Announcements

• Tuesday’s Lecture next week is cancelled– October 18th

• Assignment 4 is active, due in my mailbox by 5pm Friday (October 14th)

• Mid-term Thursday, October 27th

Project Dates• Project Description - one paragraph, plus circuit diagrams and web links –

email to me by Tuesday Nov 1st• Guidelines and a few useful links are here:

http://www.physics.udel.edu/~jholder/Phys645/Lab/Projects.htm . There are many more sites if you search the web (e.g. google “hobby electronics”)

• Kits are allowed, but circuits must be assembled on the prototyping board. $50 maximum budget.

• Once approved, I will need a complete parts list, with digikey or radioshack catalog part numbers. I will place the orders, but FINDING THE CORRECT COMPONENTS AND GETTING THEM IN TIME IS YOUR RESPONSIBILITY!!! Note that most basic components (resistors, capacitors etc.) are available in the lab.

• The project should (ideally) contain both analog and digital • You should work with your lab partner, but individual reports are required

for the projects.• The project counts for 20% of your final grade (I grade them)• I will leave copies of some good past projects in the lab (please don’t take

them away)

Lecture 12 Overview

• Op amp circuits– amplifiers– Adding/ Subtracting– Integrating Circuit– Differentiating Circuit– Active Filters

Recap: Opamps

• DC coupled, very high gain, differential amplifier.• Feed part of the output back into the inverting

input to get stable operation in the linear amplification region

• Golden rules under negative feedback:• The voltage at the inputs is the same (v+=v-)• No current flows into the opamp (i+=i-=0)

Op amp circuit 2: Inverting Amplifier

SS

Fout

F

out

S

S

F

out

S

S

FS

inFS

vR

Rv

R

v

R

v

R

vv

R

vv

ii

iii

00

0

• Signal and feedback resistor, connected to inverting (-) input.

• v+=v- connected to ground

S

F

S

out

R

R

v

vGain

0 vvv+ grounded, so:

Op amp circuit 3: Summing Amplifier

SNSN

FS

S

FS

S

Fout

F

out

SN

SN

S

S

S

S

FN

vR

Rv

R

Rv

R

Rv

R

v

R

v

R

v

R

v

iiii

.....

.....

.....

22

11

2

2

1

1

21

• Same as previous, but add more voltage sources

)...( 21 SNSSS

Fout vvv

R

Rv

SSNSS RRRR ... If 21

Summing Amplifier Applications• Adds signals from a number of waveforms• Applications - audio mixer• http://wiredworld.tripod.com/tronics/mixer.html

• Can use unequal resistors to get a weighted sum• For example - could make a 4 bit binary - decimal converter• 4 inputs, each of which is +1V or zero• Using input resistors of 10k (ones), 5k (twos), 2.5k (fours) and 1.25k (eights)

Op amp circuit 4: A non-inverting amplifier

• Feedback resistor still to inverting input, but no voltage source on inverting input (note change of current flow)• Input voltage to non-inverting input

vv FS ii

F

out

S R

vv

R

v

0

S

F

S

out

SS

Fout

S

Fout

R

R

v

v

vR

Rv

vR

Rv

1Gain

1

1

Op amp circuit 5: Differential Amplifier (subtractor)

021 ii

)( 121

2

221

2

21

1

vvR

Rv

vvRR

Rv

vv

R

vv

R

vv

out

out

Useful terms: • if both inputs change together, this is a common-mode input change• if they change independently, this is a normal-mode change • A good differential amp has a high common-mode rejection ratio (CMMR)

Differential Amplifier applications• Very useful if you have two inputs corrupted with the same noise

• Subtract one from the other to remove noise, remainder is signal

• Many Applications : e.g. an electrocardiagram measures the potential difference between two points on the body

The AD624AD is an instrumentation amplifier - this is a high gain, dc coupled differential amplifier with a high input impedance and high CMRR (the chip actually contains a few opamps)

http://www.picotech.com/applications/ecg.html

Op-amp integrator

Op-amp integrator

Integrator Application: Ramp Generator

Integrator response to a constant voltage:VIN

VOUT

tThis is a ramp generator - very useful in timing circuits...

V

V• What's the integrator response to a square wave?

Integrator Application: Ramp Generator

Integrator response to a constant voltage:VIN

VOUT

t

t

This is a ramp generator - very useful in timing circuits...

• ...Useful for waveform generators:

V

V

VIN

VOUT

• What's the integrator response to a square wave?

What does this do?

Op-amp differentiator

dt

dvCRtv

dt

dvC

R

v

ii

SSFout

SS

F

out

SF

)(

Differentiator

• Differentiator response to a square wave?:

Differentiator Application: edge detection

• Differentiator response to a square wave?:

• The differentiator is good at detecting edges, or transitions - very useful in digital circuits.

VIN

VOUT

t

N.B. Don't confuse the differentiator with a differential amplifier (subtractor)!

Other "mathematical operator" circuits can be

easily constructed:

• Logarithm

• Antilogarithm

• Multiplier

• Divider

• Square root function

What about complex impedances?

S

F

S

out

Z

Z

V

V

S

F

S

out

Z

Z

V

V1

Active low-pass filter

FF

SF

FF

FF

FFF

S

F

S

out

CRj

RRjA

CRj

RZ

CjRZ

Z

Z

V

VjA

1

/)(

1

1111

)(

e.g. RF/RS=10; 1/RFCF=1

Max Amplification: RF/RS

Low pass factor: 1/(1+ jωRFCF)Cut-off frequency (-3dB = 1/√2)when ωRFCF=1, ie ω0=1/RFCF

Active high-pass filter

SS

S

F

SS

F

SSS

S

F

S

out

CRjR

R

CjR

RjA

CjRZ

Z

Z

V

VjA

11

1

1)(

1

)(

e.g. RF/RS=10; 1/RFCF=1

Max Amplification: RF/RS

High pass factor: 1/(1+ 1/jωRSCS)Cut-off frequency: ωRFCF=1

Active band-pass filter

Combine the two:

)1)(1()(

SSFF

SF

CRjCRj

CRjjA

Advantages of active filters: 1)no inductors (large, pick-up)2)buffered (high input impedance, low output impedance) – so filter performance independent of source and load; can cascade filters