Understanding Amplifier Measurement Errors in Shunt-Based Current Sensing

Introduction

Shunt-based current sense amplifiers are used in various applications to measure the current flowing through a precision shunt resistor without interrupting the circuit. They work by measuring the voltage drop across the shunt resistor placed in series with the load. The current sense amplifier then amplifies this small voltage drop to a usable level for further processing.

The need to accurately measure current is critical in a wide variety of applications. Some common use cases for shunt-based current sensing include:

• Power Management: Monitoring and controlling power usage in systems like power supplies, battery chargers and energy management systems.
• Battery Monitoring: Measuring the charge and discharge currents in batteries to estimate the state of charge and health of batteries.
• Motor Control: Sensing the current in motor drives to provide feedback for control algorithms in applications like electric vehicles, industrial automation and robotics.
• Overcurrent Protection: Detecting overcurrent conditions to trigger protective measures in power systems, preventing damage to circuit components.
• Load Detection: Determining the presence or absence of a load, or changes in load impedance, which can be critical in systems like power supplies and lighting systems.
• Automotive Systems: Monitoring currents in automotive electrical systems for applications such as fuel injection control, power steering and battery management.
• Solar Power Inverters: Measuring the current produced by solar panels to maximize power point tracking and ensure efficient energy conversion.
• Portable Devices: Integrating into the power management systems of smartphones, laptops and tablets to optimize battery life and ensure safe charging and discharging.
• Telecommunications: Used in telecom power systems to monitor the current in power amplifiers, ensuring reliable operation of communication infrastructure.
• Fault Detection: Identifying circuit anomalies by detecting unexpected current flow, which can be indicative of short circuits or component failures.

A key component in the current sensing circuit is the shunt resistor, which converts the current flowing through it into a proportional voltage drop. Ohm’s law states the voltage drop across the resistor is equal to the product of the current and the value of the resistor. Traditionally, higher value shunt resistors have been used to create a larger voltage drop, making it easier to measure small currents with higher accuracy. However, this approach has several drawbacks:

• Power Loss: A higher resistance results in more power dissipation, which can be detrimental in power-sensitive applications.
• Heat Generation: Increased power loss leads to heat, which can affect the surrounding components and overall system reliability.
• Cost and Size: High precision, high-power resistors are typically more expensive and larger, which can be a concern for compact designs.

Selecting the proper current sense amplifier is critical in enabling an accurate measurement, especially when using a smaller value shunt resistor. The next section will review common sources of errors and the critical specifications for current sense amplifiers.    

Common Amplifier Sources of Error

We will explore in detail several critical sources of error within shunt-based current sensing as it relates to the amplifier, namely offset voltage, common mode rejection, bias current and gain accuracy.

• Offset Voltage (Vos): The offset voltage of a current sense amplifier is the voltage that appears at the output of the amplifier when the input differential voltage is zero. In other words, it's the output voltage error when there should be no output voltage. Typically, this error source is specified as input referred, meaning the voltage error as seen between the inverting and noninverting input pins. Any gain applied by the amplifier will also affect the input referred offset voltage error. Let’s walk through an example of how offset voltage can affect the accuracy of a current measurement.

Suppose you have a current sense amplifier with an input referred offset voltage (Vos) of 1 mV and you want to measure currents up to 10A. You need to choose a shunt resistor value that will give you a measurable voltage drop without causing too much power loss or exceeding the input voltage range of the amplifier.

Let's say you choose a shunt resistor value of 1 mΩ. The voltage drop across the shunt resistor at the maximum current (10A) would be:

Vshunt = I * Rshunt
Vshunt = 10A * 1 mΩ
Vshunt = 10 mV

Now, considering the offset voltage of the current sense amplifier, the actual voltage that the amplifier will measure is the sum of the voltage drop across the shunt resistor and the offset voltage:

Vmeasured = Vshunt + Vos
Vmeasured = 10 mV + 1 mV
Vmeasured = 11 mV

This means that the offset voltage introduces an error into the measurement. In this case, the error is 10% of the measured voltage (1 mV out of 10 mV), which is quite significant.

To reduce the impact of the offset voltage on the measurement accuracy, you could choose a higher value shunt resistor, which would produce a larger voltage drop for the same current. For example, if you choose a shunt resistor value of 10 mΩ, the voltage drop at 10A would be 100 mV:

Vshunt = 10A * 10 mΩ
Vshunt = 100 mV

The measured voltage would then be:

Vmeasured = Vshunt + Vos
Vmeasured = 100 mV + 1 mV
Vmeasured = 101 mV

In this case, the offset voltage introduces an error of only 1% of the measured voltage (1 mV out of 100 mV), which is a significant improvement in accuracy. However, increasing the shunt resistor value has negative consequences such as additional power loss, heat generation and added cost/size, as noted earlier. Selecting a current sense amplifier with a smaller offset voltage will enable the use of a smaller value shunt resistor while maintaining accuracy.

• Common Mode Rejection (CMR): The CMR is a key specification in the performance of shunt-based current sense amplifiers. It measures an amplifier's ability to reject common mode signals, which are the signals that appear simultaneously and in-phase on both the positive and negative inputs of the amplifier. Electrical systems often have noise that can couple into the signal lines as common mode noise. This can be due to electromagnetic interference, crosstalk from other signal lines or ground loops. This specification is typically defined as a ratio—Common Mode Rejection Ratio (CMRR)—and is specified in decibels. A high CMRR in a current sense amplifier ensures that this noise does not affect the accuracy of the current measurement.

Here is a step-by-step example of how to calculate the impact of CMRR on a current measurement. Let’s assume the specified CMRR in the current sense amplifier datasheet is 100 dB. Converting this to a unitless ratio:

CMRR ratio = 10^{(CMRR in dB/20)}
CMRR ratio = 10^(100/20)
CMRR ratio = 100,000

Let’s also assume that in this application, the common mode voltage is 10V. The error due to the common mode voltage that is not rejected by the amplifier is:

Common mode error = Common mode voltage/ CMRR ratio
Common mode error = 10V/100,000
Common mode error = 0.1 mV

Going back to the offset voltage example, using a shunt resistor value of 1 mΩ at the maximum current (10 A), the common mode rejection of the amplifier adds an error of 1% in the current measurement. 

• Input Bias Current: This parameter is the small amount of DC current required by the input terminals of the amplifier to properly operate the internal transistors. This current is necessary to bias the input transistors and is typically very small, often in the range of picoamperes (pA) to nanoamperes (nA). Input bias current is defined as the average of the currents into the two input terminals of an amplifier. This current, when passed through a resistance, will cause an error voltage that will affect the measurement accuracy. In the case of current sense amplifiers, it is sometimes desirable to place resistors in series with the inverting and non-inverting input pins for filtering purposes. In this case, the bias current of the amplifier can play a significant role in the overall error budget and must be taken into consideration when selecting the amplifier.   
  
  
• Gain Accuracy: Gain accuracy refers to the discrepancy between the actual gain of the amplifier and its expected, or ideal, gain. The gain of the current sense amplifier is the ratio of the output voltage to the voltage across the shunt resistor. Ideally, the gain should be a constant value to ensure that the output voltage accurately represents the current flowing through the shunt resistor. However, due to imperfections in the amplifier components, manufacturing variations, temperature dependencies and other factors, the actual gain may differ from the expected value.
  
  This gain error results in an incorrect scaling of the shunt voltage, leading to an inaccurate current measurement. For example, if the gain is higher than intended, the output voltage will be proportionally higher, indicating more current than is actually flowing. Conversely, if the gain is lower, the output voltage will be proportionally lower, indicating less current than actual. Gain error is generally specified for current sense amplifiers in terms of a percentage. Selecting precision current sense amplifiers with low gain error will minimize the impact of this source of error on measurement accuracy.  
• Other Sources of Errors: The above examples and explanations cover four sources of error within current sense amplifiers. Keep in mind that these are simplified calculations and explanations. In real-world applications, other factors such as temperature variations, power supply noise, shunt resistor tolerance and device mismatches can also affect the overall performance of the current sense amplifier.

Minimizing Common Amplifier Sources of Error

The internal architecture of the current sense amplifier plays a large role in minimizing these common amplifier error sources. The use of self-correcting architectures (designs that continuously correct for offset error) has become more and more popular. “Zero-drift” is an industry standard term used by many leading amplifier manufacturers to refer to any continuously self-correcting architecture. Zero-drift amplifiers are designed to minimize the offset voltage over time and temperature, which is a key factor in achieving high precision in amplification applications, including current measurement. The term "zero-drift" doesn't imply that there is no drift at all, but rather that the drift is very low compared to standard amplifiers. In addition to low initial offset and low offset drift, this architecture incorporates continuous or discrete-time feedback mechanisms that dynamically correct for any differences between the inputs, including common-mode signals. This feedback helps to maintain a high CMRR by ensuring that the amplifier responds primarily to the differential component of the input. As noted above, this is a critical factor for accurate current measurement. Another advantage of the zero-drift architecture is the elimination of 1/f noise, commonly referred to as flicker noise, which can contribute to offset drift and affect CMRR. By reducing this type of noise, the amplifier maintains a more stable operation and better common-mode rejection. These characteristics make zero-drift amplifiers particularly suitable for current sensing applications by minimizing these main sources of measurement error.

As noted previously, another major source of error is due to errors in the gain circuitry, specifically the resistor network. To minimize this source of error, some amplifiers implement resistor trimming. The trimming of resistors in the context of current sense amplifiers is a precision technique used to minimize gain errors and improve the accuracy of current measurements. Trimming is typically done during the manufacturing process and is especially important for precision applications where accurate current measurements are critical. Once the resistors are trimmed, the system can reliably measure current with minimal gain error.

Summary

Shunt-based current sensing is a critical technique employed across a wide range of applications, from power management and battery monitoring to motor control and fault detection. The accuracy of these measurements hinges on the performance of the current sense amplifier. Several sources of amplifier error can impact the accuracy of current measurements, including offset voltage, common mode rejection, bias current and gain accuracy.

Offset voltage introduces a baseline error that can significantly affect low-voltage measurements, necessitating the use of higher value shunt resistors to mitigate its impact. However, this approach can lead to increased power loss, heat generation and higher costs. Common mode rejection is essential for filtering out noise that can distort the measurement, and a high CMRR is crucial for maintaining accuracy in noisy environments. Input bias currents can become a factor if series resistors are added to the input pins of the amplifier. Gain accuracy ensures that the output voltage correctly represents the current flowing through the shunt resistor, and any deviation can lead to incorrect current readings.

To minimize these errors, advanced current sense amplifiers such as the MCP6C26 incorporate a zero-drift architecture, which continuously corrects for offset errors and maintains a high CMRR. Additionally, resistor trimming during the manufacturing process helps to reduce gain errors, ensuring precise current measurements.

In conclusion, selecting the appropriate current sense amplifier with low offset voltage, high CMRR, low bias current and accurate gain is vital for achieving precise current measurements in shunt-based sensing applications. By understanding and addressing these common sources of error, engineers can design more reliable and efficient systems that meet the stringent demands of modern electronic applications. To learn more about our portfolio of current sense amplifiers, check out the current sense amplifier web page.