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Chapter 6-4 Operational amplifier

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Instrumentation amplifier

Very high input impedance Large common mode rejection ratio (CMRR) Capability to amplify low level signals Consistent bandwidth

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Integrator

dtvRC

Vt

o inO ∫−=∴1

Lossless capacitor

( ) ( ) ( )dttxkdttxRC

tyt

o

t

o ∫∫ −=−=∴1

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Differentiation and integration

dtvRC

Vt

o inO ∫−=∴1

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Improved Integrator

Lossy capacitor

Rs is shunt resistor Rs=10R1

The use of shunt resistor is to limit the low frequency gain of the circuit. Otherwise, a small DC offset at the input would be integrated over time, eventually saturating the op amp. DC offset due to the input bias current can be minimized by R2. Choose:

s

s

RRRRR+

=1

12

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Integrator

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Example

( )Vtuev ts

215 −=

( ) Vvo 100 =

Find vo(t) for t>0

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Summing Integrator

( ) ( ) ( ) ( ) ( ) ( ) ( )2

2

1

1

2

2

1

121 R

txR

txR

tvR

tvtititic +=+=+=

( ) ( )dttiC

tvt

o cc ∫=1

( ) ( ) ( ) tdR

tvR

tvC

tvt

c ∫

+=

02

2

1

11( ) ( ) ( ) td

CRtx

CRtxty

t

∫

+−=

02

2

1

1

( ) ( ) ( )[ ] tdtxktxktyt

∫ +−=0 2211

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Differentiator

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Differentiator

The input signal to the differentiator is applied to the capacitor. The capacitor blocks any DC content so there is no current flow to the amplifier summing point, resulting in zero output voltage. The capacitor only allows AC type input voltage changes to pass through and whose frequency is dependant on the rate of change of the input signal. At low frequencies the reactance of the capacitor is "High" resulting in a low gain (Rf/Xc) and low output voltage from the op-amp. At higher frequencies the reactance of the capacitor is much lower resulting in a higher gain and higher output voltage from the differentiator amplifier.

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Differentiator

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Improved Differentiator Amplifier

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Example: Integrator and Switch An integrator and a voltage-controlled switch

An integrator is a circuit that can perform the mathematical operation of integration. The output voltage, vo(t), is related the input of the integrator, vs(t).

( ) ( ) ( )10

2

1

tvdttvKtv o

t

t s +⋅= ∫

Integrators have many applications. One is to measure a time interval t2-t1.

( ) ( ) ( )11220 tvVttKtv os +⋅−⋅=

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Example: Integrator and Switch Voltage controlled switch

- Switch can be controlled electronically. The node voltage, vc(t), is called the control voltage.

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Example: Integrator and Switch To design an integrator circuit

( ) ( )122 20010 tt

msVtvo −⋅=

( ) ( ) ( )1122 tvVttKtv oso +⋅−⋅=

msVVK s 200

10=⋅

sK 110=

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Example

KRC

dtvRC

vt

t so

=

−= ∫1

1 2

1

( ) Ω=⋅

=

=

kFsV

R

FC

100110

11

µ

µ

( ) ( )150 tttvo −−=

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Op-Amp Open Loop Gain In Op-amp, practically, the gain is so high that the output will be driven to +Vcc or –Vcc for any appreciable difference between V1 and V2. This is useful in the comparator. For practical applications other than the comparator, negative feedback is used to control the device gain.

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Comparator The extremely large open-

loop gain of an op-amp makes it an extremely sensitive device for comparing its input with zero.

For practical purposes, if V2 >V1, the output is driven to the positive supply voltage; If V2 <V1 it is driven to the negative supply voltage. The switching time for - to + is limited by the slew rate of the op-amp.

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Comparator The basic comparator will swing its output to at the slightest

difference between its inputs. But there are many variations where the output is designed to switch between two other voltage values VH and VL. Also, the input may be tailored to make a comparison to an input voltage VT other than zero.

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Comparator: application Often it is desirable that switching occurs at prescribed

voltage . Comparator can be used for this purpose.

( )

<>

=−+

−+

vvifVvvifV

tvL

Ho

VH and VL are the only two values that vo(t) can have.

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Comparator: Example

( ) ( )( )

<>

=TcL

TcHo VtvifV

VtvifVtv

For the following circuit, suppose VA >VT > vc(0), VT is a threshold voltage; and the input voltages for the comparator are

( )T

c

Vvtvv

==

−

+

The output voltage

The capacitor voltage ( ) ( )[ ] ( )RCtAcAc eVvVtv −−+= 0

At t1, the comparator voltage switches from VL to VH

( )[ ] ( )RCtAcAT eVvVV 10 −−+=

( )

−−

=AT

Ac

VVVvRCt 0ln1

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Comparator: Example For the shown circuit, the initial value of the capacitor voltage

is vc(0) =1.667V. What value of the resistance, R, is required if the comparator is to switch from VL to VH at time t1=1ms?

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Comparator: Example For the shown circuit, the comparator is used to compare the

resistor voltage vR(t) with a threshold voltage VT. Suppose VA >VT > RiL(0). At time t1, the comparator output voltage switches from VL to VH

( ) ( ) tLR

AL

AL e

RVi

RVti

−

−+= 0

( ) ( )[ ] 10t

LR

ALALT eVRiVtRiV−

−+==

( )

−−

=AT

AL

VVVRi

RLt 0ln1

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Comparator: Example For the shown circuit, the initial value of the inductor is iL(0)

=1mA. What value of the inductance, L, is required if the comparator is to switch from VL to VH at time t1=10ms?

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The Sample and Hold circuit When The Sample and Hold circuit uses two buffers to keep a voltage level stored in a

capacitor. Pressing Ssample will charge the capacitor to the present signal level, while the input buffer ensures the signal won't be changed by the charging process. From there, the output buffer will make sure that the voltage level across the storage cap won't decrease over time.

Pressing Sclear will short out the storage cap, discharging it and setting the output to 0V. We can build the Sample and Hold circuit with mechanical pushbutton switches to see it in

action. In actual practice, the switches used are various forms of transistor switch, which provides cleaner switching and also allows another circuit to control the sample and clearing operations.

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Uses of Linear Op-Amp Circuits Amplifiers

– Making signals bigger!

Summing Amp – Mixing (e.g. audio applications) – Analogue arithmetic

Integrator – Analogue computing – Active filter design

Difference Amp – Balanced line receivers

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Ideal Op-Amp Linear Circuit Analysis

When negative feedback is applied, the use of these assumptions makes design/analysis much easier (although not necessarily simple!).

Of course, they aren’t really true

! anything .3 .2

0 and 0 .1

==

==

+−

−+

OUTVVV

II