How to make precision measurements on a nanopower budget, part 1: DC gain in nanopower op amps

Heightened accuracy and speed in an operational amplifier (op amp) has a direct relationship with the magnitude of its power consumption. Decreasing the current consumption decreases the gain bandwidth; conversely, decreasing the offset voltage increases the current consumption.

Many such interactions between op amp electrical characteristics influence one another. With the increasing need for low power consumption in applications like wireless sensing nodes, the Internet of Things (IoT) and building automation, understanding these trade-offs has become vital to ensure optimal end-equipment performance with the lowest possible power consumption. In the first installment of this three-part blog post series, I’ll describe some of the power-to-performance trade-offs of DC gain in precision nanopower op amps.

DC gain

You probably remember from school the classic inverting (Figure 1) and noninverting (Figure 2) gain configurations of op amps.

Figure 1: Inverting op amp

Figure 2: Noninverting op amp

These configurations resulted in inverting and noninverting op amp closed-loop gain equations, Equations 1 and 2, respectively:

where ACL is the closed-loop gain, RF is the value of the feedback resistor and R2 is the value of the resistor from the negative input terminal to signal (inverting) or ground (noninverting).

These equations are a reminder that DC gain is based on resistor ratio, not resistor value. Additionally, the “power” law and Ohm’s law show the relationships between resistor value and power dissipation (Equation 3):

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

For nanopower gain and voltage divider configurations, Equation 3 tells you that, in order to minimize power dissipation, you need to minimize the current consumption by the resistor. Equation 4 helps you understand the mechanism to do that:

where R is the resistor value.

Using these equations, you can see that you must choose large resistor values that provide both the gain you need while minimizing power dissipation (and therefore power consumption). If you don’t minimize current through the feedback path, you’ll lose the benefit of using nanopower op amps.

Once you’ve determined what resistor values will meet your gain and power-consumption needs, you’ll need to consider some of the other op amp electrical characteristics that will affect the accuracy of signal conditioning. Summing several small systemic errors inherent in nonideal op amps will give you the total offset voltage. The electrical characteristic, VOS, is defined as a finite offset-voltage number between the op amp inputs, and describes these errors at a defined bias point. Please note that it does not describe these errors across all operating conditions. To do that, you must consider the gain error, bias current, voltage noise, common-mode rejection ratio (CMRR), power-supply rejection ratio (PSRR) and drift. Covering all of these parameters is beyond the scope of this post, but let’s look at VOS and drift – and their influence in nanopower applications – in a bit more detail.

Real-world op amps exhibit VOS across their input terminals, which can sometimes be a problem in low-frequency (close to DC) precision signal-conditioning applications. In voltage gain configurations, the offset voltage will gain up along with the signal being conditioned, introducing measurement errors. In addition, the magnitude of VOS can change over both time and temperature (drift). Therefore, in low-frequency applications requiring fairly high-resolution measurements, it’s important to select a precise (VOS ≤ 1mV) op amp with the lowest possible drift.

Equation 5 calculates the worst-case VOS over temperature:

Now that I’ve covered theory, including choosing large resistor values to create gain ratios and op amp accuracy for low-frequency applications, I’ll go over a practical example using two-lead electrochemical cells. For two-lead electrochemical cells which often emit very small signals of low frequency, and are used in diverse portable sensing applications like gas detection and blood glucose monitoring, choose a low-frequency (<10kHz) nanopower op amp.

Using oxygen sensing (see Figure 3) as the specific application example, assume that the maximum concentration of the sensor outputs 10mV (converted from current to voltage by a manufacturer-specified load resistor, RL) and the full-scale output of the op amp is 1V. Using Equation 2, you can see that ACL needs to be 100, or RF needs to be 100 times larger than R2. Choosing values of 100MΩ and 1MΩ, respectively, gives you a gain of 101, and these resistor values are large enough to limit current and minimize power consumption.

To minimize offset error, the LPV821 zero-drift nanopower op amp is a good choice. Using Equation 5 and assuming an operating temperature range from 0°C to 100°C, the worst-case offset error introduced by this device will be:

Another good choice is the LPV811 precision nanopower op amp. Using its data sheet to gather the necessary values plugged into Equation 5 gives you:

(Note that the LPV811 data sheet does not specify a maximum offset voltage drift limit, so I am using the typical value here.)

If you were to use a general-purpose nanopower op amp like the TLV8541 instead, those values would result in:

(The TLV8541 data sheet also does not specify a maximum offset voltage drift limit, so I again used the typical value here.)

As you can see, the LPV821 op amp is the best choice for this application. With 650nA of current consumption, the LPV821 can sense changes in the output of the oxygen sensor down to 18µV or lower, and introduces a maximum offset gain error of only 2.3mV. When you need both extreme precision and nanopower consumption, a zero-drift nanopower op amp will provide the best possible performance.

Thanks for reading this first installment of the “How to make precision measurements on a nanopower budget” series. In the next installment, I’ll discuss how ultra-precise nanopower op amps can help in current-sensing applications. If you have any questions about precision measurements, log in and leave a comment, or visit the TI E2E™ Community Precision Amplifiers forum.

Additional resources

  • I agree that offset drift is an important source of error to consider... Often times you can ignore the initial offset error of an amplifier since most precision applications employ some type of calibration to measure and remove this error. However, offset drift is a more dynamic error and is harder to remove via calibration. It will also be amplified by the op-amp's gain.

    I would disagree though about the offset drift being the limiting factor in resolving changes in the sensor's output voltage... Offset drift will contribute to the overall error and limit the accuracy of your system. However, offset drift is usually a very slow changing error and so it will not necessarily impact the resolution of the system. You can still measure a change in the sensor's output of less than 18 uV, as this change will likely occur much faster than than the change in the amplifier's offset. In this case, it will be the amplifier's noise that will set the limit to the smallest detectable change in sensor output.

    You'll always find that your system's resolution is better than its accuracy, since resolution is only concerned with the repeatability of the measurement (mostly limited by noise), while accuracy is the combination of noise + all of the other sources of error mentioned above.

  • Hi Chris,

    Thanks so much for reading the blog. You are absolutely correct that there are several sources of error in DC gain configurations.

    While the scope of this blog post covered only offset voltage and drift, another key source of error is indeed voltage noise. In the post I noted that readers must consider the gain error, bias current, voltage noise, common-mode rejection ratio (CMRR), power-supply rejection ratio (PSRR) and drift. Your point is well taken and we’ll plan on covering more sources of DC gain error in future blogs – thanks for the feedback!

  • And what effect does the hefty 215nV/rtHz noise spec have on this measurement?

  • Vincent

    My apologies for the delayed response to your question.  Your question is more complex than it first appears.  There are several factors you must keep in mind when calculating noise in your amplifier circuit.  The main contributors are the amplifier as you mentioned, the resistor thermal noise, and the noise of the sensor itself.  Since the LPV821 is a zero drift amplifiers, it's noise characteristic over frequency is relatively flat.  What I mean is that zero drift amplifiers benefit from having little to no 1/f noise.  So the noise density spec you are referring to is the only voltage noise parameter you need to worry about.  In order to calculate the impact of this parameter on your circuit, you can use the following equation.  Voltage Flatband noise = eN x sqrt ((pi/2) x fBW) x (1+RF/R2).  fBW is the closed loop bandwidth of your amplifier circuit plus I would imagine an anti-alias filter at the output of the amplifier which is generally needed for the ADC you are driving.  This is also generally needed for zero drift amplifiers in order to eliminate the noise that is seen from the chopping of the inputs which is occurring at approximately 1kHz on this device.  the gain is your closed loop gain of the amplifier configuration.  Modeling the voltage noise is done by placing the voltage noise at the non-inverting terminal of the amplifier.  the pi/2 is needed to model a first order roll off filter.  the derivation of this formula and performing a full noise analysis of an amplifier requires going much further than what I have described.  After analyzing the impact of the thermal noise of the resistors or the sensor noise in this circuit, you may find that the amplifier noise does not dominate the overall performance.  One last point to consider when a noise calculation is completed, is what resolution ADC will be used.  This is when you look at the SNR of the ADC to make sure that your amplifier circuit is not limiting the capability of your ADC.