chapter 5 – Operational AmplifiersNote: 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.

VO

V+

V-

V +

-

I+

I- +VDC

-VDC +

_ Io

Terminology:V+ = non-inverting input voltageV- = inverting input voltageVo = output voltageIo = output currentI+ = non-inverting input currentI- = inverting input currentVDC = positive and negative DC supply

voltages used to power the op amp (typically 5V to 30V)

V = V+ - V- = difference voltageNote: Sometimes the supply voltage connections are not shown

Reading Assignment: Chapter 5 in Electric Circuits, 9th Edition by Nilsson

1Chapter 5 EGR 271 – Circuit Theory I

Operational Amplifiers

U1

uA741

3

2

74

6

1

5+

-

V+V-

OUT

OS1

OS2

8-pin package (3D view)

8-pin package pinout

uA741 symbol in PSPICE

2Chapter 5 EGR 271 – Circuit Theory I

Typical Operational Amplifier Schematic

3Chapter 5 EGR 271 – Circuit Theory I

Open-loop versus closed-loop operation:

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

OL

OL

oo OL OL

A = open-loop gain (typical value: A = 100,000)

V = differential input voltageVIn general, V = A V or A = V

Closed-loop:

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

applicationCL

oCL

in

A = closed-loop gain VA = V

VO

V+

V-

V +

-

+

_

VO

+

_

Feedback

Vin

4Chapter 5 EGR 271 – Circuit Theory I

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.

5Chapter 5 EGR 271 – Circuit Theory I

Example: Determine an expression for Vo in the inverting amplifier shown below. Illustrate the results using both DC and AC inputs.

Vo +

_ Vin R1

R2

6Chapter 5 EGR 271 – Circuit Theory I

Example: Find Vo , I1, V2, and Io below.

Vo

+

_ 2V 4k

12k

1k

6k

3k

9k V2

+

_

I1

Io

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.

7Chapter 5 EGR 271 – Circuit Theory I

Example: Determine an expression for Vo in the non-inverting amplifier shown below.

Vo +

_

Vin

R1

R2

8Chapter 5 EGR 271 – Circuit Theory I

Example: Determine Vo in the inverting summing amplifier shown below.

Vo +

_ V1 R 1

RF

V2 R 2

V3 R 3

9Chapter 5 EGR 271 – Circuit Theory I

Example: Determine Vo in the non-inverting summing amplifier shown below.

Vo +

_

V1 R1

RF

V2 R2

V3 R3

R

10Chapter 5 EGR 271 – Circuit Theory I

Example: Determine VL in the circuit shown below.

+

_ 2k

3k

3k 2k

4k VL

+

_ 12k

4k + _ 12 V

11Chapter 5 EGR 271 – Circuit Theory I

Example: Determine Vo in the circuit shown below.

10k

+ _ 2 V

8k

+

_

20k

2k

4k +

_

12k

Vo

12Chapter 5 EGR 271 – Circuit Theory I

Practical Limitations in op ampsOperational 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)

13Chapter 5 EGR 271 – Circuit Theory I

Voltage LimitationsVo 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

DC o DC-V V V

DC o DC-V 2 V V - 2 Example: Consider the inverting amplifier shown below (covered earlier).1) Determine the voltage gain, ACL = Vo/Vin

Vo +

_ Vin 4k

12k

+12V

-12V

14Chapter 5 EGR 271 – Circuit Theory I

2) Determine Vo for various possible values of Vin (fill out the table shown below) Vin Vo Vin Vo

0V1V -1V2V -2V3V -3V4V -4V5V -5V

3) Graph Vo versus Vin . Identify the saturation and linear regions of operation. Vo

Vin

15Chapter 5 EGR 271 – Circuit Theory I

Example: Consider the inverting amplifier shown below (covered earlier).1) If R2 = 4k, determine range of values for Vin such that the op am will

operate in the linear range2) If Vin = 2V, determine R2 (max) such that the op am will operate in the

linear range

Vo

+

_Vin

2k

R2

-12V

+12V

16Chapter 5 EGR 271 – Circuit Theory I

Example: Sketch Vo (on the same graph) for the circuit shown below if Vin is a triangle wave as specified below.

Vo

+

_Vin

2k

4k

-10V

+10V

Vin 10V

-10V

20V

-20V

0V

17Chapter 5 EGR 271 – Circuit Theory I

Current LimitationsThe 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.

Vo +

_

4 V

500

1000

RL

Io

18Chapter 5 EGR 271 – Circuit Theory I

Using node equations to analyze op amp circuitsAs 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.

+ _ 2 V

1k

1k +

_

2k

Vo

3k

Note: Writing a KCL equation (node equation) at the output is only helpful for finding Io since it introduces another unknown (Io).

19Chapter 5 EGR 271 – Circuit Theory I

Example: Determine Vo in the circuit shown below.

Vo +

_ 5k

10k

2k

+ _ 10V

4k

20Chapter 5 EGR 271 – Circuit Theory I

Example: The circuit shown below is a current amplifier. Determine an expression for IL . Also find the current gain, AI = IL/IS.

Vo +

_

R1 RL

R2

IS

IL

21Chapter 5 EGR 271 – Circuit Theory I

Op amp modelsSo 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 Theory I 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.

R Vo +

- AOLV V +

_ V-

V+

Simple op-amp model

Lines added only for emphasis

Typical values for the op amp model shown:AOL = 100,000Rin = 2M - 10M

22Chapter 5 EGR 271 – Circuit Theory I

Example: Determine Vo in the circuit shown in two ways:1) by making ideal op amp assumptions

+ _

2V 1k

+

_ 4k

Vo

23Chapter 5 EGR 271 – Circuit Theory I

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.

+ _

2V 1k

+

_ 4k

Vo

24Chapter 5 EGR 271 – Circuit Theory I

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.

25Chapter 5 EGR 271 – Circuit Theory I