Introduction to operational amplifier designn

Introduction to Operational Amplifier Design

ii

Table of Contents 1 Preface ..................................................................................................... 1-1 2 Introduction............................................................................................... 2-1 3 The Ideal Voltage Feedback Op Amp.............................................................. 3-1

3.1 Ideal Characteristics .............................................................................. 3-2 3.2 Ideal Model with Feedback...................................................................... 3-3 3.3 Inverting or Non-inverting ...................................................................... 3-5 3.4 About the Transfer Function .................................................................... 3-6 3.5 About Input Impedances ........................................................................ 3-7

4 Linear Amplifiers and Attenuators.................................................................. 4-1 4.1 Voltage Follower.................................................................................... 4-1 4.2 Inverting Amplifier or Attenuator ............................................................. 4-2 4.3 Non-Inverting Amplifier .......................................................................... 4-3

5 Summation Amplifier................................................................................... 5-1 5.1 Inverting Summation Amplifier ................................................................ 5-1 5.2 Non-inverting Summation Amplifier.......................................................... 5-3

6 The Integrator............................................................................................ 6-1 6.1 Inverting Integrator............................................................................... 6-1 6.2 Non-inverting Low-pass Filter.................................................................. 6-3

7 The Differentiator ....................................................................................... 7-1 7.1 The Inverting Differentiator..................................................................... 7-1 7.2 Non-inverting High-pass Filter ................................................................. 7-2

8 Practical Considerations ............................................................................... 8-1 8.1 Device Parameters................................................................................. 8-1 8.2 Power Supplies ..................................................................................... 8-2 8.3 Offsetting and Stabilizing........................................................................ 8-3 8.4 Impedance Matching and Phase Compensation .......................................... 8-5

Appendix A. ..Commonly Used Terms ................................................................ A-1 Appendix B. ..Bibliography ............................................................................... B-1


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List of Circuits Circuit 4-1 Voltage Follower .........................................................................................4-1 Circuit 4-2 Inverting Amplifier or Attenuator...................................................................4-2 Circuit 4-3 Non-inverting Amplifier...............................................................................4-3 Circuit 5-1 Inverting Summation Amplifier .....................................................................5-1 Circuit 5-2 Non-inverting Summation Amplifier ..............................................................5-3 Circuit 6-1 Inverting Integrator ....................................................................................6-1 Circuit 6-2 The Non-inverting Integrator ........................................................................6-3 Circuit 7-1 Inverting Differentiator ................................................................................7-1 Circuit 7-2 Non-inverting Differentiator..........................................................................7-2


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List of Figures Figure 3.1-1 Loop analysis example ..............................................................................2-1 Figure 3.1-1 Ideal operational amplifier .........................................................................3-1 Figure 3.1-2 Ideal op amp input impedances ..................................................................3-1 Figure 3.2-1 Ideal op amp feedback model 1..................................................................3-3 Figure 3.2-2 Ideal op amp feedback model 2..................................................................3-4 Figure 3.3-1 Non-inverting examples ............................................................................3-5 Figure 3.3-2 Loop equations for Fig 3.3-1 ......................................................................3-5 Figure 3.4-1 Black box diagram....................................................................................3-6 Figure 3.4-2 Cascaded transfer functions .......................................................................3-6 Figure 3.5-1 Zero impedance source .............................................................................3-7 Figure 3.5-2 Source with internal impedance..................................................................3-7 Figure 4.2-1 E

- and E

+ loops for Circuit 4-2 ...................................................................4-2

Figure 4.3-1 E- and E


Figure 5.1-1 E- loop for Circuit 5-1 ...............................................................................5-1

Figure 5.1-2 Thevenized input for Circuit 5-1..................................................................5-2 Figure 5.2-1 E

+ loop for Circuit 5-2...............................................................................5-3

Figure 5.2-2 E- loop for Circuit 5-2 ...............................................................................5-3

Figure 5.2-3 Thevenized input for Circuit 5-2..................................................................5-4 Figure 6.1-1 E

- and E


Figure 6.2-1 E+ loop for Circuit 6-2...............................................................................6-3


+loops for Circuit 7-1....................................................................7-1

Figure 7.2-1 E+

loop for Circuit 7-2 ..............................................................................7-2 Figure 8.2-1 Filtering the Power Supply .........................................................................8-2 Figure 8.3-1 Avoiding common mode noise ....................................................................8-3 Figure 8.3-2 DC baseline shift example..........................................................................8-3 Figure 8.3-3 E

- loop with Vs = 0 and E

+ loop with bias VB ................................................8-4

Figure 8.4-1 Impedance matching ................................................................................8-5 Figure 8.4-2 Canceling reactance..................................................................................8-6

1 Preface

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1 Preface The scope of this course is the design of basic voltage feedback operational amplifier circuits. Using the ideal op amp model and solving for the currents and voltages at each terminal we get the transfer function as a Laplace Transform. This course provides a practical way of going from paper design to prototyping working circuits. This course is intended for professional electrical engineers. The course-taker should be familiar with the Laplace and inverse Laplace Transforms and basic AC network analysis. After completing the course, there is a quiz consisting of 16 multiple choice questions. On completion, 4 professional development hours will count towards satisfying PE licensure renewal requirements. Navigating the course is facilitated by hyperlinked table of contents on each page or the tags in the bookmark pane.

2 Introduction

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2 Introduction The voltage feedback differential amplifier (“op amp” as it is called) is used in a wide variety of electronic applications such as: linear amplifier/attenuator, signal conditioner, signal synthesizer, computer, or simulator. A practical way to approach designing and implementing an op amp circuit is to start with the ideal model and get an expression that relates the output to the input, regardless of the input. This is accomplished by working with the loop equations in the frequency or s domain [1 ]. In summary, the key to getting the transfer function is that the voltages at the input terminals of a closed-loop op amp circuit mirror each other. Also, no current flows into or out of an input terminal. When a signal is applied to either or both terminals, the output will adjust itself to meet these constraints.

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Course E04-002

http://www.cedengineering.com

3 The Ideal Voltage Feedback Op Amp

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3 The Ideal Voltage Feedback Op Amp The voltage feedback op amp is a discrete device that has 2 input terminals and one output terminal. Without feedback, the output is the difference between the input voltages, multiplied by the open-loop gain (transfer function) of the op amp.

Figure 3.1-1 Ideal operational amplifier

In the open loop model, each input terminal has infinite impedance so no current can flow into an input terminal even with a voltage source or a ground applied. The output terminal has zero output impedance.

Figure 3.1-2 Ideal op amp input impedances The ideal characteristics are summarized in Table 3-1 below

Avol is the open loop gain (transfer function) of the op amp itself, without feedback

The key is in maintaining E += E -

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Course E04-002


3 The Ideal Voltage Feedback Op Amp 3.1 Ideal Characteristics

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3.1 Ideal Characteristics

Summary Of Ideal Characteristics

Zin = ∞ the input impedance at each terminal is infinite

Zout = 0 the output impedance is zero

0=±I no current flows into either of the input terminals

Avol = ∞ the open loop gain is infinite

Bandwidth = ∞ the bandwidth is infinitely wide

No temperature drift

E o = 0 the output voltage is zero when E += E -

Table 3-1 Summary of ideal characteristics

Course E04-002


3 The Ideal Voltage Feedback Op Amp 3.2 Ideal Model with Feedback

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3.2 Ideal Model with Feedback With feedback, all or a portion of the output is tied to either or both input terminals. The difference between the voltages at the input terminals is still equal to zero and again no current flows into either of the input terminals. The voltage at each input terminal is treated as a node and is determined by the loop equations. The terminal voltages are equated and we get a transfer function or closed loop gain which provides the output over the input as a ratio (Laplace Transform). In the following subsections, we’ll look at the feedback models : the non-zero reference and the zero reference feedback models. As the names imply, the non-zero reference model is characterized by the

voltage at either input terminal, 0≠±

E , and the zero-reference model is where the voltage at either

input terminal is referenced to 0 volts or ground; 0=±E .

3.2.1 The non-zero reference model

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Course E04-002


3 The Ideal Voltage Feedback Op Amp 3.2 Ideal Model with Feedback

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3.2.2 The zero-reference model

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Course E04-002


3 The Ideal Voltage Feedback Op Amp 3.3 Inverting or Non-inverting

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3.3 Inverting or Non-inverting The determining factors for whether the output is inverted or not, are the circuit configuration and the loop equations for the terminal currents and voltages. With voltage feedback op amp circuits, which terminal the signal is connected to, by itself, does not determine whether the output is inverted or not. For example, the 2 circuits below are both inverting amplifier/attenuators circuits. The only difference is the op amp input terminals are reversed but both provide an output that is a linear amplifier or attenuator with 180° phase shift or inversion:

Figure 3.3-1 Non-inverting examples Figure 3.3-2 Loop equations for Fig 3.3-1

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Course E04-002


3 The Ideal Voltage Feedback Op Amp 3.4 About the Transfer Function

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3.4 About the Transfer Function The transfer function gives you the output over the input expressed as a ratio. To get the output for a specific input, multiply the Laplace Transform of the input by the transfer function. To convert to the time domain, take the inverse Laplace Transform [2 ]. Using Laplace Transform tables available on the internet or in printed textbooks, is a very useful tool in op amp circuit design. Some online references are listed in Appendix B. Working in the s domain (using Laplace Transforms) is advantageous and readily gives any transients that might exist

Figure 3.4-1 Black box diagram

Figure 3.4-2 Cascaded transfer functions In the time domain, you could not express the transfer function as a ratio. You would have to solve differential equations for the terminal voltages and currents and use the convolution integral to get the output as a function of time, because superposition does not apply.

[2] The time domain representation of Av (that is av(t) = L-1

[Av(s)] ) is actually the unit impulse response of the circuit. The

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Course E04-002


3 The Ideal Voltage Feedback Op Amp 3.5 About Input Impedances

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3.5 About Input Impedances An input source can be either a directly connected zero impedance source, or a thevenin equivalent source with an internal impedance. We need to be aware if a source does have internal impedance. This needs to be considered in determining both the input impedance seen by the voltage source and the transfer function of the circuit.

3.5.1 Directly connected source Consider a directly-connected source, with zero output impedance, connecting to an op amp input terminal, through a series impedance Z1 :

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Course E04-002


4 Linear Amplifiers and Attenuators 4.1 Voltage Follower

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4 Linear Amplifiers and Attenuators The most basic circuit configurations are linear amplifiers and attenuators. Ideally, they provide flat gain or loss across the device-rated bandwidth.

4.1 Voltage Follower The voltage follower circuit provides unity gain with no inversion. This circuit is used to isolate a high impedance source input and provide a buffered output.

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Course E04-002


4 Linear Amplifiers and Attenuators 4.2 Inverting Amplifier or Attenuator

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4.2 Inverting Amplifier or Attenuator The inverting configuration provides flat gain or attenuation with constant 180° phase shift.

Circuit 4-2 Inverting Amplifier or Attenuator


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Course E04-002


4 Linear Amplifiers and Attenuators 4.3 Non-Inverting Amplifier

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4.3 Non-Inverting Amplifier The non-inverting configuration provides flat gain with no phase shift.

Circuit 4-3 Non-inverting Amplifier



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Course E04-002


5 Summation Amplifier 5.1 Inverting Summation Amplifier

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5 Summation Amplifier The summation amplifier provides flat gain or loss and can be configured in an inverting or non-inverting configuration. Typical uses are signal combiner, voltage comparator or summing junction.

5.1 Inverting Summation Amplifier The inverting summation amplifier provides flat gain or loss across the rated bandwidth with constant 180° phase shift.

Circuit 5-1 Inverting Summation Amplifier

Figure 5.1-1 E- loop for Circuit 5-1

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Course E04-002


5 Summation Amplifier 5.1 Inverting Summation Amplifier

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Course E04-002


5 Summation Amplifier 5.2 Non-inverting Summation Amplifier

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5.2 Non-inverting Summation Amplifier The non-inverting summation amplifier provides flat gain across the rated bandwidth with no phase shift.

Circuit 5-2 Non-inverting Summation Amplifier

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Course E04-002



5-4

TOP

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⎞⎜⎜⎝

⎛+

⋅=⎟⎟⎠

⎞⎜⎜⎝

⎛++

+=

⋅=++=

1321

1

1321

321

131

3

RR

VVVV get, we implifyingS RR

RR

3VRV

RV

RV

get, we RR

Rk ngSubstituti

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RV

RV

getwe, Vk-

ngSubstituti

fo

f

o

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Figure 5.2-3 Thevenized input for Circuit 5-2


( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛+

=++=f

o RRR

k where , VVVk

V that know We

dependent.-voltagebetogoingissource each by seen impedance input The

1

13213

1

terminal. -

thefor equations loop the atlook we below, 3-5.2 Figure From

RZand

VVVV so ; Z impedancethevenin with V source equivalent

oneintosources3thethevenizetohaveweratio,aof form the infunctiontransfer the get To

eqeq

E

ii 33321 =

++=

2.-5 Circuitfor functiontransfer the is RR

A

so , RR

VV

get we , RR

Rk ngSubstituti

okVV us giving

0 R

okVV

RokVV

sI ; have we sI Expanding

okV substitute , R

VsI with

0IsI

: have We

fv

fo

f

⎟⎟⎠

⎞⎜⎜⎝

⎛+=

⎟⎟⎠

⎞⎜⎜⎝

⎛+=⎟⎟

⎠

⎞⎜⎜⎝

⎛+

=

=

=⎟⎟⎠

⎞⎜⎜⎝

⎛ −⋅=

−=

−−

−=

==

=

−

1

11

1

1

1

3

3

3

i

i

ii

i EE

circuit. open an is 2-5 Circuitfor impedance input heT

VZ making I us gives I into VokV ngSubstituti

RokVV

sII where I

VZ isV by seen impedance input The

ininin

inin

in

∞====

⎟⎟⎠

⎞⎜⎜⎝

⎛ −⋅===

00

3

ii

iii

Course E04-002



5-5

TOP

( )( ) ( )

( )

( )( ) ( )

V2V

V3RZ

input. the at sourcesother the by seen impedances input the getting to apply nscalculatio same The

average. an calculate can we so sourcesother the of tscoefficien

magnitude and content harmonic the about something know to have we , Zfor value nominal a get To

output. the and sourcesother the from current drawing is V means impedance negative A

VVV when impedance negative a is and ,

VVV when circuit open an is Z So

VV2V

V3RZ

to simplifies which

3RVV2V

VIV

Z is V source by seen impedance input the so

3R

VV2V

R

VVVVI , VVV

- ngSubstituti

R

-V

I current input the soR of impedance series a has V source 2,-5 Circuit In

example;For

source. each of impedance series the is Z and Z

-V

I where

IV

Z is source each by seen impedance input TheVk-

at voltage the that know also We

mn

nin

in

1

in

in

in1

1

nn

nn

n

nino

n

1

1

1

1

n

⎟⎟⎠

⎞⎜⎜⎝

⎛

−⋅=

+<

+−

⎟⎟⎠

⎞⎜⎜⎝

⎛+−

⋅=

+−==

+−=

++−=++=

−=

−=

==

∑

22

31

31

321

321

321

1

321

1

1

1

3213211

1321

11

E

E

E

E .

Course E04-002


6 The Integrator 6.1 Inverting Integrator

6-1

TOP

6 The Integrator Typical uses of the integrator circuit are: noise reduction, simulation of a first order RC low-pass circuit, low pass filter, calculating an integral or just phase compensation.

6.1 Inverting Integrator The inverting integrator provides low-pass filtering with constant +90° phase shift. The roll-off starts at DC. Typical use is direct integration of a time domain function, noise reduction, or low pass filter.

Circuit 6-1 Inverting Integrator




.i

i

ii

iii

1

1

1

1

1

R is 16 Circuitfor V source by seen impedance input The

R

R

V

VZ

R

VI With

R

VII case this in

I

VZ is V by seen Z impedance input The

inin

1inin

inin

−

===

===

zero to out balance voltages terminal the* 0

- 0

oV

:arevoltages terminalthe1,-6CircuitFor

o

==

=

=

+

+

EE

E

E

1.-6 Circuitfor functiontransfer the is sCR

A

sCRVoV

R

VVsC

so II , I and III With

sCVI and , R

VI

us gives I and I into 0 ngSubstituti

VsC

sC

VI and ,

R

VI

: have we loop thefor 1,-6.1 Figure From

v

o

ff

of

f

oo

f

1

1

11

11

1

11

11

1

0

1

−=

−=−=

−===+

==

=

⎟⎠⎞

⎜⎝⎛ −=

−=

−=

∴

−−

−

−−−

−

i

i

i

i

E

EEE

E

Course E04-002


6 The Integrator 6.1 Inverting Integrator

6-2

TOP

6.1.2 Bandwidth Considerations

.components DC have that signals input with working are we if this offset to want may We supply. single a using are we if volts 0or voltage, supply

negative the at saturated be will circuit the of output the means which A (DC), 0s at see We

js at (s)vA of value the us gives js ngsubstituti ; sCR

A 1,6 CircuitFor

v

v

∞−==

ω=ω=−=− .1

1

See Section 8.3.2 for offsetting the baseline.

0

0

0

0

0101

0

11

221

21

21

ω=ω

=ωω

=ω

ω

ω=ωω

⋅ω=ω

ωω

°ω

=

π

⋅=ω

−=

at occurs bandwidth 3dB-our So

)(A

)(A iprelationsh direct the us gives This

)(A)(A which at the is bandwidth 3dB-Our

A

1CR i.e ; at magnitude gain desired the us give to CR select

would we then , frequency lfundamenta a at design the start we If of tindependen is shift phase

90 constant the that noting ; CR1

A where eA A as CRj

A rewrite can We

v

v

vv

v

v

j

vvv

.

Course E04-002


6 The Integrator 6.2 Non-inverting Low-pass Filter

6-3

TOP

6.2 Non-inverting Low-pass Filter The non-inverting low-pass filter provides filtering with phase shift that varies with the complex transfer function.

Circuit 6-2 The Non-inverting Integrator


1RR

VV

A

sCR1

RR

sCR1

k

VV

so VksCR

1V ,

- With

12

ov

121

oo

1

⎟⎟⎠

⎞⎜⎜⎝

⎛+

⋅⎟⎟⎠

⎞⎜⎜⎝

⎛+==

⎟⎟⎠

⎞⎜⎜⎝

⎛+

⋅⎟⎟⎠

⎞⎜⎜⎝

⎛+=⎟⎟

⎠

⎞⎜⎜⎝

⎛+

==⎟⎟⎠

⎞⎜⎜⎝

⎛+

=+

11

11

11

1

3

3

i

i iEE

6.2.1 The input impedance

To calculate the input impedance seen by Vi we analyze the E + loop.

Figure 6.2-1 E+


. sC

R is 2-6 Circuitfor V source by seen impedance input The

sCR

sCsCR

sCRsC

V

VZ so

sCRsC

V to simplifies I in1

1

11

11

1

11

1

1

+

+=+

=

⎟⎟⎠

⎞⎜⎜⎝

⎛+

⋅

=⎟⎟⎠

⎞⎜⎜⎝

⎛+

⋅

i

i

ii

divider voltage a beingk

RRR

k where Vk -

divider voltage a being sCR

1

sCR

1V

sCR

sC1

V

V

:arevoltages terminalthe2,-6CircuitFor

2

2o

1

11

oo

3

1

11

+==

⎟⎟⎠

⎞⎜⎜⎝

⎛+

⎟⎟⎠

⎞⎜⎜⎝

⎛+

=⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

+=

=

+

E

E

E

i i

RsCR

VV

I so sCR

V Recall

R

V I have we 1,-6.2 Figure From

I I , 2-6 CircuitFor

I


1

1

1in

inin

1

1

1

1

11

+−

=+

=+

+−

=

=

=

ii

i

i

ii

E

ECourse E04-002


6 The Integrator 6.2 Non-inverting Low-pass Filter

6-4

TOP

6.2.2 Bandwidth considerations

( )

( ) ( )

( ) 11

10v

v

1

v0v

0v

v0vv

0v0

1-1

1

v

vvv1

v

212

ov

0

CR3

ω whereor ωCR

1 where is point 3dB- The

ωCR

1

)(ωA

)ω(A ,

ωCR

1k1

)ω(A and k1

)(ωA Since

)(ωA

)ω(Aor )(ωA )ω(A where is bandwidth 3dB- The

radians and k1

)(ωA ,ω at that see We

ωCRtan and ωCR

1k1

A where

j-e A A us gives js gsubstituin and form,phasor in A Rewriting

sCR1

k1

A so k1

with

RR

replace slet' ; sCR

1RR

VV

A be to functiontransfer the found we ,Previously

0.ωoffrequencylfundamentaawithfilter pass-loworder first a is 2-6 Circuit

==+

=+

=⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

+⋅==

=⋅=

==

=⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

+⋅=

θ⋅=ω=⎟⎟

⎠

⎞⎜⎜⎝

⎛+

⋅=

⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛+

⋅⎟⎟⎠

⎞⎜⎜⎝

⎛+==

=

θ

θ

21

1

21

11

21

21

0

1

1

11

1

2

22

2

33

i

Course E04-002


7 The Differentiator 7.1 The Inverting Differentiator

7-1

TOP

7 The Differentiator Typical uses of the differentiator circuit are: simulation of a first order RC high-pass circuit, high pass filter, calculating a derivative or just phase compensation.

7.1 The Inverting Differentiator The inverting differentiator provides high-pass filtering with constant - 90° phase shift. The roll-off starts at DC. Typical use is direct differentiation of a time domain function, or high pass filter.

Circuit 7-1 Inverting Differentiator


+loops for Circuit 7-1


sC is 1-7 ircuitCfor V source by seen impedance input The

sCV

VZ sCVI with

CIIwhereI

VZ is V by seen impedance input The

inin

inin

in

1i

i

ii

ii

==

==

0 -

0

V


oo

==

=

=

+

+

EE

E

E

. Circuit orf

functiontransfer the is sCRVoV

vA

sCRVoV

RoV

sCV get we

, fI CI into ngSubstituti

RoV

fI and

sC

VCI

, at voltage the With

RoV

fI and

sC

VCI

where fI CI , Iwith; IfICI

: have we loop thefor 1,-7.1 Figure From

17

1

11

0

11

0

1

1

−

−==

−==

−=

=

=−

−−

−−

=

−===+

−

∴−

=

=

−−

i

ii

i

i

E

EE

E

Course E04-002


7 The Differentiator 7.1 The Inverting Differentiator

7-1

TOP


volts 0 be will circuit the of output the means whichA (DC), 0s at see We

js at (s)vA of value the us gives js ngsubstituti ; sCRA 1,7 CircuitFor

v

v

01

==

ω=ω=−=− .

0

0

0

0101

0

11

2

2

2

2

ω=ω

=ωω

=ω

ω

ω⋅=ωω

ω=ω

ωω

°ω=

π

⋅=ω−=−

at occurs bandwidth 3dB-our So

)(A

)(A iprelationsh direct the us gives This

)(A)(A which at the is bandwidth 3dB-Our

A

CR i.e ; at magnitude gain desired the us give to CR select

would we , frequency lfundamenta a at design the start we If of tindependen is shift phase

90 - constant the that noting ; CR A where eA A as CRjA rewrite can We

ov

v

vv

v

v

j

vvv

.

Course E04-002


7 The Differentiator 7.2 Non-inverting High-pass Filter

7-2

TOP

7.2 Non-inverting High-pass Filter The non-inverting differentiator provides high-pass filtering with frequency-dependent phase shift. Typical use is direct integration of a time function, or noise reduction. The total phase shift is overall frequency dependent (with an imaginary zero and complex pole).

Circuit 7-2 Non-inverting Differentiator


sCRRR

VV

A1

1

2

3ov ⎟⎟

⎠

⎞⎜⎜⎝

⎛+

⋅⎟⎟⎠

⎞⎜⎜⎝

⎛+==

11

i


To calculate the input impedance seen by Vi, we look at the E + loop

Figure 7.2-1 E+


sCR is 7.2 Circuitfor V by seen impedance input The

sCR

sCRCs

V

VZ us gives

I

VZ into I I gubstitutinS

sCRCs

VsCR

sCRVCsI , gSimplifyin

1

1

1

inin

inCin

11

1c

1

1

1

111

+

+=

⎟⎟⎠

⎞⎜⎜⎝

⎛+

⋅

===

⎟⎟⎠

⎞⎜⎜⎝

⎛+

=⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛+

−=

i

i

ii

ii

⎟⎟⎠

⎞⎜⎜⎝

⎛+

⋅⎟⎟⎠

⎞⎜⎜⎝

⎛+=⎟⎟

⎠

⎞⎜⎜⎝

⎛+

=

=⎟⎟⎠

⎞⎜⎜⎝

⎛+

=

+==

⎟⎟⎠

⎞⎜⎜⎝

⎛+

=⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

+=

≡

+

+

11

11

1

11

3

1

1

2

3

1

1o

o1

1

2

2o

1

1

1

1

oo

sCRsCR

RR

sCRsCR

k

VV

VksCR

sCRV so

-

RRR

k where Vk -

sCR

sCRV

sCR

RV

V


i

i

i i

EE

E

E

E

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛+

−=⎟⎟⎠

⎞⎜⎜⎝

⎛+

⋅=+

⎟⎟⎠

⎞⎜⎜⎝

⎛ +−=

+−

=

=

=

11

1

1

1c

1

1

c

Cin

inin

sCRsCR

VVCsI so sCR

sCRV Recall

VsC

sC

VI have we 1,-7.2 Figure Form

I I 2,-7 CircuitFor

I


iii

ii

ii

E

EECourse E04-002


7 The Differentiator 7.2 Non-inverting High-pass Filter

7-3

TOP


( )

( ) ⎟⎠⎞

⎜⎝⎛ −⋅

==⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

+⋅=

=+

⎟⎠⎞

⎜⎝⎛ −π

==⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

+⋅=

φ⋅=ω=⎟⎟

⎠

⎞⎜⎜⎝

⎛+

⋅=

⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛+

⋅⎟⎟⎠

⎞⎜⎜⎝

⎛+==

+

∂

θφθ

14

121

2

21

1

11

1

21

2

2

3

kCR

ω at elyapproximat is ωCR

1k1

)ω(A oS

)ω(A where elyapproximat is bandwidth 3dB The

and ωCRtan , ωCR

ωCRk1

A where

je A A us gives js gsubstituin and form,phasor in A Rewriting

sCRsCR

k1

A so k1

with

RR

replace slet' ; sCR

sCRRR

VV

A be to functiontransfer the found we ,Previously

ed.approximat be will bandwidth 3dB The

0. be cannot and DC beyond just frequency low a is ,ω frequency lfundamenta the So

(t). impulse unit a be will output the signal input an asapplied is functionstepunitaIf DC.passnotwillandfilter pass-highorder first a is 2-7 Circuit

1

v

v

1-1

1

1v

vvv1

1v

21

1

2

3ov

0

i

Course E04-002


8 Practical Considerations

8-1

TOP

8 Practical Considerations Device selection, component tolerances and power supply stability should be the priorities when designing and prototyping a circuit. Practical considerations are device and application specific. Various types of op amps ranging from general purpose, low and high frequency, to application specific devices have their own specifications and recommendations for optimal performance.

8.1 Device Parameters Some commonly used terms and their textbook definition are listed in Appendix A. Manufacturers may use the same terms, call them by other names or introduce new parameters to thoroughly characterize their op amp. Manufacturers may also include application notes on how best to make offset or compensation adjustments for voltage, current and phase. Most of these parameters are centered on an open loop mode. So a circuit designer may not need to be concerned with all of the specifications when designing a circuit. It’s important to select a device that exceeds expectations. For example, the common mode rejection ratio is a value based on open loop gain and small, simultaneous signal variations on larger input levels; essentially nolise. A widely accepted minimum for the CMRR is 70dB. This value implies a level of stability that applies to a closed loop circuit and other parameters of the op amp. Less than 70dB indicates a noisier or less stable device. Below are data sheets for 2 op amps that can be used for comparison. [* links open in new browser window ]

Device Description Overview and Specs PDF

99http://www.national.com/mpf/LM/LM741.html LM741 - Operational Amplifier

General purpose low frequency

99http://www.national.com/ds/LM/LM741.pdf

99http://www.national.com/pf/LM/LMH6609.htmlLMH6609 - 900MHz Voltage Feedback Op Amp

High speed high frequency

99http://www.national.com/ds/LM/LMH6609.pdf

Course E04-002


8 Practical Considerations 8.2 Power Supplies

8-2

TOP

8.2 Power Supplies The decision to use single or dual voltage power supplies may be arbitrary or a design constraint. The better choice is to use a dual balanced supply to minimize circuitry required to offset the DC baseline for AC inputs. If there is no choice and a design must be a single voltage supply, each of the circuits above needs to be modified.

8.2.1 Bypassing the power supply Use a well regulated power supply and bypass with electrolytic capacitors, choke coils or a combination of the 2 to further filter the supply voltage to the circuits. Keep lead lengths or printed circuit board layouts as short as possible.

The best case for filtering out power supply connections is a series choke coil shunted by a capacitor (electrolytic or mylar) to minimize if not eliminate any noise and ringing on the supply rails. Choke coils may be expensive and impose additional space requirements in a final product, but they provide excellent filtering for a prototype.

Figure 8.2-1 Filtering the Power Supply Large electrolytic capacitors shunt out high frequency components and help keep the supply voltage regulated by absorbing voltage spikes or instantaneous load changes. Filtering power supplies helps keep the op amp operating in the range of its rated PSRR

Course E04-002


8 Practical Considerations 8.3 Offsetting and Stabilizing

8-3

TOP

8.3 Offsetting and Stabilizing The op amp data sheet may have specifications for offsetting and stabilizing. Below are cases for avoiding common-mode noise and shifting the DC baseline.

8.3.1 Common mode noise When the intention to apply a constant 0 volts to either input terminal, tie the terminal directly to ground rather than through a resistor. This would prevent any voltage appearing due to leakage currents and having to offset or null it with additional biasing. Recommendations for offsetting mentioned in the op amp data sheet should also be followed.

Figure 8.3-1 Avoiding common mode noise

8.3.2 Shifting the DC baseline Working with AC sources that alternate between positive and negative voltages, and being constrained to using single supply op amps, requires shifting the DC baseline to avoid clipping of the output signal.

Figure 8.3-2 DC baseline shift example

Take Circuit 4 2 Inverting amplifier or attenuator as an example. If we are using a single supply and apply a sine wave as an input, the output produced would only be the positive portion of the input signal. Modifying the circuit as in the figure to the left will provide the DC shift that is needed to provide the expected output; an amplified or attenuated sine wave alternating about a DC baseline With no signal but the DC bias applied, V1 = V2 = VB and R is the thevenin equivalent of voltage dividers as shown in Figs 8.3-3.

Course E04-002


8 Practical Considerations 8.3 Offsetting and Stabilizing

8-4

TOP

Figure 8.3-3 E- loop with Vs = 0 and E

+ loop with bias VB

With no signal applied, the output Vo = VB which is now the baseline for this circuit.

( ) ( )

circuitsator differentior integrator inverting thefor done be can same the circuit, attenuator /amplifier inverting the to shift baseline DC a applied just We

VV beingpeak negative

VV beingpeak positive

voltage. supplypower theand specs amp op the of range the in peaks voltage output the keep to is here constraint design The

RR

tsinVV(t)v outputour , tsinV(t)v inputour and V of magnitude a has V If

RR

VVV becomes amp op the of output the nda V V V becomes

V ,V signal a apply and figure, hand-left the inresistor first the from ground the remove we If

domain. time the in voltage constant a is which

V being Laplace inverse the s

V(s) is VV so domain frequency the in working are we that Note

mDC

mDC

fmDComsDCB

fSBoBS1

1S

DCDC

BB

−

+

⋅ω−=ω=

−=+=

=

2

2

Course E04-002


8 Practical Considerations 8.4 Impedance Matching and Phase Compensation

8-5

TOP

8.4 Impedance Matching and Phase Compensation

Figure 8.4-1 Impedance matching

An input voltage source may have an internal impedance that needs to be matched to achieve: maximum power transfer cancel out any reactances pre-condition the phase The figure to the top left represents either a directly connected voltage source with an internal impedance or a downstream thevenin equivalent source. Shunting the input source with an impedance Zm using RLC components will satisfy the requirements.

components phase any gintroducin without

V V

XjRor Xjor RZ when

ZZ where impedance an Matching

ZZ

ZV becomes then V

g

ggggg

mg

mg

mg

2=

+±=

=

+

⋅

i

i

Course E04-002


8 Practical Considerations 8.4 Impedance Matching and Phase Compensation

8-6

TOP

Figure 8.4-2 Canceling reactance

( )

source the to circuit short a present will

Z with gterminatinreactance, a purely is Z if

R

Xtan of angle phase a gintroducin and

reactance the cancelling thereby RZ

becomes V by seen Z

R

Xj RV V be will input the and

XjR Z Xj RZ with then

ZZ of impedance an seu

portion,reactancethecancelTo

gg

g

g1-

gin

gin

g

ggg

gggggg

gm

∗

∗

∗

∗

=θ

=

=

=±=

=

m

m

m

2

2i

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Appendix A Commonly Used Terms

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Appendix A. Commonly Used Terms Common-Mode Voltage Range Typically the range of voltages on the input terminals for which the amplifier’s performance is specified Common-Mode Rejection Ratio The ratio of differential voltage amplification to common-mode voltage amplification. It is measured by determining the ratio of a change in input common-mode voltage to the resulting change in input offset voltage change. Gain Bandwidth Product The product of a given input frequency and the op-amp open loop gain at that frequency (usually specified in MHz, voltage feedback amplifiers only.) Input bias current The Input Current specification is the average of the currents drawn by the two input pins. Input current is also often called "bias current" Input Offset Current The difference of the currents entering the two input terminals of a balanced amplifier Input Offset Voltage The DC error voltage which exists between the input terminals due to non-ideal balancing of the input stage to the output. It is multiplied by the closed loop gain Offset Current Temperature Coefficient The average rate of change in offset current for junction temperature variation over a specified temperature range Offset Voltage Temperature Coefficient The average rate of change in offset voltage for the junction temperature variation over a specified temperature range Output Offset Voltage The output voltage when the 2 input terminals are grounded. Output Voltage Swing The maximum peak-to-peak output voltage swing under specified load and supply voltages Power Supply Rejection Ratio Power Supply Rejection Ratio (PSRR) can be one of two specifications. DC PSRR is the ratio of the change in a specified parameter (e.g., Full Scale Error) that results from a specified change in the power supply voltage. AC PSRR is measured with a signal of specified frequency and amplitude riding upon the power supply and is the ratio of the output amplitude of that signal at the output to its amplitude on the power supply pin. PSRR is usually specified in dB

Course E04-002


Appendix A Commonly Used Terms

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Slew Rate The rate that an amplifier output changes from one voltage level to another, usually given in V/µsec, when a step or square wave input is applied. Typically it is the average rate measured from 10% to 90% of the total output voltage change Unity Gain Bandwidth The frequency where the amplifier open loop gain equals to one. It equals GBW if the op amp has a single pole roll-off in its frequency response

Course E04-002


Appendix B Bibliography

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Appendix B. Bibliography Printed Material Millman, Jacob. Microelectronics Digital and Analog Circuits and Systems. New York: McGraw-Hill

Book Company,1979

Online Reference List [* links open in new browser window ] Table of Laplace Transforms, s.v. 11http://www.vibrationdata.com/Laplace.htm (September 30, 2007)

Laplace transform:” Table of selected Laplace transforms”.

11http://en.wikipedia.org/wiki/Laplace_transform#Table_of_selected_Laplace_transforms (September

30, 2007)

National Semiconductor, High-Performance Analog for Energy-Efficient PowerWise Designs.

11http://www.national.com/ (September 30, 2007)

Course E04-002


Introduction to operational amplifier designn

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