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AN102 Dataforth Corporation Page 1 of 9 DID YOU KNOW ? George Westinghouse (1846-1914) made a fortune with his invention of air breaks for railroad...

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AN102

Dataforth Corporation

Page 1 of 9

DID YOU KNOW ? George Westinghouse (1846-1914) made a fortune with his invention of air breaks for railroad trains. He then used his wealth to form Westinghouse Electric Company; hired Nikola Tesla and Charles Proteus Steinmetz, shrewdly purchased the patent for the transformer, won the dispute with Thomas Edison over ac versus dc, and became a true giant in United States industry.

Errors, What Are They And How Bad Can They Be Preamble

Definitions: Reference Figure 1

Modern integrated circuit (IC) operational amplifiers (Op Amps) have made quality instrumentation signal conditioning economically practical. Although accurate and stable Op Amp ICs are available for designing instrumentation products, there are errors associated with their applications. Specific topologies with internal IC errors often create application errors. Instrumentation Engineers should be aware of IC Op Amp errors and their impact on specific application topologies.

1. Rdi is the differential input resistance between positive and negative input terminals. It is typically large enough to neglect in most practical situations; however, its value should always be examined. Data sheets specify input resistance as the resistance seen at one input with the other grounded. This data sheet parameter is Rdi in parallel with 2Rcm in Figure 1 and is essentially Rdi.

A complete error analysis for IC based instrumentation devices is beyond the scope of this application note; nonetheless, common internal errors specific to voltage feedback IC Op Amp circuits and a few guidelines for application topologies will be presented here. IC Op Amp Errors Figure 1 illustrates an Op Amp model used to identify those error parameters specified on data sheets. This model provides a first order approximation (FOA) of how these error parameters may affect application topologies. The "x" on parameters designates assumed equal values. Vios

Vn

EVcm

2Rcm

Vo

Ib EVpsr

Rdi

Vn' Ibx Vp

2Rcmx

Ro

0.5xIbos Gol

Vp

Figure 1 Op Amp Model with Error Parameters

Vo'

2. Rcm is the common mode input resistance referenced to ground as seen by a common input source connected to both positive and negative inputs. This resistance is typically in the range of hundreds of megohms and generally neglected. Data sheets seldom give this value. 3. Ro is the small internal output resistance as seen looking into the output terminal. In a voltage amplifier feedback topology with feedback factor "H", the effect of Ro is small (H*Ro/Gol) and is generally neglected. 4. Ib (bias current) and Ibos (offset bias current) are associated with the positive (Vp) and negative (Vn) voltage inputs, which support input currents in a "live" topology. Input currents Ip and In are specified in data sheets via parameters Ib and Ibos. Equations 1 and 2 show the definitions relating data sheet items and actual Op Amp input currents. Ib (data sheet) ≡ [Ip + In]/2

Eqn 1

Ibos (data sheet) ≡ [Ip - In]

Eqn 2

Current sources in Figure 1 support these equations. 5. Vios (input offset voltage) is an internal IC device voltage error (referenced to the input) that relates output voltage for zero input. IC Op Amps have internal circuits that depend on matched devices. Perfect matching can not be achieved; therefore, a mismatch voltage error term exists as Vios in Figure 1. Note that an applied voltage equal to Vios between Vn, Vp such that the voltage between Vn', Vp is zero, forces the output to zero, neglecting all other error terms.

AN102

Dataforth Corporation

6. PSRR, power supply rejection ratio, is responsible for a voltage error term referenced to the input, which relates changes in output voltage for changes in the IC supply voltages. The error term EVPSR in Figure 1 has a value of (PSRR* ∆supply voltage) for PSRRs given in data sheets as µV/V. PSRR may be given in dB for which -PSRR/20 ). EVpsr in Figure 1 is (∆supply voltage * 10 7. CMRR, common mode rejection ratio, determines a voltage error term referenced to the input, which relates the output voltage to a common mode voltage (Vcm) applied to both positive and negative inputs. Figure 1 shows this error term referenced to the input as EVcm. Equation 3 illustrates how this error term is calculated. EVcm =

Vcm 10 CMR / 20

Eqn 3

b

g

Where; CMR ≡ 20∗ Log10 CMRR and where

CMRR ≡

LM Differential Gain (G ) OP N Common Mode Gain (Gcm) Q

See Dataforth's Application Note AN103 for more detail on Common Mode issues. Error Budget Calculations The technique used in calculating impacts of error terms for a given application topology begins by using Figure 1 in a specific application topology and solving for the analytical output voltage (Vo) expression using Eqn 4, which neglects Ro.

b

g

Eqn 4

Where Vp is the external voltage on the positive input as determined by the application topology and Vn' is the negative external input voltage (Vn) as determined by the application topology plus the accumulated internal errors. RF

RS1

V1

RA VCC

RS2

R1 V2

V1in

VEE

R2

V2in

Figure 2 Single Stage Difference Amplifier

Figure 2 is the difference amplifier topology chosen for analysis in this Application Note because it is particularly vulnerable to resistor tolerances. Errors dominated by external resistor tolerances may justify a topology change; therefore, errors due to external resistors should always be examined first before internal IC errors are analyzed. RS1 and RS2 are the source resistors for input source voltages V1in and V2in respectively. Often users forget to include these resistors when considering a specific application. When these resistors are large compared to RA and R1, they cause additional errors. Later in this Application Note, a topology will be recommended in which the impact of source resistors is diminished. For now, assume the input voltage sources are near ideal (i.e. RS1=RS2=0). Using concepts embodied in Eqn 4, the output voltage (Vo) in Figure 2 is illustrated by Eqn 5. Eqn 5 Vo = Gp∗ V2 - Gn∗ V1 Where terms Gn and Gp are the negative gain and positive gain respectively as shown;

ol

Vo = Vo' = Gol∗ Vp - Vn'

Page 2 of 9

Vo RL

o t Gn = [RF / (RF + RA)]∗ oG ol / [1 + G ol ∗ RA / (RF + RA)]t

Gp = [R2 / (R2 + R1)]∗ G ol / [1 + G ol ∗ RA / (RF + RA)]

The terms Rcm, Rdi, RS1, RS2, and Ro are neglected in deriving Gp and Gn in Eqn 5. If G ol ∗ RA / (RF + RA) >> 1 and if RA=R1, RF=R2; then Eqn 5 becomes the classic difference gain equation shown in Eqn 5a.

b

gb

Vo = V2 − V1 ∗ RF / RA

g

Eqn 5a

It is clear that mismatches in {RA; R1} and {RF; R2}, can cause errors; moreover, Eqn 5a is less correct if, G ol ∗ RA / (RF + RA) is not >> 1 Note: Equations 5, 5a conform to the general feedback equations; namely, Gain closed loop =Gol/(1+Gol*H); where H is the voltage feedback factor and Gol is the amplifier open loop gain. For Gol*H>>1, Gain closed loop ≅1/H. Gain Error due to Resistance Tolerance Table 1 illustrates how resistor tolerances in Figure 2 impact the circuit gain for a random lot with open loop gain (Gol) constant. Note that the net percent error due to resistor tolerances alone can be very significant in this topology.

AN102

Dataforth Corporation

Next after examining the variations in gain due to resistor tolerance, the effects of CMMR, PSRR, Vios, Ib, and Ibos are analyzed. The following error calculations are derived with; Eqns 3,4,and 5; V1=V2=zero; Rdi, Rcm, Ro, RS1, RS2 neglected; and G ol ∗ RA / (RF + RA) >> 1 . Throughout all these calculations RF=R2 and RA=R1.

PSRR Error Another error due to Op Amp internal mismatches is an output voltage change for changes in the power supply voltages. Figure 1 shows this error term referenced to the input as EVpsr. Equation 9 is the output error voltage for an Op Amp PSRR given in data sheets as µV/V.

Internal Offset Voltage (Vios) Error

a fa f Eqn 9 Vo error = a ∆ supply voltsf∗ d10 i * a1 + RF / RAf Vo error = PSRR ∗ ∆ supply volts ∗ 1 + RF / RA

The output voltage error caused by an Op Amp's internal mismatch voltage error term Vios is shown in Eqn 6 for the topology of Figure 2, using the Op Amp error model in Figure 1. Vo error = ± Vios ∗ (1 + RF / RA ) Eqn 6 The Vios term is always shown in data sheets as a positive value; however, it is randomly either negative or positive.

Input Current Error Input currents Ip and In on both the positive and negative inputs flow through the DC Thevenin Resistance associated with each input and develop unwanted voltages, which are amplified by the application topology. Eqn 7 shows this error for the topology in Figure 2, using the error model in Figure 1 with Eqns 1, 2. Vo error = ......

Page 3 of 9

a

Ib∗ ( R T− − R T+ ) ± Ibos∗ ( R T− + R T+ ) / 2 ∗ 1 + RF / RA

f Eqn 7

Note: Ib Error term is zero IF R T− = R T+ where; R T− = RF∗ RA / ( RF + RA ) and R T+ = R1∗ R 2 / ( R 2 + R1) Reminder: Input Ib on data sheets is positive (into) for "n-type" devices and negative (out) for "p-type" devices; however, Ibos is always randomly either positive or negative.

CMRR Error As previously discussed internal mismatches in the Op Amp cause output errors. Another example of this type error is the term EVcm, which is referenced to the input in Figure 1. The associated output error due to this term is shown in Eqn 8 for the topology in Figure 2. Vo error = VcmT ∗ (10 − CMR / 20 ) ∗ (1 + RF / RA ) Eqn 8 Note: In Figure 2, one can assume that the external voltage between Op Amp inputs is essentially zero. Therefore, any Thevenin voltage on the Op Amp positive (+) input is essentially the common mode voltage (a quick trick to identifying, Vcm T ).

When PSRR is given in dB, Eqn 9 becomes; - PSRR / 20

Example of Typical Error Calculations Typical Op Amp values for the difference amplifier topology of Figure 2 at 25° C is shown below. Change in power supply voltage is assumed to be 500mV. Rdi = 800 kΩ RA = 5kΩ Ibos = 200 nA IbosTC = 1nA/°C PSRR = 20 µV/V RS1 = 10 Ω

Rcm = 65 MΩ R2 = 200kΩ Vios = 5 mV ViosTC= 5µV/°C CMRR = 90 dB RS2 = 10 Ω

RF = 200 kΩ R1 = 5kΩ Ib = 500 nA Ib TC =No Value Gol= 50k-200k

Vcm T = 15 volts

Individual error calculations Most parameters have temperature coefficients (TC), which should be examined. The following calculations use only the TC values for Vios, and Ibos. The temperature multiplier is TC*(Ta −25°C). The term (Ta) is ambient temperature and limited to 40°C. In this example, input referenced error terms are multiplied by the closed loop gain, which is given as [G ol / [1 + G ol ∗ RA / (RF + RA)] and reduces to; 41 for G ol = ∞ ; 40.97 for G ol = 50k; and 40.99 for G ol = 200k. ! !

Vios Error = [5mV+5µV/*(40-25) ]*41 = 208.08 mV Ib Error = Zero, since R T− = R T+ if RF=R2; RA=R1

! ! !

Ibos Error =[200nA+1nA/°C* (40-25)]*4.88k*41=43mV CMRR Error = 15V* 10 -90/ 20 *41 = 19.45mV PSRR Error = 20µV/V*500mV*41 =410µV Total Error ≅ (on the order of) 271 mV.

!

These calculations are not precise; nonetheless, this approach predicts error magnitudes and illustrates the most dominant parameter, Vios in this case. Clearly this particular configuration is not suitable for low-level dc measurements; for example, measuring current with a 100 ampere, 50mV resistance shunt (500µΩ ) Table 2 illustrates how error parameters in Figure 1 impact the total output voltage for the difference amplifier in Figure 2.

AN102

Dataforth Corporation

Single Stage Difference Amplifier Observations The above analysis of Figures 1,2 shows; 1. Resistor tolerances do cause serious errors. 2. Thevenin resistance at each (±) input should be equal 3. Avoid high Vcm voltages. 4. Input source resistors RS1, RS2 should be zero or RS1 much less than RA and RS2 much less than R1. 5. Op Amp open loop gains (Gol) should be very high. 6. Avoid large ambient temperature swings.

Page 4 of 9

It is interesting to examine the effects Op Amp gains and non-identical RFs. This can be achieved by writing two node equations at Vn1 and Vn2, then solving for Vo1 and Vo2. Equation 11 illustrates the results. Vout = (Vo2-Vo1) =

LM RF + RF + 1OP∗ LM G + 1 OP − V1∗ LM RF + RF + 1OP∗ LM G + 1 OP N RG Q N G Q N RG Q N G Q LM RF + 1OP∗ 1 + LM RF + 1OP∗ 1 + LM RF + RF + 1OP∗ LM 1 OP 1+ N RG Q G N RG Q G N RG Q N G ∗ G Q 1

V 2∗

2

1

V1

V1n G1 200k

100k RF1 RG 5k 100k RF2

Vo Vo1

G3 1

1

2

1

1

2

Eqn 11

Although the gains (G1,G2) may not be equal, they can be assumed very large numbers and, therefore, set to a single very large gain (G) in Equation 11. In addition, if this gain (G) is >>> than [(RF1+RF2)/RG +1], then Equation 11 becomes; RF1 + RF2 Vout = ( Vo 2 - Vo1 ) = ( V2 − V1) ∗ + 1 Eqn 12 RG Note: The single resistor (RG) is responsible for changing gains of an Instrument Amplifier since RFs are internally fixed in the die. Moreover, the matching of RFs is usually so close that Equation 10 is valid. Furthermore, if the TC of RG and RF match, then the instrument amplifier gain expression is essentially independent of temperature.

FG H

IJ K

Table 3 illustrates how random values of gain and resistor values can impact the instrumentation amplifier net gain.

Vo2

The error parameters of the Op Amp shown in Figure 1 cause output errors in an Instrument Amplifier. Errors are analyzed here to obtain first order approximation (FOA) insight into how they impact the output. The analytical process begins by substituting the model of Figure 1 for the amplifiers G1 and G2 in Figure 3.

G2 200k V2 V2n

Figure 3 Basic Instrumentation Amplifier Topology In calculating the overall gain for this topology, amplifiers G1, G2, are assumed to be near ideal with G3 an ideal unity gain amplifier. Specifically Ro, Rdi, Rcm, and error parameters in Figure 1 are neglected. The output stage G3 is typically the difference amplifier of Figure 2. Equation 10 is the ideal expression for output voltage.

Vout = ( Vo 2 - Vo1 ) = ( V2 - V1)∗

2

2

1

2

Figure 3 illustrates the basic instrumentation amplifier topology. In general, all individual internal Op Amps are fabricated on a single die or substrate and matched within the fabrication process capabilities. Resistors RF1, RF2 are internally fabricated on the die and matched. Resistor RG is usually external and controls the amplifier gain.

2

1

2

The Instrument Amplifier

1

FG 2RF + 1IJ H RG K

Eqn 10

Some reasonable assumptions are made to ease the math burden but not mask the dominant impact caused by error parameters. These assumptions are; (a) neglect Rdi, Rcm, and PSRR, (b) resistors RP1, RP2 (source resistors of V1in and V2in) exist in the two input lines, (c) Ip1, Ip2 are the two input currents and assumed equal to Ip (illustrates the effects of Rp1 ≠ Rp2), (d) CMRR1 ≠ CMRR2; Vios1 ≠ Vios2; Ibn1 ≠ Ibn2, (e) RF1 = RF2; G1 = G2 = G, (f) Inputs V1 and V2 are the common mode voltages (Vcm) on amplifiers G1 and G2 in Figure 3, and (g) G3 in Figure 3 is an ideal unity gain amplifier.

AN102

Dataforth Corporation

Instrument amplifier major errors are due to external topology and the front-end Op Amp cells G1 and G2. The error equations shown below neglect non-zero errors in G3 (difference cell). These equations are presented to illustrate the impact of external application topologies. These assumptions predict (Vo2-Vo1) errors as follows;

RF I + 1J g FGH 2RG K F 2 RF + 1IJ Ip Error = b Rp1 - Rp 2 g∗ Ip ∗ G H RG K In Error = bIn2 - In1g∗ RF

b

Vios Error = Vios1 - Vios2 ∗

e

Eqn 13 Eqn 14 Eqn 15

j FGH 2RGRF +1IJK

CMR Error = V1∗10−CMR1/ 20 − V2∗10−CMR2/ 20 ∗

Eqn 16

Note: Instrument Amplifier CMR is specified in data sheets as a net quantity, which includes the effect of all internal gain cells.

Page 5 of 9

Table 3 illustrates the impact of error parameters on the output voltage of the instrument amplifier in Figure 3. Premium IC instrumentation amplifiers have well matched front-end Op Amps (G1,G2); consequently, Eqns 13 and 15 reduce to near zero. Moreover, if the engineer ensures an application, which has Rp1=Rp2, then Eqn 14 reduces to near zero. Instrumentation amplifiers with high CMR in cells G1,G2, and G3 minimize the impact of Eqn 16. Clearly the Instrumentation Amplifier is a superior conditioning and instrumentation front-end topology compared to the single stage difference topology. Unfortunately, instrumentation amplifiers are not completely error free. Manufactures of Integrated Circuit (IC) Instrumentation Amplifiers do specify in their data sheets a set of net "error" terms, which apply to the total IC amplifier. For example; Vios, CMR, Ib, Ibos, Rinputs, etc are all specified as net device terms.

DATAFORTH MEASUREMENT DEVICES Integrated circuit operational amplifier internal error terms do cause circuit topology dependent errors. Dataforth design engineers are imminently aware of these phenomena and use every available technique to minimize the impact of these error components on Dataforth's products. For example, Dataforth uses only premium IC's in their design together with unique patented circuit topologies to minimize errors. Moreover, all Dataforth modules are thoroughly tested and subjected to a thermal burn-in. In addition, internal voltage offset errors and gain errors due to resistor tolerance are removed by individual tuning on each module. Consequently, Dataforth has developed a quality cost effective product line of signal conditioning modules. The reader is encouraged to visit Dataforth's website www.Dataforth.com for detail information on all Dataforth's product The following are just a few of Dataforth's outstanding module benefits; ! Dataforth signal conditioners use high performance amplifiers internally, which have low offset voltages (Vos) and low Vos TC. Residual errors due to Vos internal errors are calibrated out prior to shipment. !

Zero and Span errors caused by internal resistor tolerances are calibrated out prior to shipment. High performance amplifiers and discrete components ensure low drift over the wide operating range of -40C to +85C. Dataforth's amplifiers and associated adjustment networks provide stable calibration; therefore, after the modules are sealed no periodic calibrations are required.

!

All Dataforth circuitry is designed to be insensitive to variations in power supply voltage. SCM5B modules operate over 4.75V to 5.25V with a power supply rejection (PSR) as low as 2uV per % variation in supply voltage, referred to input. SCM7B and DSCA modules operate over a much wider supply voltage range of 14 to 35V with PSR as low as 0.0001% of output per % variation in supply voltage.

!

High input impedances (50 Meg ohms for 5B30-xx modules and 200 Meg ohms for 5B40-xx modules) allow interfacing to sensors with high output impedance. The use of FET input amplifiers result in low bias currents of 0.5nA, benefiting the user in allowing interfacing to sensors with high output impedance.

!

Dataforth's patented unique iso-chopper isolation barrier allows continuous input common mode signal levels up to 1500Vrms (2200V peak). Common Mode Rejection of up to 160dB ensures signal integrity in extreme applications.

As an example consider measuring steady-state line current of a three-phase 3-wire delta connected AC motor using Dataforth's SCM5B40/41 wide bandwidth analog voltage module and a four-wire shunt sensor. Figure 4 illustrates the modular structure of Dataforth's SCM5B40/41 used in this example. Three phase line current shunt measurements on delta 3wire devices must be done with low voltage (typically 50mV) shunts to maintain balanced load conditions. Such low voltage measurements require accurate modules, which must maintain accuracy at common mode voltages equal to AC line values.

AN102

Dataforth Corporation

Page 6 of 9

Figure 4 Dataforth SCM5B40/41 Isolated Analog Module !

5 Vdc Isolated Supply

4-W Shunt

3-Phase 3-Wire Supply

Vout

Dataforth SCM5B40

DAS Common

3-Phase 3-Wire, AC Motor Machine Chassis Gnd

Figure 5 3-Phase Line Current Measurement Figure 5 illustrates a line current measurement for a 100 horsepower 3-phase 460 volts AC (126 A rms full load), 60 Hz delta connected motor. Dataforth's SCM5B40-02 module (output −5 to +5 volts, input −50mV to +50mV, gain 100V/V) is used to sense line current in a 300A, 50mV, 166.667µΩ shunt. Shown below are error calculations using Dataforth's specifications. See Dataforth's AN104 for more specification details. !

Input Resistance: 200MΩ ,40kΩ off/overload This has insignificant effect on the net Rshunt resistance.

CMV: 100 dB (1500Vrms input/output max). Common mode voltage input/output is 267 (462÷√3) Vrms, for this balanced motor with negligible IR drops in the building ground structure. The error is 267V*10(-100/20) = 2.67 mV rms See AN103 on CMR. ! Power Supply Sensitivity: 2µV/% RTI. The error is ±2µV/%*5%*100V/V = ± 1mV rms, for a 5% variation in the 5 volt module power supply.. ! Input Bias Current: ±0.5nA. The error is ±0.5nA*Rshunt*100V/V, certainly negligible. ! Accuracy: Includes nonlinearly, hystersis, and repeatability; (a) ±0.05% of Span; (b) ±10µV RTI; (c) ±0.05% of Vz. Errors are determined as follows; a) (±0.05%)*10V = ± 5mV rms , b) ( ±10µV)*100 V/V = ± 1mV rms , c) (±0.05%)*0mV =± 0 V rms (Vz =0 V) ! Stability: Input offset ±1µV/°C; Output offset ±40µV/°C; Gain ±25 ppm/°C of reading. For a temperature of 122°F, (25°C change from 25°C room), stability calculations in volts rms are; * Input offset ±1µV/°C*25°C*100 V/V= ± 2.5mV * Output offset ±40µV/°C*25° = ± 1mV. * Gain 25µV/°C*25°C*5 = ± 3.1 mV, max. Random (±) terms will likely not be the same sign; hence, adding would give an unlikely net error. Another method for adding ± random mutually exclusive rms values is the square root of the sum of squares of each (±) term. This method gives an estimated net error of ± 7.14mV rms. Note A 10 mV error represents only a 0.6 ampere error.

AN102

Dataforth Corporation

Page 7 of 9

Table 1 Single Stage Op Amp Difference Amplifier Gain Error Reference Figure 2 Table 1 is available on Sheet #1 of the interactive Excel Workbook from Dataforth's Web site. The reader is encouraged to download this Excel file http://www.dataforth.com/catalog/pdf/an102.xls , choose their own values, follow instructions, and examine the effects of their own selected resistor, gain, temperature, and tolerance values.

R% 5

Gol

RFo

2.0E+05 2.0E+05

RAo

R1o

R2o

V1-

V2 +

5000

5000

2.0E+05

1.20

1.10

Nominal Values GnGp+ Vout 39.992

39.992

-3.999

RF

RA

Gn-

Gn% Error

R1

R2

Gp+

Gp+ % Error

Actual Vout

Output % Error % Error 0.72 Max

209898

5188

40.45

1.15

4892

201175

40.47

1.19

-4.03

192146

4944

38.87

-2.81

5007

204481

38.91

-2.71

-3.84

-3.89

7.48

192585

4998

38.53

-3.66

5147

193480

38.50

-3.74

-3.89

-2.78

Min

209156

5227

40.02

0.06

5219

199629

39.96

-0.07

-4.06

1.53

-6.88

206009

4996

41.23

3.11

5208

206813

41.19

2.99

-4.17

4.38

203990

5036

40.50

1.28

4907

201595

40.51

1.29

-4.04

1.13

205909

5186

39.71

-0.71

4834

206645

39.77

-0.56

-3.90

-2.41

203815

4893

41.65

4.15

4845

204523

41.65

4.16

-4.16

4.04

194064

4863

39.90

-0.22

5111

193484

39.84

-0.37

-4.06

1.45

202765

5079

39.92

-0.17

4875

192133

39.90

-0.22

-4.02

0.40

192751

4803

40.13

0.35

4757

200604

40.17

0.45

-3.97

-0.71

194706

5000

38.94

-2.63

4788

206005

39.03

-2.42

-3.80

-4.97

196937

4854

40.57

1.45

4862

193200

40.54

1.38

-4.09

2.25

209832

5225

40.16

0.41

5151

200225

40.12

0.31

-4.06

1.53

198148

4989

39.72

-0.69

4963

207961

39.76

-0.58

-3.92

-1.87

203014

4792

42.36

5.92

4862

196456

42.30

5.78

-4.30

7.48

205060

5055

40.56

1.43

4772

192139

40.55

1.39

-4.07

1.86

201209

5201

38.69

-3.27

4897

190500

38.68

-3.27

-3.87

-3.20

199252

4923

40.48

1.21

5212

205734

40.44

1.13

-4.08

2.12

206517

4968

41.57

3.94

4788

203140

41.58

3.96

-4.14

3.63

198588

5249

37.83

-5.40

5173

208742

37.88

-5.27

-3.72

-6.88

206699

5182

39.89

-0.26

4852

207714

39.95

-0.11

-3.92

-1.87

202608

5116

39.60

-0.97

5106

190928

39.54

-1.14

-4.03

0.83

209891

4987

42.09

5.25

4939

199391

42.04

5.12

-4.26

6.64

196508

5099

38.54

-3.64

5034

204021

38.58

-3.53

-3.81

-4.74

206259

5219

39.52

-1.17

5183

207945

39.53

-1.16

-3.95

-1.35

203276

4920

41.32

3.31

5155

190426

41.19

3.00

-4.27

6.73

AN102

Dataforth Corporation

Page 8 of 9

Table 2 Single Stage Op Amp Difference Amplifier Error Budget 1 Reference Figure 1 Table 2 is available on Sheet #2 of the interactive Excel Workbook from Dataforth's Web site. The reader is encouraged to download this Excel file http://www.dataforth.com/catalog/pdf/an102.xls , choose their own values, follow instructions, and examine the effects of their own selected values.

o

T

Temp C

Vcm

Res %

40

5

5

RFo

RAo

R2o

2.00E+05 5.00E+03 2.00E+05

R1o 5.00E+03

CMR-db

Random Total

90

Error

Error

Max

Min

1.29E+00 -1.18E+00

Manufacture's Variation Ib

Ibos

Vios

Ib%

%Ibos

%Vios

Ib TC

Ibos TC

Vios TC

5.00E-07

2.00E-07

5.00E-03

30

30

50

3.00E-09

1.00E-09

1.00E-03

Ib

Ibos

Vios

CMR

Total

Error

Error

Error

Error

Error

Vout

Vout

Vout

Vout

Vout -7.32E-01

(T-25)*TC 4.50E-08

1.50E-08

1.50E-02

RF

RA

R2

R1

Ib

Ibos

Vios

193102

5038

206774

4989

4.83E-07

1.93E-07

-1.97E-02

7.32E-04

3.76E-02 -7.77E-01

6.22E-03

191335

5153

195247

4830

5.55E-07

2.10E-07

1.99E-02

6.44E-03

3.94E-02 7.60E-01

6.03E-03

8.12E-01

205315

4808

193496

4908

5.67E-07

2.48E-07

-1.87E-02

-2.21E-03

5.20E-02 -8.19E-01

6.91E-03

-7.63E-01

205654

5117

207763

4798

6.28E-07

-1.88E-07

2.20E-02

7.82E-03 -3.79E-02 9.06E-01

6.51E-03

8.82E-01

191690

4861

203498

5218

5.80E-07

2.38E-07

1.91E-02

-8.14E-03

4.79E-02 7.72E-01

6.39E-03

8.19E-01

204455

5249

204525

4962

6.86E-07

1.74E-07

-1.78E-02

7.49E-03

3.51E-02 -7.11E-01

6.32E-03

-6.63E-01

191123

4893

196013

5084

5.50E-07

-1.74E-07 -2.16E-02

-4.08E-03 -3.44E-02 -8.67E-01

6.33E-03

-8.99E-01

-6.40E-03

194164

4903

200494

5214

5.26E-07

2.69E-07

198688

4795

191002

5071

6.45E-07

-2.51E-07 -1.94E-02

2.08E-02

190055

5050

203453

4765

4.37E-07

-2.71E-07

199956

5233

207930

4819

4.44E-07

-2.73E-07 -2.16E-02

193480

4864

198482

5069

4.50E-07

-2.56E-07

1.94E-02

202350

4950

193810

5083

4.48E-07

2.74E-07

2.05E-02

-2.28E-03

204159

4831

203058

5213

6.18E-07

1.85E-07

-2.05E-02

209620

4889

194672

5121

4.69E-07

2.43E-07

-1.88E-02

198405

5243

206783

5187

6.84E-07

-1.91E-07 -2.24E-02

195662

5221

192646

4898

4.43E-07

-2.71E-07

1.85E-02

202552

4912

203547

5165

4.82E-07

2.38E-07

2.24E-02 -2.02E-02

2.05E-02

206336

4998

196925

4917

6.59E-07

1.62E-07

205725

4821

197022

4800

5.44E-07

-1.79E-07 -2.24E-02

201991

5003

192550

4836

4.14E-07

2.69E-07

1.94E-02

191320

4781

207967

5020

6.53E-07

-2.33E-07

1.85E-02

Note: 1

5.47E-02 8.45E-01

6.42E-03

8.99E-01

-7.07E-03 -5.20E-02 -8.24E-01

6.71E-03

-8.76E-01

4.45E-03 -5.06E-02 7.92E-01

6.11E-03

7.52E-01

6.78E-03 -5.31E-02 -8.48E-01

6.20E-03

-8.89E-01

-3.63E-03 -5.12E-02 7.90E-01

6.45E-03

7.42E-01

5.68E-02 8.57E-01

6.62E-03

9.18E-01

-9.71E-03

3.98E-02 -8.86E-01

6.84E-03

-8.49E-01

-4.36E-03

5.28E-02 -8.27E-01

6.94E-03

-7.71E-01

1.27E-03 -3.83E-02 -8.70E-01

6.14E-03

-9.01E-01

6.08E-03

6.71E-01

-4.92E-03

5.26E-03 -5.21E-02 7.12E-01 5.01E-02 9.45E-01

6.68E-03

9.97E-01

2.32E-03

3.35E-02 -8.52E-01

6.69E-03

-8.10E-01

5.83E-04 -3.72E-02 -9.77E-01

6.91E-03 -1.01E+00

2.83E-03

5.40E-02 8.02E-01

6.54E-03

8.66E-01

-6.35E-03 -4.64E-02 7.60E-01

6.48E-03

7.14E-01

Gol*RA/(RA+RF) Assumed >>>1 with Ro, Rdi, Rcm, PSRR neglected

AN102

Dataforth Corporation

Page 9 of 9

Table 3 Instrument Amplifier Error in Gain (2RF/RG+1) Including Error Parameter Analysis 1 Reference Figure 3 Table 3 is available on Sheet #3 of the interactive Excel Workbook from Dataforth's Web site. The reader is encouraged to download this Excel file http://www.dataforth.com/catalog/pdf/an102.xls , choose their own values, follow instructions, and examine the effects of their own selected values Exact G1o 2.00E+05

G2o 2.00E+05

RF1o

RF2o

RGo

V1

∆21 Vout

1.00E+05

1.00E+05

5000

1.00

4.099

Eqn 12 ∆21 Vout 4.100

G%

G%

R%

R%

R%

V2

Gain

20

20

0.1

0.1

1

1.10

41

Error Analysis for RF1o = RF2o

Eqns 13,14,15,16

% Error ∆21 Vout

2.05E-02

Errors

CMR1-db

CMR2-db

Rp1

Rp2

Ip2 = Ip1

∆21 In

∆12 Vios

100

90

6.00E+03

4.00E+03

5.00E-08

2.00E-09

1.000E-03

∆21 Vout 2.58E-02

Error

Error

Error

Error

-1.02E-03

4.10E-03

2.00E-04

4.10E-02

∆21 Vout

Eqn 12

Exact

Random Gain Error Analysis G1

G2

RF1

RF2

RG

∆21 Vout

% Error

Gain

Gain

203525 226311 205449 160380 189823 229027 198000 185516 180830 163181 196510 184617 204613 171270 238467

174864 183534 184110 174330 184638 200575 222777 173917 205588 166445 169837 234514 235265 187169 172733

99962 99953 99982 100090 100038 100042 99944 100097 99969 100079 100055 100029 99966 100018 99916

100005 100078 99958 100013 99986 99997 100077 99960 100007 100042 99930 99989 100084 100037 99923

5031 5030 4965 4965 4972 4967 5037 5042 5034 5032 5013 5036 5043 4959 4953

4.074 4.076 4.126 4.130 4.122 4.126 4.070 4.067 4.071 4.076 4.088 4.071 4.066 4.133 4.134

-6.32E-01 -5.92E-01 6.30E-01 7.23E-01 5.33E-01 6.46E-01 -7.23E-01 -8.02E-01 -7.00E-01 -5.82E-01 -2.82E-01 -7.18E-01 -8.37E-01 8.01E-01 8.21E-01

40.749 40.766 41.267 41.305 41.228 41.274 40.713 40.680 40.722 40.770 40.893 40.715 40.666 41.338 41.345

40.741 40.757 41.258 41.296 41.219 41.265 40.703 40.671 40.713 40.761 40.884 40.706 40.657 41.328 41.337

Note: 1

Ro, Rdi, Rcm, PSRR neglected