DC Gain of Nanopower Op Amps

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The precision and speed of an operational amplifier (op amp) directly affect the magnitude of power consumption. Reducing current consumption reduces gain bandwidth; conversely, reducing offset voltage increases current consumption.

Many of the electronic characteristics of an op amp interact and influence each other. As the market demand for low power applications increases, such as wireless sensing nodes, the Internet of Things (IoT), and building automation, it is important to understand the trade-offs between these characteristics to ensure that end equipment performance is optimized while power consumption is minimized. In the first of a three-part series, I will look at the power vs. performance trade-offs with respect to DC gain in nanopower precision op amps.

DC Gain

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

Figure 1 : Inverting operational amplifier

Figure 2 : Non-inverting operational amplifier

These configurations yield the closed-loop gain equations for the inverting and non-inverting op amps, Equation 1 and Equation 2, respectively:

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

These equations show that the DC gain is related to the resistor ratio and is independent of the resistor value. In addition, the "power" law and Ohm's law show the relationship between the resistor value and the power dissipated (Equation 3):

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

For nanopower gain and a voltage divider configuration, Equation 3 shows that the minimum current consumption through the resistor results in the minimum power consumption. Equation 4 will help you understand this principle:

R is the resistance value.

From these equations, you can see that you must choose large resistor values that provide gain while minimizing the power dissipated (also called power dissipation). If you cannot minimize the current flowing through the feedback path, there is no advantage to using a nanopower op amp.

Once the resistor values are chosen to meet the gain and power requirements, other electronic characteristics that affect the accuracy of the op amp’s signal conditioning need to be considered. Counting several small systematic errors inherent in non-ideal op amps will give the total offset voltage. Electronic Characteristics – V_OS is defined as the finite offset voltage between the op amp inputs and describes the error at a particular bias point. Note that the error is not documented for all operational cases. To do this, gain error, bias current, voltage noise, common mode rejection ratio (CMRR), power supply rejection ratio (PSRR), and drift must be considered. While this blog post cannot fully discuss all of the parameters involved, we will take a closer look at V_OS and drift and how they affect nanopower applications.

In reality, the op amp presents V_OS across its input terminals, but this can sometimes be a problem in low-frequency (near DC) precision signal conditioning applications. In the voltage gain stage, as the signal is conditioned, an offset voltage will rise, creating measurement errors. In addition, the magnitude of V_OS varies with time and temperature (drift). Therefore, low-frequency applications require fairly high-resolution measurements, and it is important to select a precision op amp with the lowest drift (V_OS ≤ 1mV).

Equation 5 calculates the maximum V_OS as a function of temperature:

Having introduced the theoretical part, such as choosing a large resistor value to improve the gain ratio and accuracy of the op amp for low frequency applications, I will now explain it using a two-lead electrochemical cell as an example. Two-lead electrochemical cells often emit small low-frequency signals, which are used in various portable sensing devices such as gas detectors and blood glucose monitors. A low-frequency (<10kHz) nanopower op amp is selected.

Using oxygen sensing (see Figure 3) as a specific application example, assuming the sensor's maximum output voltage is 10mV (converting current to voltage via the manufacturer's specified load resistor R_L), the full-scale output voltage of the op amp is 1V. Using Equation 2, it can be seen that the value of A_CL needs to be 100, or R_F is 100 times R_2. Choosing 100MΩ and 1MΩ resistors, respectively, gives a gain of 101, and the resistor values are large enough to limit current and minimize power consumption.

Figure 3: Oxygen sensor

To minimize offset error, the LPV821 zero-drift nanopower op amp is an ideal device. Using Equation 5 and assuming an operating temperature range of 0°C-100°C, the maximum offset error produced by this device is:

Another ideal device is the LPV811 precision nanopower op amp. Gathering the necessary values from its data sheet and plugging them into Equation 5 yields:

(Note that the LPV811 datasheet does not specify a maximum upper limit for the offset voltage shift, so the typical value is used here).

If a general-purpose nanopower op amp, such as the TLV8541 , is used instead, the values change to:

( The TLV8541 datasheet does not specify a maximum upper limit for the offset voltage shift, so the typical value is used here.)

As you can see, the LPV821 op amp is an ideal choice for this application. With a current consumption of 650nA, the LPV821 can sense changes in the oxygen sensor output voltage as low as 18V or less, and has only a maximum offset gain error of 2.3mV. If you need to meet both extreme precision and nanopower consumption, a zero-offset nanopower op amp will be your best choice.