SLYA042 July   2024 FDC1004 , FDC1004-Q1

 

  1.   1
  2.   Abstract
  3.   Trademarks
  4. 1 Introduction
  5. 2 CSAs and Input Bias Stage
  6. 3 CSA and Gain Error Factor
  7. 4 Applications for Resistance at Input Pins of Current Sense Amplifiers
    1. 4.1 Input Resistance Design Considerations
  8. 5 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. 6 Design Procedure and Error Calculation for External Input Resistance on CSA
    1. 6.1 Calculating eEXT for INA185A4 With 110Ω Input Resistors
  10. 7 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. 8 Design Procedure for Input Resistance at CSA Reference Pins
  12. 9 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

6 Design Procedure and Error Calculation for External Input Resistance on CSA

When using a single-stage, difference CSA and determining input external resistance error, follow the procedure below.

  1. Determine what the system's maximum and minimum ambient temperatures is and use Equation 6 to determine worst-case temperature change from the standard 25°C testing condition (ΔTA, MAX).
  2. Using data sheet information determine the typical (or nominal) values of the internal resistors for CSA's first stage (RBIAS, RINT, and RFB).
    1. Note that typical process values assume TA = 25°C and PV = 0%
  3. Also identify values for bias turn on currents (IB, CM ON) and input offset current (IOS).
    1. IB, CM ON can be determined by calculating the vertical shift in IB, CM as shown in Figure 2-2.
    2. Assuming ±20% variation in this values is a conservative approximation.
  4. Using Equation 8 and Equation 3, calculate the new typical attenuated gain (GainTOTAL, typical) assuming typical process variation (PV = 0%) for RBIAS, RINT, and RFB, nominal tolerance (eREXT = 0%) for REXT, and nominal device gain error (EG = 0%).
    1. Note: Equation for GEF is usually provided in the data sheet.
  5. Calculate the worst-case maximum and minimum resistance values of all resistors using Equation 7 and Equation 9.
    1. Note that the tolerance error for any internal resistance (e.g., RFB) is the process variation (PV) value. Additionally, the temperature coefficient (TC) for any internal resistance is the process value's temperature coefficient (PV_TC).
    2. Note for the calculation of RINT with Equation 9, incorporating the maximum device's internal gain error (EG, MAX) generates a very conservative total gain error approximation. However, given the statistical independence between resistor matching (EG) and resistor tolerance (PV), it is also fair to simply let EG = 0%, but add EG, MAX later during a final root sum square error calculation, E G ,   T o t a l   =   E G , M A X 2   +   E G , E X T 2 .
      1. To simply calculate the gain error caused by the external resistors (EG, EXT), set EG =0% for equation Equation 9.

  6. Calculate the total maximum (positive) gain (GainMAX) and minimum (negative) gain (GainMIN) at 25° ( ΔTA = 0°) using equation set Equation 18 where the inputs and conditions for function Equation 8 are noted.

    1. Maximum gain occurs when:
      1. RBIAS, RINT, and RFB are maximum (positive) tolerance and drift
      2. REXT is at minimum (negative) tolerance and drift
    2. Minimum gain occurs when:
      1. RBIAS, RINT, and RFB are minimum (negative) tolerance and drift
      2. REXT is at maximum (positive) tolerance and drift
  7. Using equation set Equation 11, calculate the new maximum and minimum gain errors at 25°C relative to the new attenuated shunt voltage gain determined in step 4.
  8. Calculate maximum and minimum gains (GainTotal, MAX and GainTotal, MIN) at the maximum temperature swing (ΔTA = ΔTA, MAX) using equation set Equation 18.
    1. Calculate the gain errors relative to the GainTotal, typical using Equation 11
  9. Calculate gain error drift EG, EXT drift in parts per million per degrees Celsius (ppm/°C) using equation Equation 12.
    1. Note that gain error drift cannot remain constant over process variation.
    2. Note that these equations can use any two temperatures for TA1 and TA2, although choosing them at 25°C and 25°C+ΔTA, MAX is most convenient given these gain errors have already been calculated.
  10. Calculate the maximum (positive) offset (VOS_EXT, MAX RTI) and minimum (negative) possible offset (VOS_EXT, MIN RTI) due to REXT at 25°C ( ΔTA = 0°) using Equation 13 with conditions defined by Equation 14.
    1. Using the same conditions, calculate the GEF using Equation 16 and convert RTI offsets into RTS using Equation 4.

    2. See Section 11 at end of this document on how this equation was derived.

  11. Calculate the maximum (positive) offset (VOS_EXT, MAX RTI) and minimum (negative) possible offset (VOS_EXT, MIN RTI) due to REXT at maximum temperature swing (ΔTA = ΔTA, MAX) using function Equation 13 with conditions defined by Equation 14.
    1. Using the same conditions, calculate the GEF using Equation 16and convert RTI offsets into RTS using Equation 4.
  12. Calculate input offset drift due to REXT using Equation 15
  13. Calculate total system error
    1. Equation 5. E T o t a l   =   E G , M A X 2   +   E G , E X T 2   +   ( V O S ,   D e v i c e V S H U N T ) 2   +   ( V O S ,   E X T V S H U N T ) 2   +   ( V O S ,   D e v i c e   D r i f t V S H U N T ) 2 +   ( V O S ,   E X T   D r i f t V S H U N T ) 2
    2. Note that device's input offset (VOSI) and drift specification are referred to the input (RTI). Thus these values need to be referred to the shunt using Equation 4.
    3. If a one point calibration is performed, then offset components at 25°C can be removed.

Error Equations for Resistance at Input Pins of Single-Stage Current Sense Amplifier

Equation 6. ∆ T A ,   m a x   =   M A X { T A ,   h i g h   -   25 ° C ,   25 ° C   -   T A ,   l o w   }
Equation 7. R M A X   =   R N O M I N A L   ( 1   ±   e t o l e r a n c e ) ( 1   ±   Δ T A , M A X × T C R )
Equation 8. G E F   =   R B I A S 2 × R I N T R B I A S 2 × R E X T   +   R B I A S 2 × R I N T   +   R E X T
Equation 9. R I N T ,   M A X   =   R F B ,   M A X G a i n D e v i c e ,   t y p i c a l × ( 1 + E G ,   M A X ) R I N T ,   M I N   =   R F B ,   M I N G a i n D e v i c e ,   t y p i c a l × ( 1 + E G ,   M I N )
Equation 10. G E F M A X   =   G E F P V   =   m a x i m u m   ( e . g . ,   + 20 % ) P V _ T C   =   m a x i m u m   ( e . g . ,   + 30   p p m / C ∘ ) e R E X T   =   m i n i m u m   ( e . g . ,   - 1 % ) T C R E X T   =   m i n i m u m   ( e . g . , - 50   p p m / C ∘ ) E G   =   t y p i c a l   ( e . g . ,   0 % ) G E F M I N   =   G E F P V   =   m i n i m u m   ( e . g . ,   - 20 % ) P V _ T C   =   m i n i m u m   ( e . g . ,   - 30   p p m / C ∘ ) e R E X T   =   m a x i m u m   ( e . g . ,   + 1 % ) T C R E X T   =   m a x i m u m   ( e . g . , + 50   p p m / C ∘ ) E G   =   t y p i c a l   ( e . g . ,   0 % ) G a i n T o t a l ,   M A X   =   ( G a i n D e v i c e = R F B R I N T ) ×   ( G E F M A X ) G a i n T o t a l ,   M I N   =   ( G a i n D e v i c e = R F B R I N T ) ×   ( G E F M I N )
Equation 11. E G ,   E X T   M A X   =   G a i n T o t a l ,   M A X   -   G a i n T o t a l ,   t y p i c a l G a i n T o t a l ,   t y p i c a l E G   E X T ,   M I N   =   G a i n T o t a l ,   M I N   -   G a i n T o t a l ,   t y p i c a l G a i n T o t a l ,   t y p i c a l
Equation 12. E G   D r i f t ,   E X T   M A X   =   E G ,   M A X   T A , 2     -   E G ,   M A X   T A , 1   T A , 2   -   T A , 1 × 10 6 E G   D r i f t ,   E X T   M I N   =   E G ,   M I N   T A , 2     -   E G ,   M I N   T A , 1   T A , 2   -   T A , 1 × 10 6
Equation 13. V O S ,   E X T   R T I   =   ( V R E F - V B U S ) ( 1 - C E V )   +   I B , C M   O N ( R S H + R E X T 2 - R E X T 1 C E V )   -   I O S 2 ( R S H + R E X T 2 + R E X T 1 C E V ) 1   +   ( R S H + R E X T 2 ) ( 1 R I N T + 1 R B I A S )   +   R E X T 1 C E V R B I A S C e v   =   1 + R S H + R E X T 2 R F B + R I N T 1   +   R E X T 1 R F B + R I N T
Equation 14. V O S ,   E X T   M A X   =   V O S ,   E X T P V ,   P V _ T C   =   m i n i m u m I B , C M   O N ,   V C M =   m a x i m u m V R E F   =   m i n i m u m I O S   =   m i n i m u m R E X T 2   =   m a x i m u m R E X T 1 =   m i n i m u m   V O S ,   E X T   M I N   =   V O S ,   E X T P V ,   P V _ T C   =   m i n i m u m I B , C M   O N ,   V C M =   m a x i m u m V R E F   =   m i n i m u m I O S   =   m a x i m u m R E X T 2   =   m i n i m u m R E X T 1 =   m a x i m u m  
Equation 15. V O S ,   E X T   D r i f t   M A X   =   V O S ,   E X T   M A X   a t   T A , 2   - V O S ,   E X T   M A X   a t   T A , 1   T A , 2   -   T A , 2 V O S ,   E X T   D r i f t   M I N   =   V O S ,   E X T   M I N   a t   T A , 2   - V O S ,   E X T   M I N   a t   T A , 1   T A , 2   -   T A , 2
Equation 16. L e t   C E G = R E X T 1 R F I + R E X T 1 V O S ,   E X T   R T I V S H = G E F = 1 ( 1 + R E X T 2 R I N T )   +   R E X T 1 + R E X T 2 R B   -   C E G ( R E X T 1 - R E X T 2 ) R B V O S ,   E X T   R T S   =   V O S ,   E X T   R T I G E F