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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
1. CURRENT-TO-VOLTAGE CONVERTERS
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.
1. CURRENT-TO-VOLTAGE CONVERTERS
• 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)
1. CURRENT-TO-VOLTAGE CONVERTERS
• 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
1. CURRENT-TO-VOLTAGE CONVERTERSSPICE SIMULATIONS OF I-V CONVERTER
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
>>
1. CURRENT-TO-VOLTAGE CONVERTERSSPICE SIMULATIONS OF I-V CONVERTER
Figure 1.5 Transient characteristics of the transresistance amplifierR=1k
1. CURRENT-TO-VOLTAGE CONVERTERS
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
1. CURRENT-TO-VOLTAGE CONVERTERS
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
1. CURRENT-TO-VOLTAGE CONVERTERS
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
1. CURRENT-TO-VOLTAGE CONVERTERS
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
2. VOLTAGE-TO-CURRENT CONVERTERS
• 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.
2. VOLTAGE-TO-CURRENT CONVERTERS
FLOATING TYPE V-I CONVERTORS
Figure 2.2. Floating-type V-I converters
IO vRi
R
vi IO
(2.4)
(2.5)
2. VOLTAGE-TO-CURRENT CONVERTERS
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
FLOATING TYPE V-I CONVERTORS
2. VOLTAGE-TO-CURRENT CONVERTERS
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)
FLOATING TYPE V-I CONVERTORS
2. VOLTAGE-TO-CURRENT CONVERTERS
• 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.
FLOATING TYPE V-I CONVERTORS
2. VOLTAGE-TO-CURRENT CONVERTERS
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)
2. VOLTAGE-TO-CURRENT CONVERTERS
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)
2. VOLTAGE-TO-CURRENT CONVERTERS
Figure 2.5 AC characteristics of the floating V-I converter
The -3dB cut-off frequency of the circuit is 538kHz.
SIMULATIONS OF FLOATING TYPE V-I CONVERTORS
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
>>
2. VOLTAGE-TO-CURRENT CONVERTERS
Figure 2.6 Transient characteristics of the floating V-I converter
SIMULATIONS OF FLOATING TYPE V-I CONVERTORS
2. VOLTAGE-TO-CURRENT CONVERTERS
GROUNDED V-I CONVERTORS
Figure 2.7 Howland current pump and its Norton equivalent circuit
2. VOLTAGE-TO-CURRENT CONVERTERS
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
GROUNDED V-I CONVERTORS
2. VOLTAGE-TO-CURRENT CONVERTERS
satL VRR
Rv
21
1
Voltage compliance of the circuit is
Saturation voltage of theoperational amplifier
(2.18)
GROUNDED V-I CONVERTORS
2. VOLTAGE-TO-CURRENT CONVERTERS
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)
2. VOLTAGE-TO-CURRENT CONVERTERS
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
2. VOLTAGE-TO-CURRENT CONVERTERS
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)
SIMULATIONS OF GROUNDED V-I CONVERTORS
2. VOLTAGE-TO-CURRENT CONVERTERS
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.
SIMULATIONS OF GROUNDED V-I CONVERTORS
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)
3. CURRENT AMPLIFIERS
FLOATING TYPE CURRENT AMPLIFIER
Figure 3.1 Floating type current amplifier
3. CURRENT AMPLIFIERS
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)
3. CURRENT AMPLIFIERS
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)
3. CURRENT AMPLIFIERS
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)
3. CURRENT AMPLIFIERS
SIMULATIONS OF FLOATING TYPE CURRENT AMPLIFIER
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
3. CURRENT AMPLIFIERS
SIMULATIONS OF FLOATING TYPE CURRENT AMPLIFIER
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)
4. DIFFERENCE AMPLIFIERS
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
4. DIFFERENCE AMPLIFIERS
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)
4. DIFFERENCE AMPLIFIERS
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
4. DIFFERENCE AMPLIFIERSEFFECTS OF RESISTANCE MISMATCHES
• 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
4. DIFFERENCE AMPLIFIERSEFFECTS OF RESISTANCE MISMATCHES
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.
4. DIFFERENCE AMPLIFIERS
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.
4. DIFFERENCE AMPLIFIERS
SIMULATIONS OF DIFFERENTIAL AMPLIFIER INA105 from BURR-BROWN
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)
4. DIFFERENCE AMPLIFIERS
SIMULATIONS OF DIFFERENTIAL AMPLIFIER INA105 from BURR-BROWN
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
4. DIFFERENCE AMPLIFIERS
SIMULATIONS OF DIFFERENTIAL AMPLIFIER INA105 from BURR-BROWN
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)
5. INSTRUMENTATION AMPLIFIERSSPICE SIMULATIONS OF A MONOLITHIC INSTRUMENTATION AMPLIFIER
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)
5. INSTRUMENTATION AMPLIFIERSSPICE SIMULATIONS OF A MONOLITHIC INSTRUMENTATION AMPLIFIER
• 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)
5. INSTRUMENTATION AMPLIFIERSSPICE SIMULATIONS OF A MONOLITHIC INSTRUMENTATION AMPLIFIER
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.
6. INSTRUMENTATION APPLICATIONSACTIVE GUARD DRIVE
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. INSTRUMENTATION APPLICATIONSACTIVE GUARD DRIVE
(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.
6. INSTRUMENTATION APPLICATIONSACTIVE GUARD DRIVE
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
6. INSTRUMENTATION APPLICATIONSSIMULATIONS OF CURRENT OUTPUT INSTRUMENTATION AMPLIIFIERS
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
>>
6. INSTRUMENTATION APPLICATIONSSIMULATIONS OF CURRENT OUTPUT INSTRUMENTATION AMPLIIFIERS
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.
7. TRANSDUCER BRIDGE AMPLIFIERSTHE TRANSDUCER BRIDGE
)/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
7. TRANSDUCER BRIDGE AMPLIFIERSTHE TRANSDUCER BRIDGE
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.
7. TRANSDUCER BRIDGE AMPLIFIERS
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)
7. TRANSDUCER BRIDGE AMPLIFIERS
STRAIN GAUGE BRIDGES
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
7. TRANSDUCER BRIDGE AMPLIFIERS
STRAIN GAUGE BRIDGES
Figure 7.3 Strain-gauge bridge and instrumentation amplifier
Load cell
7. TRANSDUCER BRIDGE AMPLIFIERS
STRAIN GAUGE BRIDGES
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.
7. TRANSDUCER BRIDGE AMPLIFIERS
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)
7. TRANSDUCER BRIDGE AMPLIFIERS
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)
7. TRANSDUCER BRIDGE AMPLIFIERS
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)
7. TRANSDUCER BRIDGE AMPLIFIERS
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)
7. TRANSDUCER BRIDGE AMPLIFIERS
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
7. TRANSDUCER BRIDGE AMPLIFIERS
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.