rc amplifier

7/30/2019 rc amplifier

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2000 Prentice Hall Inc.

Figure 1.17 Model of an electronic amplifier, including input resistance Riand output resistance Ro.


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Figure 1.25 Current-amplifier model.


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Figure 1.28 Transconductance-amplifier model.


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Figure 1.30 Transresistance-amplifier model.


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Figure 1.35 Periodic square wave and the sum of the first five terms of its Fourier series.


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Figure 1.46 Setup for measurement of common-mode gain.


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Figure 1.47 Setup for measuring differential gain. Ad= vo/vid.


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Figure 1.44 The input sources vi1 and vi2 can be replaced by the equivalent sources vicm and vid.


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Operational amplifier Operational amplifier, or simply OpAmp refers to an integrated

circuit that is employed in wide variety of applications (including

voltage amplifiers)

OpAmp is a differential amplifier having both inverting and non-inverting terminals

What makes an ideal OpAmp infinite input impedance

Infinite open-loop gain for differential signal

zero gain for common-mode signal

zero output impedance

Infinite bandwidth

1iv

)21( iido vvAv

2iv

Noninverting input

Inverting input

ovidv

oi

ii

1iv 2iv

ivovA


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Summing point constraint In a negative feedback configuration, the

feedback network returns a fraction fo the outputto the inverting input terminal, forcing thedifferential input voltage toward zero. Thus, theinput current is also zero.

We refer to the fact that differential input voltage

and the input current are forced to zero as thesumming point constraint

Steps to analyze ideal OpAmp-based amplifiercircuits

Verify that negative feedback is presentAssume summing point constraints

Apply Kirchhoffs law orOhms law


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Some useful amplifier circuits Inverting amplifier

Noninverting amplifier

Voltage follower if and open circuit (unity gain)

2R

inv

1R

lRoutv 0

//

1

12

out

in

inoutv

Z

RZ

RRvvA

2R

inv

1R

lRoutv 0

/1/ 12

out

in

inoutv

Z

Z

RRvvA

02 R 1R


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Amplifier design using OpAmp Resistance value of resistor used in

amplifiers are preferred in the range of(1K,1M)ohm (this may change depending

on the IC technology). Small resistance

might induce too large current and largeresistance consumes too much chip area.


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OpAmp non-idealities I Nonideal properties in the linear range of operation

Finite input and output impedance Finite gain and bandwidth limitation

Generally, the open-loop gain of OpAmp as a function of frequency

is

Closed-loop gain versus frequency for non-inverting amplifier

Gain-bandwidth product:

Closed-loop bandwidth for both non-inverting and inverting

amplifier

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OpAmp non-idealities II Output voltage swing: real OpAmp has a maximum and minimum

limit on the output voltages

OpAmp transfer characteristic is nonlinear, which causesclipping at output voltage if input signal goes out of linear range

The range of output voltages before clipping occurs depends onthe type of OpAmp, the load resistance and power supplyvoltage.

Output current limit: real OpAmp has a maximum limit on the output

current to the load The output would become clipped if a small-valued load

resistance drew a current outside the limit

Slew Rate (SR) limit: real OpAmp has a maximum rate of change ofthe output voltage magnitude

limit

SR can cause the output of real OpAmp very different from anideal one if input signal frequency is too high

Full Power bandwidth: the range of frequencies for which theOpAmp can produce an undistorted sinusoidal output with peakamplitude equal to the maximum allowed voltage output

SR

dt

dvo

max2 oFP v

SRf


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Slew Rate

Linear RC Step Response: the slope of the step response is

proportional to the final value of the output, that is, if we

apply a larger input step, the output rises more rapidly.

If Vin doubles, the output signal doubles at every point,therefore a twofold increase in the slope.

But the problem in real OpAmp is that this slope can not

exceed a certain limit.

Copyright Mcgraw Hill Company


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Slewing in Op Amp


In the above case, if input is too large, output of the OpAmp

can not change than the limit, causing a ramp waveform.

Output resistant

of OpAmp


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OpAmp non-idealities III DC imperfections: bias current, offset current and offset voltage

bias current : the average of the dc currents flow into the noninverting

terminal and inverting terminal , offset current: the half of difference of the two currents,

offset voltage: the DC voltage needed to model the fact that the output isnot zero with input zero,

The three DC imperfections can be modeled using DC current and voltagesources

The effects of DC imperfections on both inverting and noninverting amplifieris to add a DC voltage to the output. It can be analyzed by considering theextra DC sources assuming an otherwise ideal OpAmp

It is possible to cancel the bias current effects. For the inverting amplifier, wecan add a resistor to the non-inverting terminal

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When Vin=0, Vout is NOT 0 due to mismatch of transistors in real circuit

design. It is more meaningful to specify input-referred offset voltage, defined as

Vos,in=Vos,out / A.

Offset voltage may causes a DC shift of later stages, also causes limited

precision in signal comparison.

DC offset of an differential pair


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OpAmp non-idealities IV

Nonlinear OpAmp gain (harmonic distortion)ideal case:

real case:

Assume

and note that

then (1) becomes

We can neglect ifUis very small.


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OpAmp non-idealities IV

Text copied from W. Sansen, Distortion in elementary transistorcircuits, IEEE Transactions on

Circuits and Systems II, Vol 46, No. 3, March 1999.


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OpAmp non-idealities IV As you probably can see, when you have a fully

differential amplifier, the even order (2nd, 4th etc) orderharmonic distortion cancels each other.

Therefore, in typical circuit design, third order harmonic

distortion (HD3) component is most dominant distortion

component. ( in applications where mixed frequency

components are process, distortion caused by inter-

modulation is also to be considered.)


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Behavioral modeling of OpAmp Behavioral models is preferred to include as many non-idealities of

OpAmp as possible.

They are used to replace actual physical OpAmp for analysis and fast

simulation.


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Important amplifier circuits I Inverting amplifer

AC-coupled inverting amplifier

Summing amplifier

Noninverting amplifier

AC-coupled noninverting amplifier

Bootstrap AC-coupled voltagefollower

0

/

1

12

out

in

v

Z

RZ

RRA

0

/

1

12

out

in

v

Z

RZ

RRA

0

/

2

1

/

out

BBin

AAin

BAfv

Z

vforRZ

vforRZ

RRA

0

/1 12

out

in

v

Z

ZRRA

0

/1 12

out

biasin

v

Z

RZ

RRA

0

1

out

in

v

Z

Z

A

Graphs from Prentice Hall


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Important amplifier circuits II Differential amplifier

Instrumentation qualify Diff Amp

Voltage-to-current converter

Howland voltage-to-currentconverter for grounded load

Current-to-voltage amplifier

Current amplifier

0 143

out

in

ZvforRRZ

0

out

in

Z

Z

out

in

finom

Z

Z

RviG /1/

out

Lin

m

Z

RRRRZ

RG

)/(

/1

221

2

0

0

out

in

fm

Z

Z

RR

out

in

vi

Z

Z

RRA

0

)/1( 12

Graphs from Prentice Hall


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Important amplifier circuits III Integrator circuit: produces an

output voltage proportional to

the running time integral of the

input signal

Differentiator circuit: produces

an output proportional to the

time derivative of the input

voltage

rc amplifier

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