E80 Spring 2012 - Harvey Mudd College 5 - Op Amp le… ·  · 2014-02-03E80 Spring 2014 . E80 Lecture 4.2 ... Agenda: Operational Amplifier o Recap: Non-inverting amplifier and unity

E80 Lecture 4.1: Basic Electrical Measurements

Op Amps Circuits

E80 Spring 2014

E80 Lecture 4.2: Basic Electrical Measurements

Agenda: Operational Amplifier

o Recap: Non-inverting amplifier and unity gain buffer

o Inverting amplifier (multiplication)

o Summing amplifier (add and subtract)

o Differentiator and integrator

o Difference amplifier

o Instrumentation amplifier

o Transimpedance amplifier

o Active filters

2

E80 Lecture 4.3: Basic Electrical Measurements

Recap: Opamp Model

3

1 v+ = v− (2) 𝑖+= 0, 𝑖− = 0

V-

V+

V+

V-

E80 Lecture 4.4: Basic Electrical Measurements

Recap: Non-inverting Amplifier

4

• Non-inverting amplifier is designed to produce positive voltage gain

Special case:

R1=∞, Rf=0

Unity-gain buffer

𝑣0 = (1 +𝑅𝑓

𝑅1)𝑣𝑖

E80 Lecture 4.5: Basic Electrical Measurements

Inverting amplifier

5

• Inverting amplifier reverses the polarity of the input signal while amplifying (or attenuating) it

i

f

o vR

Rv

1

E80 Lecture 4.6: Basic Electrical Measurements

Summing amplifier

6

• Summing Amplifier is an op amp circuit that combines several inputs and produces an output that is the weighted sum of the inputs.

3

3

2

2

1

1

vR

Rv

R

Rv

R

Rv

fff

o

Q: Is it possible to construct a non-inverting summing amp?

E80 Lecture 4.7: Basic Electrical Measurements

Opamp Circuit With Capacitor

7

Inverting amplifier

What does this circuit do?

How is Vo related to Vi?

E80 Lecture 4.8: Basic Electrical Measurements

Opamp Circuit With Capacitor

8

Integrator circuit

What does this circuit do?

How is Vo related to Vi?

)0()(1

)(0

C

t

io vdvRC

tv

E80 Lecture 4.9: Basic Electrical Measurements

Example

9

What does the output waveform look like?

E80 Lecture 4.10: Basic Electrical Measurements

Solving Differential Equation Using

Opamp Circuit

10

𝑣0 + 3𝑣0 + 2𝑣0 = 4cos (10𝑡)

RC=1 sec

E80 Lecture 4.11: Basic Electrical Measurements

Difference Amplifier

11

• Difference amplifier is a device that amplifies the difference between two inputs but rejects any signals common to the two inputs.

𝑣0 =1 + 𝑅2/𝑅11 + 𝑅3/𝑅4

𝑣2 −𝑅2𝑅1

𝑣1 𝑅1 = 𝑅2 𝑎𝑛𝑑 𝑅3 = 𝑅4

𝑣0 = 𝑣2 − 𝑣1

Special case:

E80 Lecture 4.12: Basic Electrical Measurements

Instrumentation Amplifier

E80 Lecture 4.13: Basic Electrical Measurements

Instrumentation Amplifier Application

(1) Only amplify difference

(2) Infinite Input resistance

zero Output resistance

E80 Lecture 4.14: Basic Electrical Measurements

Transimpedance amplifier for

photodiode

𝑣0 = 𝑖 ∙ 𝑅

D

R

Vbias

photon

voi

• Much easier to measure voltage than current

• Provide large amplification

E80 Lecture 4.15: Basic Electrical Measurements

Active filter

• RC and OpAmp (<1MHz, bulky inductor

in RLC filters)

• 1st order filters

– Low pass

– High pass

– Inverting

– Non-inverting

• 2nd order low pass filter

15

E80 Lecture 4.16: Basic Electrical Measurements

Active Filter Example

Say Rf>Ri

𝐻 𝑗𝜔 = −𝑅𝑓/𝑅𝑖

1 + 𝑗𝜔𝑅𝑓𝐶𝑓

Low pass filter

Sketch Bode Plot

E80 Lecture 4.17: Basic Electrical Measurements

Active Filter Example

17

Non-inverting 1st order low pass active filter

𝐻 𝑗𝜔 =1 + 𝑅2/𝑅31 + 𝑗𝜔𝑅1𝐶1

E80 Lecture 4.18: Basic Electrical Measurements

Active Filter Example

18

Say Rf>Ri

𝐻 𝑗𝜔 = −𝑗𝜔𝑅𝑓𝐶𝑖

1 + 𝑗𝜔𝑅𝑖𝐶𝑖

High pass filter

Sketch Bode Plot

E80 Lecture 4.19: Basic Electrical Measurements

Active Filter Example

19

Non-inverting 1st order high pass active filter

𝐻 𝑗𝜔 =𝑗𝜔𝑅1𝐶1(1 +

𝑅2𝑅3

)

1 + 𝑗𝜔𝑅1𝐶1

E80 Lecture 4.20: Basic Electrical Measurements

Active Filter Example

20

Say R2>R1

𝐻 𝑗𝜔 =−𝑗𝜔𝑅2𝐶1

(1 + 𝑗𝜔𝑅1𝐶1)(1 + 𝑗𝜔𝑅2𝐶2)

Bandpass filter

Sketch Bode Plot

E80 Lecture 4.21: Basic Electrical Measurements

2nd order Active Filter

Sallen-Key Low Pass Filter

21

Find frequency response function of unity-gain Sallen Key

Topology

𝐻 𝑗𝜔 =1

1 + 𝑗𝜔(𝑅1+𝑅2)𝐶1 −𝜔2𝑅1𝑅2𝐶1𝐶2