How to achieve precision measurement with nanopower budget

Part 1: DC Gain of Nanopower Operational Amplifier

The high precision and high speed of the operational amplifier (op amp) directly affect the magnitude of power consumption. The decrease in current consumption reduces the gain bandwidth; on the contrary, the decrease in offset voltage increases the current consumption. 

Many electronic characteristics of operational amplifiers interact and influence each other. As the market’s demand for low-power applications is increasing, such as wireless sensor nodes, Internet of Things (IoT) and building automation, to ensure that terminal device performance optimization and power consumption are as low as possible at the same time, understand the balance between various electronic characteristics Vital. This series of blog posts consists of three parts. In the part, I will introduce the balance between DC gain power and performance in nanopower precision operational amplifiers. 

DC gain 

You may remember the typical inverting (Figure 1) and non-inverting (Figure 2) gain configurations of op amps learned in school. 

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Figure 1: Inverting operational amplifier

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Figure 2: Non-inverting operational amplifier

According to these configurations, the closed-loop gain equations of inverting and non-inverting operational amplifiers can be obtained respectively, equation 1 and equation 2:

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In the equation, A_CL is the closed-loop gain, R_F is the feedback resistance value, and R_2 is the resistance value from the negative input to the signal (inverting) or ground (non-inverting).

These equations show that the DC gain is related to the resistance ratio, not the resistance value. In addition, the "power" law and Ohm's law show the relationship between resistance value and power consumption (Equation 3):

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P is the power consumed by the resistor, V is the voltage drop of the resistor, and I is the current flowing through the resistor.

For nanopower gain and voltage divider configuration, Equation 3 shows that the current consumption through the resistor consumes power. Equation 4 helps you understand the principle:

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R is the resistance value.

According to these equations, it can be seen that you must choose a large resistance value that can provide gain and reduce power consumption (also called power consumption). If the current flowing through the feedback channel cannot be made, there is no advantage to using a nanopower operational amplifier.

Once you have selected the resistance value that can meet the gain and power requirements, you also need to consider other electronic characteristics that affect the accuracy of the operational amplifier's signal conditioning. Count several small systematic errors inherent in non-ideal op amps, and you will get the total offset voltage. Electronic characteristics-V_OS is defined as the finite offset voltage between the input terminals of the operational amplifier and describes the error of a specific bias point. Please note that not all errors in the calculation are recorded. For this reason, gain error, bias current, voltage noise, common mode rejection ratio (CMRR), power supply rejection ratio (PSRR), and drift must be considered. This blog post cannot fully discuss all the parameters involved. We will discuss in detail V_OS and drift, and their impact on femto power applications.

In fact, the op amp displays V_OS through the input, but it can sometimes be a problem in low frequency (approximately DC) precision signal conditioning applications. In the voltage gain link, as the signal is adjusted, the offset voltage will rise, resulting in measurement errors. In addition, the size of V_OS changes with time and temperature (drift). Therefore, low-frequency applications require very high-resolution measurement methods. It is very important to choose a precision (V_OS ≤ 1mV) operational amplifier equipped with drift.

Equation 5 calculates the temperature-dependent V_OS:

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I have introduced the theoretical part, such as: choosing a large resistance value for low frequency applications that can improve the gain ratio and the accuracy of the operational amplifier. Now I will use a two-lead electrochemical battery to make an example explanation. Two-lead electrochemical batteries often emit low-frequency small signals, which are used in various portable sensing devices, such as gas detectors, blood glucose monitors, etc. Choose a low-frequency (<10kHz) nanopower operational amplifier.

Using oxygen sensor (see Figure 3) as a specific application example, assuming that the output voltage of the inductor is 10mV (the current is converted into voltage R_L through the load resistance specified by the manufacturer), the full-scale output voltage of the operational amplifier is 1V. Through Equation 2, it can be seen that the value of A_CL needs to be 100, or R_F is 100 times that of R_2. The 100MΩ resistor and 1MΩ resistor are selected respectively, and the gain value is 101, and the resistance value is large enough to limit the current and reduce the power consumption.

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Figure 3: Oxygen sensor

In order to reduce the offset error, the LPV821 zero-drift nanopower operational amplifier is an ideal device. Using Equation 5 and assuming the operating temperature range is 0°C-100°C, the offset error generated by this device is:

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Another ideal device is the LPV811 precision nanopower operational amplifier. Collect the necessary values from its data table and insert it into Equation 5 to get:

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(Please note that the LPV811 data sheet does not specify the upper limit of the offset voltage offset, so the typical value is used here).

If a general-purpose nanopower operational amplifier is used instead, such as TLV8541, the relevant value changes will result in:

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(The TLV8541 data sheet does not specify the upper limit of the offset voltage offset, so the typical value is still used here).

As you can see, the LPV821 operational amplifier is ideal for this application. The LPV821 with a current consumption of 650nA can sense changes in the output voltage of the oxygen sensor as low as 18μV or less, and only has an offset gain error of 2.3mV. If you need to meet extremely high precision and nanopower consumption at the same time, zero-offset nanopower operational amplifiers will be your choice.

Thank you for reading the part in the "How to achieve precision measurements with nanopower operational amplifiers" series. In the second part, I will discuss how ultra-precision micro-power operational amplifiers can help current-sensing applications. If you have questions about precision measurement, please register and leave a message, or visit the Texas Instruments Online Support Community Precision Amplifier Forum.