# DC Error Budget Calculator Simplifies Selection of Optimal Current-Sense Amplifiers

Abstract: This article describes a systematic approach for calculating the total DC error budget of a current-sense amplifier (CSA). The individual sources of error are discussed and a method for estimating the total error budget is presented. Finally, a step-by-step process explains how to use calculator software, developed to help quickly compute the total error of the selected CSA.

*Elektronikpraxis*magazine.

## Introduction

## Error Sources in a Current-Sense Amplifier

### Input Offset Voltage

_{OS}) of a CSA is defined as the voltage that must be applied across the CSA's inputs to drive the output voltage to zero. Offset errors are usually not measured directly, because in single-supply situations the output of the CSA cannot go below the output voltage low (V

_{OL}) limit. Hence, the input V

_{OS}is more accurately inferred as the intersection between the linear regression of the observed V

_{OUT}and the V

_{SENSE}transfer curve on the V

_{SENSE}axis as shown in

**Figure 1**.

*Figure 1. A plot of output voltage versus sense voltage is used to determine the offset voltage.*

_{OUT1}is the measured output voltage with V

_{SENSE}= V

_{SENSE1}, and if V

_{OUT2}is the measured output voltage with V

_{SENSE}= V

_{SENSE2}, then V

_{OS}can be calculated with the following formula:

(Eq. 1) |

ERROR_{VOS} = G × V_{OS} |
(Eq. 2) |

_{SENSE}resistor is a delicate balance between an acceptable voltage drop or power dissipation across the resistor and the offset error of the CSA. For high-current precision applications where a larger sense resistor cannot be used, a precision CSA can be a better option.

### Gain Error

(Eq. 3) |

(Eq. 4) |

(Eq. 5) |

### Gain Nonlinearity

### Common-Mode Rejection Ratio

(Eq. 6) |

ERROR_{CMRR} = G × Maximum [Abs Value (Min V_{CM} - Data Sheet V_{CM}), Abs Value (Max V_{CM} - Data Sheet V_{CM})] × 10^{-CMRR/20} |
(Eq. 7) |

Data sheet V

_{CM}= common-mode voltage at which the CSA's gain error and offset error are characterized on the data sheet.

Min V

_{CM}= minimum common-mode voltage applied in the user's circuit.

Max V

_{CM}= maximum common-mode voltage applied in the user's circuit.

### Power-Supply Rejection Ratio

_{CC}. The PSRR specification on a data sheet is usually referred back to the input so that its effect can be compared with the applied differential signal. The maximum output referred error from a variation in the supply voltage is specified as:

ERROR_{PSRR} = G × Maximum [Abs Value (Min V_{DD} - Data Sheet V_{DD}), Abs Value (Max V_{DD} - Data Sheet V_{DD})] × 10^{-PSRR/20} |
(Eq. 8) |

Data sheet V

_{DD}= supply voltage at which the CSA's gain error and offset error are characterized on the data sheet.

Min V

_{DD}= minimum supply voltage as applied in the user's circuit

Max V

_{DD}= maximum supply voltage as applied in the user's circuit

### Sense Resistor Tolerance

(Eq. 9) |

### Output Resistor Tolerance

(Eq. 10) |

_{M}= transconductance gain.

## System Error Budget

(Eq. 11) |

(Eq. 12) |

## Current-Sense Error Budget Calculator

### Using the Current-Sense Error Budget Calculator

- Input trip point = 50A (unidirectional)

- Sense-resistor tolerance = 0.5%

- Sense resistor = < 1mΩ

- Supply voltage range = 4.5V to 5.5V

- Input common-mode voltage range = 12V to 18V

- Total error budget = < 2%, which implies a CSA gain error < 2% and V
_{OS}< 1mV since the individual errors cannot exceed the total error budget

#### Step 1. Parametric search

#### Step 2. Current-sense error calculator inputs

**Figure 2**).

*Figure 2. Input fields that must entered by the user.*

#### Step 3. Verify the data sheet specifications

**Figure 3**for the MAX9922 CSA.

*Figure 3. Calculator prefills the relevant specifications from the selected CSA data sheet.*

#### Step 4. Data sheet overrides

**Figure 4**. The calculator prompts the user to reduce the gain because the output voltage cannot exceed the Output Voltage High limit of the part.

**Figure 5**shows the resulting total error budget.

More detailed image (PDF, 1.3MB)

*Figure 4. Error message example if any of the device constraints are not satisfied.*

#### Step 5. Selecting a different CSA

**Table 1**lists the error budget numbers for all the CSAs shortlisted for this example. Results show that only the MAX9922 and MAX9918 meet the total error budget criteria of this application.

Table 1. Total Error Budget Computed Using the Calculator | |||

Part | Total Error (%) | Conditions | |

T = 25°C | T = -40°C to +85°C | ||

MAX9922 | 0.64 | 0.79 | Gain = 60 |

MAX9918 | 1.13 | 1.93 | Gain = 60 |

MAX9929F | 1.39 | 3.45 | — |

MAX4080S | 1.43 | 2.55 | — |

MAX4373F | 2.84 | 6.18 | — |

MAX4172 | — | 2.57 | O/P termination = 6kΩ |