Op Amps - curl.bu.educurl.bu.edu/static/content/ek307_spr2020/inclass/Ek307spr2020/ek307lectures_opamps...Op Amps Real and Ideal Op Amps Modeling an Op Amp 1 Ideal Most of the time,

Op Amps

Op Amps

Real and Ideal Op AmpsWorking with real op ampsAmplifiersApplicationsStages and Cascading

Carruthers (ECE @ BU) EK307 Notes Spring 2020 81 / 275

Op Amps Real and Ideal Op Amps

Operational Amplifier

An operational amplifier or op amp is an active circuit elementwith many uses

op amp circuits can sum, amplify, integrate, di↵erentiate signalsand perform other useful functions.



Modeling an Op Amp

1 Ideal Most of the time, op amps are considered to be ideal. Thisis a simple yet accurate description of how a correctly configuredop amp works.

2 VCVS Circuit Model We can use this model to explain why theideal op amp functions the way it does. It also describes “howgood” a particular op amp is.

3 Transistors The actual circuit for an op amp consists of anumber of transistors. This full description can be approximatedby the VCVS circuit model.

Lets examine each of these.



Ideal Op Amp Model: Inputs and Outputs

The simplified op amp circuit element is:

�

+v2

v1vo

There are two inputs:

the inverting input v1

the non-inverting input v2,

and the output vo.



Ideal Op Amp Model: Function

For an ideal op amp:

there is no current into vN or vP terminals.

the input terminals have the same voltage: vN = vP

How is this achieved?



Ideal Op Amp Model: Rules

For an ideal op amp to function according to the “rules” for the inputs(no current, equal voltage), we need the following conditions:

the power must be on: ±Vcc

a connection (R < 1) between the output and the inverting inputmust be present.

the output must be between the power rails �Vcc and +Vcc

When these conditions are not present, we need to think about theVCVS model for the op amp.



VCVS Circuit Model for Op Amp

v0 = A(vP � vN )

A is called the open loop voltage gain and is typically 105 or more.The op amp is a voltage controlled voltage source.



Op Amp Amplifier (Ideal)

�+vs

10 k⌦�

+ +vo

�

20 k⌦

Find the relationship between vo and vs assuming an ideal op-amp.Solution: vo/vs = �2


Vg currentloop Vdropsefok 2Vs

10k Isgso

VotVdrop O Vos 2b

V 24 0


Example 2: non ideal op amp

Find vo/vs assuming an open-loop gain of 2⇥ 105, input resistance of 2M⌦, and output resistance of 50 ⌦.



Model for example 2

Solution: vo/vs = �2.000



Feedback: output modifies input

The concept of feedback is critical to many systemsExamples of systems with feedback:

autopilot of aircraft, telescope-pointing, furnace/thermostat,thryroid hormone (all negative feedback);

musical feedback (microphone or guitar pickup is near thespeaker) and oscillators (both positive feedback).


Op Amps Working with real op amps

Practical Op Amp: 8 Pin Chip

This is the National/Fairchild 741 op amp pin diagram.


cma 1cm

I


Practical Op Amp: Needs Power

Connect VCC to pin 7 and �VCC to pin 4.



Practical Op Amp: KCL still applies

i0 = i1 + i2 + i+ + i�



Practical Op Amp: The output voltage is limited

�VCC vo VCCCarruthers (ECE @ BU) EK307 Notes Spring 2020 95 / 275

P

Op Amps Amplifiers

Inverting Amplifier: vo = �Rf

R1vi


i

gamRI i

Ri

Op Amps Amplifiers

Inverting Amplifier Features

Rf is the feedback resistor

input and feedback connect to inverting input

noninverting input is grounded

the ampifier inverts the sign of the input voltage and providesgain Rf/R1

the input/output relationship does not depend on the op ampparameters (as long as Ri, A, and Ro are su�ciently ideal)


i

Op Amps Amplifiers

Inverting Amplifier Equivalent Circuit

vo = �Rf

R1vi


Op Amps Amplifiers

Example Problem

vi = 100 mV; find vo and current in the 10-k⌦ resistor.

Solution: v0 = �250 mV and i = 10 µA.


Op Amps Amplifiers

Example Problem:+ terminal not at ground

Find v0


Op Amps Amplifiers

Transimpedance Amp:convert current-to-voltage

Show thatvo

is= �R.


Op Amps Amplifiers

Noninverting Amp: v0 =

✓1 +

Rf

R1

◆vi


Op Amps Amplifiers

Voltage Follower / Bu↵er: v0 = vi

Note: this is noninverting amp with R1 = 1 or Rf = 0.


Op Amps Amplifiers

Example Problem

Find v0.

[answer: vo = �1 V.]


Op Amps Amplifiers

Example Problem

Find v0.

[answer: vo = 7 V.]Carruthers (ECE @ BU) EK307 Notes Spring 2020 105 / 275

Op Amps Applications

Summing Amplifier

vo = �✓Rf

R1v1 +

Rf

R2v2 +

Rf

R3v3

◆


Or


Di↵erence Amplifier

vo =R2

R1

✓(1 +R1/R2)

(1 +R3/R4)v2 � v1

◆



Di↵erence Amplifier

When R1/R2 = R3/R4, then the circuit is a di↵erence amplifier and

vo =R2

R1(v2 � v1)

and when also R2 = R1 then the circuit is a subtractor and

vo = v2 � v1



Instrumentation Amplifier




vo =R2

R1

✓1 +

2R3

R4

◆(v2 � v1)

Normally, we set R = R1 = R2 = R3

and control the gain through RG = R4.Thus v0 = Av(v2 � v1) with Av = 1 + 2(R/RG) and the circuit elementis





Op Amps Stages and Cascading

Cascaded Op Amp Circuits

A cascade connection:

Output of one stage is input to the next.Stages do not a↵ect each others input/output relationship.



Example 1

Determine v0 and i0.


o


Example 2

Find v0 if v1 = 0.2 V and v2 = 0.15 V.


v i y

Bis Vos 3kt 514kt1 2 341 104

Vo 031011 2 153 101110 4

10


Re-connecting the output





KCL at +: i0 + v/(2R) + (v � v0)/R = 0KCL at �: (vs � v)/(2R) = (v � v0)/RHence i0 = �vs/(2R)


vzfstvrI.io VpYtdotV OZRr rT b

d tVsfr


va = vs2 � R2

R1(vs1 � vs2)

vo = vs2 � R1

R2(va � vs2) = vs2 � R1

R2

⇣�R2

R1(vs1 � vs2)

⌘= vs1


Documents

Op Amps - curl.bu.educurl.bu.edu/static/content/ek307_spr2020/inclass/Ek307spr2020/ek307lectures_opamps...Op Amps Real and Ideal Op Amps Modeling an Op Amp 1 Ideal Most of the time,