SLYA042 July   2024 FDC1004 , FDC1004-Q1

 

  1.   1
  2.   Abstract
  3.   Trademarks
  4. Introduction
  5. CSAs and Input Bias Stage
  6. CSA and Gain Error Factor
  7. Applications for Resistance at Input Pins of Current Sense Amplifiers
    1. 4.1 Input Resistance Design Considerations
  8. Applications for Input Resistance at Reference Pins of Current Sense Amplifiers
    1. 5.1 Bidirectional CSA and Applications
    2. 5.2 Driving CSA Reference Pin With High-Resistance Source Voltage
    3. 5.3 Input Resistance at Reference Pin Design Considerations
  9. Design Procedure and Error Calculation for External Input Resistance on CSA
    1. 6.1 Calculating eEXT for INA185A4 With 110Ω Input Resistors
  10. Design Procedure for Input Resistance on Capacitively-Coupled Current Sense Amplifier
    1. 7.1 Bench Verification of Input eEXT for Capacitively-Coupled Current Sense Amplifiers
  11. Design Procedure for Input Resistance at CSA Reference Pins
  12. Input Resistance Error Test with INA185 Over Temperature
    1. 9.1 Schematic
    2. 9.2 Methods
    3. 9.3 Theoretical Model
    4. 9.4 Data for INA185A4 with 110Ω Input Resistors
      1. 9.4.1 Data Calculations
    5. 9.5 Analysis
  13. 10Input Resistance Error Test with INA191 Over Temperature
    1. 10.1 Schematic
    2. 10.2 Methods
    3. 10.3 Theoretical Model
    4. 10.4 Data for INA191A4 With 2.2kΩ Input Resistors
      1. 10.4.1 Data Analysis
    5. 10.5 Analysis
  14. 11Derivation of VOS, EXT for a Single Stage Current Sense Amplifier (CSA)
  15. 12Summary
  16. 13References

Theoretical Model

Data is checked against a potential theoretical model of the device using equations from Section 6. Although, nearly impossible to back calculate internal device parameters from measured data given many possible combination of error sources, data checks were performed here to verify equations.

First, circuit conditions and all resistors tolerances and drifts were set as shown in Table 9-2.

Table 9-2 Circuit and Device Parameters for Prediction Model
ValueToleranceppm/°C
IB, CM ON (A)5.80E-053.00%300
IOS (A)-5.00E-08-3.00%10
PV (%)0%-0.45%-25
REXT1 (Ω)1100.23%33
REXT2 (Ω)1100.12%30.3
Ra (Ω)4.99E+04-0.200%30
Rb (Ω)15000.300%25

Next, theoretical values of resistors and constants were calculated for each temperature. All values were calculated using equations from Section 6. The total predicted gain (GTotal, predicted) was calculated by multiplying the GEF of modeled internal resistors and the measured device gain. Note that the GEF found in Equation 22 was used.

Equation 22. GTotal, predicted = (GainCSA, Measured=RFBRINT)×GEF
Table 9-3 Prediction Model Resistors and Constants Over Temperature
TA (°C)-4025125
REXT1 (Ω)110.0165073110.253110.6168349
REXT2 (Ω)109.915095110.132110.4657
RBIAS (Ω)2492.7942192488.752482.528125
RINT (Ω)2493.5043062490.0222682483.970779
RFB (Ω)498558.8438497750496505.625
IOS (A)-4.8468E-08-4.8500E-08-4.8549E-08
IB, CM ON (A)5.8575E-055.9740E-056.1532E-05
GDevice, Measured(V/V)199.9430451199.8978107199.883843
CEG0.0002195230.0002203520.000221633
GTotal, predicted(V/V)176.5801647176.4662982176.3379943
CEV0.9999997980.9999997580.999999697
VOS, EXT predicted-2.64999E-06-4.18505E-06-6.62529E-06

Lastly, the prediction model was finished by calculating variable external resistances at the REF pin. Error constants c and m are dependent upon REXT and thus two values are calculated for each REXT. The parameters here have the same terminology and follow the same equations as this Driving Voltage Reference Pins of Current-Sensing Amplifiers, application note.

Table 9-4 Prediction Model Parameters for eEXT, REF
TA (°C)-4025125
Ra (Ω)49703.0896149800.249949.6006
Rb (Ω)1502.0551881504.51508.26125
Rx (Ω)1457.9937991460.380841464.053195
Vref_x (V)0.1466703390.1466239940.146553043
c0.0029098630.002919360.002934036
m0.002901420.0029108620.002925452
c (REXT = 110Ω)0.0029092240.0029187170.002933385
m (REXT = 110Ω)0.0029007850.0029102230.002924806

Note that this theoretical models only assume linear resistor temperature coefficients; when realistically the temperature coefficient can be highly non-linear. Thus the model was tuned to get best matching to the data for change in ambient temperature from 25°C to 125°C.