Positive Feedback Opamp

CIRCUITS WITH RESISTIVE FEEDBACK

Serhan YAMAÇLI

15th October 2007

Presentation Outline

1. Current-to-voltage Converters

2. Voltage-to-current Converters

3. Current Amplifiers

4. Difference Amplifiers

5. Instrumentation Amplifiers

6. Instrumentation Applications

7. Transducer Bridge Amplifiers

Amplifiers

Voltage-mode amplifiers

Transimpedance amplifiers

Transconductance amplifiers

Currentamplifiers

Voltage Voltage

Current Voltage CurrentVoltage

CurrentCurrent

(Section 1)

(Last lecture)

(Section 2)

(Section 3)

1. CURRENT-TO-VOLTAGE CONVERTERS

• A current-to-voltage converter is a circuit in which current is the input and voltage is the output .

• Voltage-to-current converters are also called transresistance amplifiers.

• The gain of a voltage-to-current converter is the ratio of the output voltage to input current and given in A/V.

Current Voltage

in

out

I

VA (1.1)

Figure 1.1 Transresistance amplifier block diagram


Figure 1.2 Basic I-V converter

00

R

vi OI

IO Riv

(1.2)

(1.3)

Magnitude of the gain is also called sensitivity.


• If a sensitivity of 1V/μA is aimed, R must be 1MΩ.

• The feedback element may also be a frequency dependent element, then the input-output of the circuit can be expressed as:

IO isZv )(0

• The circuit is called a transimpedance amplifier.

• For this type of amplifier, opamp eliminates the input and output loadings.

(1.4)


• If the opamp is non-ideal, then the circuit parameters can be given as

T

rR

T

rRrR

TRA o

ood

i

11

)(||

/11

1

where

od

d

rRr

rT

(1.5)

(1.6)

1. CURRENT-TO-VOLTAGE CONVERTERSSPICE SIMULATIONS OF I-V CONVERTER

The circuit is simulated using LM324 opamp macromodel.

Note: A macromodel is an equivalent circuit that models both linear and non-linear characteristics of a circuit/element [2, 3].

Note 2: LM324 supply voltages are taken as [4]

I_I1

-30mA -20mA -10mA 0A 10mA 20mA 30mA1 V(U3A:OUT) 2 I(I1)

-20V

-10V

0V

10V

20V1

-40mA

-20mA

0A

20mA

40mA2

>>(19.948m,-19.937)

(-19.271m,19.267)

Figure 1.3 DC characteristics of the transresistance amplifier

V15


Frequency

1.0Hz 10Hz 100Hz 1.0KHz 10KHz 100KHz 1.0MHz 10MHz 100MHzV(U3A:OUT) I(I1)

0

0.5

1.0

(1.2669M,704.663m)

Figure 1.4 AC characteristics of the transresistance amplifier

The -3dB cut-off frequency of this amplifier is 1.26MHz.

Time

0s 0.5ms 1.0ms 1.5ms 2.0ms 2.5ms 3.0ms 3.5ms 4.0ms1 V(U3A:OUT) 2 I(I1)

-10V

-5V

0V

5V

10V1

-10mA

-5mA

0A

5mA

10mA2

>>


Figure 1.5 Transient characteristics of the transresistance amplifierR=1k


HIGH-SENSITIVITY I-V CONVERTERS

• High sensitivity values require high resistance values thus they may not be realizable as integrated circuit (IC) form.

• The circuit of Figure 1.6 shows a high-sensitivity I-V converter.

Fig.1.6 High-sensitivity I-V converter


02

1

1

11

R

vv

R

v

R

v O

IRiv 1

(1.7)

(1.8)

Combining (1.7) and (1.8) gives

IO kRiv

R

R

R

Rk 2

1

21

(1.9)

(1.10)

HIGH-SENSITIVITY I-V CONVERTERS

1. CURRENT-TO-VOLTAGE CONVERTERSSPICE SIMULATIONS OF HIGH SENSITIVITY I-V CONVERTER

I_I1

-6.0mA -4.0mA -2.0mA 0A 2.0mA 4.0mA 6.0mA 8.0mA-6.8mA1 V(U3A:OUT) 2 I(I1)

-20V

0V

20V1

-10mA

0A

10mA2

>>(6.6414m,-19.876)

.4502m,19.253)

Figure 1.7 DC characteristics of the high-sensitivity I-V converter

1. CURRENT-TO-VOLTAGE CONVERTERSSPICE SIMULATIONS OF HIGH SENSITIVITY I-V CONVERTER

Frequency

1.0Hz 10Hz 100Hz 1.0KHz 10KHz 100KHz 1.0MHz 10MHz 100MHzV(U3A:OUT) I(I1)

0

1.0

2.0

3.0

(503.501K,2.1926)

Figure 1.8 AC characteristics of the high-sensitivity I-V converter

The -3dB cut-off frequency of this circuit is found to be 503kHz.

SPICE SIMULATIONS OF HIGH SENSITIVITY I-V CONVERTER


Time

0s 0.5ms 1.0ms 1.5ms 2.0ms 2.5ms 3.0ms 3.5ms 4.0ms1 V(U3A:OUT) 2 I(I1)

-20V

-10V

0V

10V

20V1

-10mA

-5mA

0A

5mA

10mA2

>>

Figure 1.9 Transient response of high-sensitivity I-V converter


PHOTODETECTOR AMPLIFIERS

• I-V converters are primarily used in photodetector circuits.

Figure 1.10. Photoconductive (a), and photovoltaic detectors

• The incident light amplitude varies the photodiode current and then it is converted to voltage for further processing. For example in fiberoptic detectors.

2. VOLTAGE-TO-CURRENT CONVERTERS

• A voltage-to-current converter (V-I converter), also called transcoductance amplifier, gets a voltage input and generates a current output proportional to the input voltage.

CurrentVoltage

Figure 2.1 V-I converter block diagram

IO Avi (2.1)

LO

IO vR

Avi1

(2.2)

Ideal case

Practical caseVoltage of load


• For true V-I conversion

OR (2.3)

• (2.3) means an open-circuit. This may cause the circuit not to operate properly since the output current may not have a path.

• Voltage compiance is the range of permissible values of vL for which the circuit works properly.

• Floating-type V-I converter: Both terminals of the load is uncommitted.

• Grounded-type V-I converter: One of the terminals of the load is grounded.


FLOATING TYPE V-I CONVERTORS

Figure 2.2. Floating-type V-I converters

IO vRi

R

vi IO

(2.4)

(2.5)


LIO vvv

OHOOL VvV

)()( IOHLIOL vVvvV

From circuit of Figure 2.2(a):

(2.6)

Opamp output swing voltage region:

(2.7)

Combining (2.6) and (2.7) yields

(2.8)

Voltage compliance of the circuit



For Figure 2.2(b)

R

vi IO

0

The circuit swings to the voltage LO vv

Voltage compliance is then

OHLOL VvV

The voltage compliance is greater than the previous circuit.

(2.9)

(2.10)



• These circuits are said to be bidirectional since the input voltage can be either positive or negative, no matter the polarity, the circuits work properly.

• If the load is a capacitor, the the input-output relation of the circuit would be

IO sCvi

which represents a lossless integrator.

(2.11)

• Integrators are primarily used in waveform generators, V-F, F-V converters, and ADCs.



PRACTICAL V-I CONVERTOR LIMITATIONS

Figure 2.3 V-I converter with practical opamp model

0 DOoLDI virvvv (2.12)

0

R

vv

r

vi DI

d

DO (2.13)

dOO

d

rrRr

rR

RA

//1

/1

(2.14)

odO rrRR )1)(||( (2.15)


SIMULATIONS OF FLOATING TYPE V-I CONVERTORS

V_V3

-15V -10V -5V 0V 5V 10V 15V-I(RL)

-8.0mA

-4.0mA

0A

4.0mA

8.0mA

(-7.4603,-7.4542m)

(7.1693,7.1377m)

Figure 2.4 DC characteristics of the floating V-I converter

Frequency

1.0Hz 10Hz 100Hz 1.0KHz 10KHz 100KHz 1.0MHz 10MHz-I(RL)

0A

0.5mA

1.0mA

(538.270K,706.845u)


Figure 2.5 AC characteristics of the floating V-I converter

The -3dB cut-off frequency of the circuit is 538kHz.


Time

0s 0.5ms 1.0ms 1.5ms 2.0ms 2.5ms 3.0ms 3.5ms 4.0ms1 -I(RL) 2 V(V4:+)

-8.0mA

-4.0mA

0A

4.0mA

8.0mA1

-10V

-5V

0V

5V

10V2

>>


Figure 2.6 Transient characteristics of the floating V-I converter



GROUNDED V-I CONVERTORS

Figure 2.7 Howland current pump and its Norton equivalent circuit


3412

2

// RRRR

RRO

Output resistance of the Howland current pump is

(2.16)

In order to have an infinite output resistance (the ideal current source),

1

2

3

4

R

R

R

R (2.17)

Balanced bridge



satL VRR

Rv

21

1

Voltage compliance of the circuit is

Saturation voltage of theoperational amplifier

(2.18)



EFFECTS OF RESISTANCE MISMATCHES

The balanced bridge can not be implemented in practice. The non-ideality can be modelled by imbalance factor ε

)1(1

2

3

4 R

R

R

R(2.19)

The output resistance of the circuit is found as

1RRo (2.20)


SIMULATIONS OF GROUNDED V-I CONVERTORS

V_V3

-15V -10V -5V 0V 5V 10V 15V-I(R5)

-10mA

-5mA

0A

5mA

10mA

(-7.4474,-7.4396m)

(7.0263,7.0210m)

Figure 2.8 DC characteristics of the grounded-type V-I converter


Figure 2.9 AC characteristics of the grounded-type V-I converter

The -3dB cut-off frequency of the circuit is 178kHz

Frequency

1.0Hz 10Hz 100Hz 1.0KHz 10KHz 100KHz 1.0MHz 10MHz-I(R5)

0.2mA

0.4mA

0.6mA

0.8mA

1.0mA

(176.198K,716.320u)



Time

0s 0.5ms 1.0ms 1.5ms 2.0ms 2.5ms 3.0ms 3.5ms 4.0ms1 V(R1:1) 2 I(R5)

-10V

-5V

0V

5V

10V1

-10mA

-5mA

0A

5mA

10mA2

>>

Figure 2.10 Transient characteristics of the grounded-type V-I converter

• Note the inverse direction of the current.


2. VOLTAGE-TO-CURRENT CONVERTERSEFFECTS OF FINITE GAIN OF OPAMP

If the open-loop gain of opamp is α, then the output resistance of the Howland current pump is

12

21 /11)||(

RRRRRO

RO decreased from infinite to this finite number.

(2.21)

2. VOLTAGE-TO-CURRENT CONVERTERSEFFECTS OF FINITE GAIN OF OPAMP

Figure 2.11 Improved Howland circuit

1

22

3

4

R

RR

R

R BA (2.22)

Balance condition:

IB

O vR

RRi

2

12 / (2.23)

Transfer characteristics:

The advantage of the circuit is to provide power saving.

3. CURRENT AMPLIFIERS

Opamps can be used as current amplifiers.

The transfer characteristics of a practical current amplifier:

LO

IO vR

Aii1

Output current Gain Output resistance Load voltage

Ideally, iO must be independent of vL, that is

OR

(3.1)

(3.2)


FLOATING TYPE CURRENT AMPLIFIER

Figure 3.1 Floating type current amplifier


FLOATING TYPE CURRENT AMPLIFIER

01

2 II

O iR

Rii

1

21R

RA

IO Aii

(3.3)

(3.4)

(3.5)

For infinite-gain opamp:

Note that output resistanceapprocahes infinity.

If

If the open-loop gain of opamp is α

/11

/1 12

RRA (3.6)

)1(1 RRO (3.7)

Voltage compliance is:

)()( 1212 RiVvRiV OLLOH

(3.8)


GROUNDED TYPE CURRENT AMPLIFIER

Figure 3.2 Grounded type current amplifier

LO

SO vR

Aii1

1

2

R

RA

SR

R

RRO

1

2

Input-output relation:

Where the gain is

Output resistance is:

Source resistance

If A=-1, the circuit is called as current reverser

or current mirror.

(3.9)

(3.10)

(3.11)


SIMULATIONS OF FLOATING TYPE CURRENT AMPLIFIER

Figure 3.3 DC transfer characteristics of grounded current amplifier

I_I1

-16mA -12mA -8mA -4mA 0A 4mA 8mA 12mA 16mAI(I1) - I(RL)

-20mA

-10mA

0A

10mA

20mA

(14.820m,-

(-14.050m,14.060m)



Frequency

1.0Hz 10Hz 100Hz 1.0KHz 10KHz 100KHz 1.0MHz 10MHzI(I2) -I(RL)

0A

0.5mA

1.0mA

(1.1538M,712.435u)

Figure 3.4 AC transfer characteristics of grounded current amplifier

Time

0s 0.5ms 1.0ms 1.5ms 2.0ms 2.5ms 3.0ms 3.5ms 4.0msI(I2) I(RL)

-1.0mA

-0.5mA

0A

0.5mA

1.0mA



Figure 3.5 Transient characteristics of grounded current amplifier

4. DIFFERENCE AMPLIFIERS

A difference amplifier is an amplifier that has one output and two inputs andsatisfies:

• Amplification of the difference voltage at the input terminals• Rejection of the common voltage at the input terminals

Figure 4.1 Difference amplifier (a), differential and commoninputs (b)


1

2

3

4

R

R

R

R

The bridge balance must be satisfied to operate:

(4.1)

)( 121

2 vvR

RvO (4.2)

Output voltage Differential input voltage


Differential mode component:

12 vvvDM

Common mode component:

221 vv

vCM

Input voltages can be expressed in terms of differential mode and common mode inputs (Figure 4.1b):

21DM

CM

vvv

22DM

CM

vvv

(4.3)

(4.4)

(4.5)

(4.6)


The common mode and differential mode input resistances can be exxpressed as

Figure 4.2 Differential mode and common mode input resistances

12RRid 2

21 RRRic

(4.7) (4.8)

4. DIFFERENCE AMPLIFIERSEFFECTS OF RESISTANCE MISMATCHES

A difference amplifier is insensitive to common mode for infinite gain and perfectlybalanced resistances. If the opamp is ideal but the resistances are mismatched:

)1(' 22 RR (4.9)

imbalance factor

CMCMDMdmO vAvAv

2

21

21

21

1

2 RR

RR

R

RAdm

21

2

RR

RACM

(4.10)

(4.11)

(4.12)Figure 4.3 Differential mode and common

mode input resistances


• Adm is called the differential mode gain.• Acm is called the common mode gain.

cm

dm

A

ACMRR

Common mode rejection ratio

(4.13)

cm

dmdB A

ACMRR 10log20 (4.14)

CMRR in dB


If ε<<1, then

21

2

1

2 /RR

R

R

R

A

A

cm

dm (4.15)

12

10

/1log20

RR

A

A

dBcm

dm (4.16)

• For a fixed imbalance factor, CMRR increases with increasing R2/R1.


SIMULATIONS OF DIFFERENTIAL AMPLIFIER INA105 from BURR-BROWN

• INA105 is a monolithic differential amplifier that employs very good matched resistors (2/10000 sensitivity).

Figure 4.4 INA 105 monolithic differential amplifier [5]

V_V1

-5.0V -4.0V -3.0V -2.0V -1.0V 0.0V 1.0V 2.0V 3.0V 4.0V 5.0VV(V1:+) V(U1:OUT)

-5.0V

0V

5.0V

(3.5702,-3.5518)

(-1.1491,1.0851)

(-429.825m,429.950m)

Figure 4.5 DC sweep of INA 105 monolithic differential amplifier

• Note that, in the linear region, if the input voltage is 429.825mV (applied to invertingterminal), output voltage is -429.950mV.



Frequency

1.0Hz 10Hz 100Hz 1.0KHz 10KHz 100KHz 1.0MHz 10MHzV(V1:+) V(U1:OUT)

0V

0.5V

1.0V

(1.4610M,719.235m)



Figure 4.6 AC sweep of INA 105 monolithic differential amplifier

• Note that, -3dB cut-off frequency is 1.45MHz.

Time

0s 0.5ms 1.0ms 1.5ms 2.0ms 2.5ms 3.0ms 3.5ms 4.0msV(V5:+) V(U1:OUT)

-400mV

-200mV

0V

200mV

400mV



Figure 4.7 Transient response of INA 105 monolithic differential amplifier

4. DIFFERENCE AMPLIFIERSDIFFERENCE AMPLIFIER CALIBRATION

Figure 4.8 Difference amplifier calibration circuit

• Rpot is adjusted toachieve calibrated difference amplifier.

4. DIFFERENCE AMPLIFIERSDIFFERENCE AMPLIFIER WITH VARIABLE GAIN

Figure 4.9 Differential amplifier withvariable gain

The CM gain can be given as:

GCM R

R

R

RA 2

1

2 12

(4.17)

• Note that gain is inveresely proportionalwith RG.

4. DIFFERENCE AMPLIFIERSDIFFERENCE AMPLIFIER WITH VARIABLE GAIN

Figure 4.10 Differential amplifier withlinearly adjustible gain

31

2

RR

RRA GCM

The CM gain can be given as:

(4.18)

A linearly tuneable gain is achieved.

4. DIFFERENCE AMPLIFIERSGROUND-LOOP INTERFERENCE PROBLEM

Figure 4.11 An inverting amplifier that is subject to ground-loop interference

Zg is the distributed impedance of theground line. Amplifier sees vi and vgin series, so;

)(1

2giO vv

R

Rv

Figure 4.11 A difference amplifier that eliminates cross-talk for common ground

terminal connections

(4.19)iO v

R

Rv

1

2 (4.20)

5. INSTRUMENTATION AMPLIFIERS

An instrumentation amplifier is a difference amplifier that satisfies:

1. Extremely high (ideally infinite) common mode and differential mode input resistances

2. Very low (ideally zero) output impedance

3. Accurate and stable gain, typically between 1V/V and 1000V/V

4. Extremely high common mode rejection ratio

• Instrumentation amplifiers are used in the areas in which the differential mode input signal level is very low such as transducer output in an industrial application or biomedical engineering.

• The 2nd, 3rd and 4th expressions may be satisfied by a difference amplifier but extremely high input impedance can not be satisfied.

5. INSTRUMENTATION AMPLIFIERSTRIPLE OPAMP INSTRUMENTATION AMPLIFIER

Figure 5.1 Triple opamp instrumentation amplifier configuration

First stage Second stage

)(2

1 213

21 vvR

Rvv

GOO

(5.1)

From the first stage:

From the second stage:

)( 121

2OOO vv

R

Rv (5.2)

Combining these two equations yields:

1

2321.

R

R

R

RAAv

GIIIO

(5.3)

5. INSTRUMENTATION AMPLIFIERSDUAL OPAMP INSTRUMENTATION AMPLIFIERS

Figure 5.2 Dual opamp instrumentation amplifier

14

33 )1( v

R

Rv (5.5)

For OA1 For OA2

21

23

1

2 1 vR

Rv

R

RvO

(5.6)

5. INSTRUMENTATION AMPLIFIERSDUAL OPAMP INSTRUMENTATION AMPLIFIERS

Combining these equations yields:

1

21

432

1

2

/1

/11 v

RR

RRv

R

RvO

If

2

1

4

3

R

R

R

R

then, the input-output relationship becomes:

)(1 121

2 vvR

RvO

(5.7)

(5.8)

(5.9)

5. INSTRUMENTATION AMPLIFIERSDUAL OPAMP INSTRUMENTATION AMPLIFIERS WITH VARIABLE GAIN

Figure 5.3 Variable gain instrumentation amplifier

GR

R

R

RA 2

1

2 21 (5.10)

5. INSTRUMENTATION AMPLIFIERSDUAL OPAMP INSTRUMENTATION AMPLIFIER

• Although dual opamp instrumantation amplifiers take the advantage of lower number of active and passive devices, it suffers from high-frequency performance degredation.

• The reason for the performance decrement is: v1 and v2 input voltages meet at different times since v1 has to pass through OA1 to catch v2.

5. INSTRUMENTATION AMPLIFIERSMONOLITHIC INSTRUMENTATION AMPLIFIER

• The monolithic instrumentation amplifiers allows better optimization of CMRR, lineraity and noise.

• Also, monolithic laser trimmed resistances allows the impalance factor to be minimized.

• The SPICE simulations of a monolithic instrumentation amplifer from Burr-Brown, namely INA-101 are carried.

• INA-101 allows the adjustement of the gain by an external resistor.

5. INSTRUMENTATION AMPLIFIERSSPICE SIMULATIONS OF A MONOLITHIC INSTRUMENTATION AMPLIFIER

Figure 5.4 Simulated instrumentation amplifier INA 101 [6]

GR

kA

40

1 (5.4)

Gain

Figure 5.5 Simulated DC characteristics of INA 101 instrumentation amplifier(RG=20k, A=3V/V)


V_V1

-15V -10V -5V 0V 5V 10V 15VV(U1:+) V(RL:2)

-20V

-10V

0V

10V

20V

(3.2984,9.889)

(-3.3246,-9.912)

Figure 5.6 Simulated AC characteristics of INA 101 instrumentation amplifier(RG=20k, A=3V/V)


• Note that –dB cut-off frequency is 338kHz.

Frequency

1.0Hz 10Hz 100Hz 1.0KHz 10KHz 100KHz 1.0MHz 10MHzV(V4:+) V(RL:2)

0V

1.0V

2.0V

3.0V

(385.478K,2.1408)


Figure 5.7 Simulated transient characteristics of INA 101 instrumentation amplifier(RG=20k, A=3V/V)

Time

0s 0.5ms 1.0ms 1.5ms 2.0ms 2.5ms 3.0ms 3.5ms 4.0msV(U1:+) V(RL:2)

-4.0V

-2.0V

0V

2.0V

4.0V

5. INSTRUMENTATION AMPLIFIERSFLYING CAPACITOR TECHNIQUES

• A capacitor is flipped back and forth between source and amplifier to achieve high common mode rejection ratio (CMRR).• Circuit ignores common mode input hence provides high common mode

rejection ratio.

Figure 5.8 Employing switched capacitor to achieve high commpn mode rejection ratio

)(1 121

2 vvR

RvO

(5.5)

In fact, a noninverting amplifier

6. INSTRUMENTATION APPLICATIONSACTIVE GUARD DRIVE

• In the situations where source and amplifier are far apart the signal is trnasmitted by shielded wires such as coaxial lines.

• The signal is transmitted in a double ended form for achieving the same noise pick-up.

• The common noise is considered as common mode signal and rejected by the difference amplifier.

• For this reason, double ended transmission is also named as balanced transmission.

THE DISADVANTAGE:

• The distributed capacitance of the cable decreases the CMRR.

• Consider the circuit of Figure 6.1.


Figure 6.1 The distributed capacitance of the balanced line

• Since Rs1.C1 and Rs2.C2 time constants will not be the same, this unbalance will decrease common mode rejection ratio because the amplifier will see a CM input.

First coaxial linemodel

Second coaxial line model

cmdmdB CfR

CMRR21

log20 10


(6.1)

21 ssdm RRR

221 CC

Ccm

CMRR due to imbalance is:

where(6.2)

(6.3)

• For example, if f=60Hz, Rdm=1kΩ and Ccm=1nF, CMRR=68.5dB.


Figure 6.2 Reducing Ccm by using an active guard

• Vcm is fed to shield of the balanced line, thus reducing CM input at the input of amplifier.

6. INSTRUMENTATION APPLICATIONSDIGITALLY PROGRAMMABLE GAIN

• In automatic instrumentation such as data acquistion systems, the programming of instrumentation amplifier electronically may be needed.

• The gain of the first stage is

Figure 6.3 Digitally programmable IA

inside

outsideI R

RA 1

12RRoutside

132 )....(2 nninside RRRRR

(6.4)

(6.5)

(6.6)

6. INSTRUMENTATION APPLICATIONSOUTPUT OFFSETTING

• In some applications, like a voltage-to-frequency converters, the output may need to have an offset value.

• The need comes from the fact that: the input of the succeeding circuit mya have only one polarity.

Figure 6.4 IA with offset control

ref

O

VRRRRR

vvAv

)]/()[/1(

)(

21112

22

(6.7)

refO VvvAv )( 12 (6.8)

6. INSTRUMENTATION APPLICATIONSCURRENT OUTPUT INSTRUMENTATION AMPLIIFIERS

Figure 6.5 Current output IA

• The current output is generated using Howland current pump at the output stage

)(/21

121

3 vvR

RRi GO

(6.9)

6. INSTRUMENTATION APPLICATIONSCURRENT OUTPUT INSTRUMENTATION AMPLIIFIERS

Figure 6.6 Current output IA with dual opamps

LO

O vR

vvR

i1

)(1

12

313245

12

/)(/

/R

RRRRR

RRRO

(6.10)

(6.11)

122|| vvVv satL (6.12)

V_V2

-5.0V -4.0V -3.0V -2.0V -1.0V 0.0V 1.0V 2.0V 3.0V 4.0V 5.0V1 V(V2:+) 2 I(RL)

-5.0V

0V

5.0V1

-20uA

-10uA

0A

10uA

20uA2

>>

(3.6075,14.240u)

(-3.8037,-14.978u)

6. INSTRUMENTATION APPLICATIONSSIMULATIONS OF CURRENT OUTPUT INSTRUMENTATION AMPLIIFIERS

Figure 6.7 DC characteristics of current output IA with LM324


Frequency

1.0Hz 10Hz 100Hz 1.0KHz 10KHz 100KHz 1.0MHz 10MHzI(RL)

0A

1.0uA

2.0uA

3.0uA

Figure 6.8 AC characteristics of current output IA with LM324

Time

0s 0.5ms 1.0ms 1.5ms 2.0ms 2.5ms 3.0ms 3.5ms 4.0ms1 V(V5:+) 2 I(RL)

-1.0V

-0.5V

0V

0.5V

1.0V1

-4.0uA

-2.0uA

0A

2.0uA

4.0uA2

>>


Figure 6.9 Transient characteristics of current output IA with LM324

6. INSTRUMENTATION APPLICATIONS

CURRENT INPUT INSTRUMENATION AMPLIFIER

Figure 6.10 Current input instrumentation amplifier

32 Rivv ICMO

ICMO iRvv 31

)( 121

2OOO vv

R

Rv

IO iRR

Rv 3

1

22

(6.13)

(6.14)

(6.15)

(6.16)

7. TRANSDUCER BRIDGE AMPLIFIERS

• Resistive transducer: A device whose resistance varies by a physical paramater such as temperature, light frequency/amplitude, pressure.

• Resistive transducer transducer are made a part of a circuit to generate an electrical signal proportional to the physical parameter.

• Parameter’s magnitude and the electrical signal are wanted to be in a linear relationship.

7. TRANSDUCER BRIDGE AMPLIFIERSTRANSDUCER RESISTANCE DEVIATION

• Transducer resistances are expressed as

RR

Resistance at a reference condition Deviation

It can be also expressed as

)1( RRR

R

Fractional deviation

(7.1)

(7.2)

7. TRANSDUCER BRIDGE AMPLIFIERSTHE TRANSDUCER BRIDGE

• ΔR is converted to a ΔV by means of a voltage divider.

Figure 7.1 Transducer bridge with instrumentation amplifier

• This voltage dividers are referred to as bridge legs.


)/1(//2)1(

)1(

111111 RRRRRR

VV

RR

R

RR

RVv REF

REFREF

(7.3)

REFVRR

Rv

12 (7.4)

)1)(/1(/1)(

1121

RRRR

AVvvAv REFO(7.5)

If 1

4//2 11

REFREFO

AV

RRRR

AVv

(7.6)

If R1=R


Figure7.2 Bridge calibration of a transducer bridge

Due to the tolerances of bridge resistances and IA’s reference voltage, a calibration is needed. R3 is varied to achieve vO=0V at ΔR=0.


STRAIN GAUGE BRIDGES

A resistor with resistivity ρ, cross-sectional area S and lenght l has a resistance of:

S

lR

(7.7)

If the wire is strained,

lll '

SSS '

SS

llR

)(

(7.8)

(7.9)

(7.10)



The volume of the resistor is not changed, so

SlSSll ))(( (7.11)

l

lR

l

l

l

lRR

22 (7.12)

Unstrained resistance Fractional elognation



Figure 7.3 Strain-gauge bridge and instrumentation amplifier

Load cell



RRRVRRRRRRVv BB 2/)()/()(1

RRRVv B 2/)(2

(7.13)

(7.14)

BB VRRVvv /21

REFO AVv

(7.15)

(7.16)

• Note that, voltage deviation is perfectly linear with fractional elongation.

• Also, in the circuit R3 adjusts sensitivity, R2 nulls the voltage in the absence of strain.


BRIDGE AMPLIFIER WITH SINGLE OPAMP AMPLIFIER

Figure 7.4 Single opamp bridge amplifier

)1)(/1(/ 211

2

RRRRV

R

Rv REFO

(7.17)

For 1

211

2

//1 RRRRV

R

Rv REFO

(7.18)


BRIDGE LINEARIZATION

• Bridge circuits except strain-gauge has a nonlinear voltage response with the fractional elognation.

• The linear response may be achieved using a current source to drive the bridge.

Figure 7.5 Bridge linearization using a current source

Current source(V-I converter)


BRIDGE LINEARIZATION

1R

VI REFB (7.19)

2/)1(1 BREF IRVv (7.20)

2/2 BREF RIVv (7.21)

2/21 BIRvv (7.22)

12R

ARVv REFO (7.23)


BRIDGE LINEARIZATION WITH SINGLE TRANSDUCER

Figure 7.6 Bridge linearization using single transducer

REFVR

Rv

11

)1( (7.24)

1

21

1

2

R

RVv

R

Rv REFO

(7.25)

From (7.24) and (7.25),

1

2

R

RVv REFO (7.26)


SIMULATIONS OF BRIDGE LINEARIZATION WITH SINGLE TRANSDUCER

• The bridge transducer witgh single transducer element has been simulated in OrCad SPICE.

• The output voltage is plotted versus the transducer resistance value.

• In rder to plot the variation, a parametric sweep in OrCad SPICE is utilized [7, 8, 9].

• Supply voltages and reference voltage are taken as 15V.

• R1=R=10k are taken.

• LM324 opamp macromodels are used.

RL

0 0.1K 0.2K 0.3K 0.4K 0.5K 0.6K 0.7K 0.8K 0.9K 1.0K 1.1KV(U2A:OUT)

-15V

-10V

-5V

0V


SIMULATIONS OF BRIDGE LINEARIZATION WITH SINGLE TRANSDUCER

Figure 7.7 Variation of output voltage via the change of transducer resistance

Note that, vo is negative since, fractinal elongation is negative (i.e. transducer resistance is below 1k.)

7. REFERENCES

1. S. Franco, Design with operational amplifiers and analog integrated circuits, McGraw Hill, USA, 2001.

2. S. Kılınç, M. Saygıner, U. Çam and H. Kuntman, Simple and accurate macromodel for current operational amplifier (COA), Proceedings of ELECO 2005: The 4th International Conference on Electrical and Electronics Engineering, (Electronics), pp.1-5, 7-11 December 2005, Bursa, Turkey.

3. H. Kuntman: Simple and accurate nonlinear OTA macromodel for simulation of CMOS OTA-C active filters, International Journal of Electronics, Vol.77, No.6, pp.993-1006, 1994.

4. LM324 datasheet, National Semiconductors, http://cache.national.com/ds/LM/LM124.pdf, accessed on 10th Oct. 2007.

5. INA105 datasheet, Texas Instruments, http://focus.ti.com/lit/ds/symlink/ina105.pdf, accessed on 10th Oct. 2007.

6. INA101 datasheet, Burr-Brown, www.hardware.dibe.unige.it/DataSheets/INA101.pdf, accessed on 12th Oct. 2007.

7. Pspice Reference Guide, ece-classweb.ucsd.edu/spring06/ece139/PspiceRef.pdf, accessed on 13th Oct. 2007.

8. DC Simulation and analysis, http://ecen4303.okstate.edu/ecen1322/lab2ar.rtf, accessed on 13th Oct. 2007.

9. Pspice Notes v.3.0, http://www-ferp.ucsd.edu/najmabadi/CLASS/COMMON/PSPICE/PSpice_Notes_v3.0.doc, accessed 13th Oct. 2007.

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