Accurate Power Management in Battery-Powered Systems Using 0-to-1V Analog Multipliers

Importance of Load Power Measurement

Load power measurement is often very important in notebook applications where the entire circuit (load) is powered by a lithium-ion (Li+) battery or by an AC adapter that simultaneously charges the battery. Because the output voltage of each power source is different, the load current is also different. Typically, the AC adapter outputs 16V, and the battery pack consists of three Li-ion cells, which are about 12.6V when fully charged and about 9V when fully discharged.

To accurately manage power in a circuit, simply measuring the load current is not enough because it does not give information about what type of voltage source is being used. In addition, the microcontrollers in some portable applications have limited pins available, so it is necessary to measure power directly rather than measuring voltage and current separately and then multiplying them in firmware.

Building a 0-to-1V Analog Multiplier with the MAX4210D/E/F

The MAX4210D/MAX4210E/MAX4210F are high-side current and power monitors with an internal true analog multiplier. These devices can directly multiply the battery current and an input voltage from 0 to 1V. But if you need to simply multiply two 0 to 1V signals, the input common-mode voltage threshold (4.5V minimum) will prevent the circuit from working.

Figure 1 shows a circuit that uses the MAX4210D/E/F with a MAX4477 op amp and n-channel MOSFET to build a 0 to 1V analog multiplier. This circuit can multiply two independent input voltages up to 1V.

Figure 1: Using the MAX4210D/E/F and the MAX4477 to build a general-purpose 1V analog multiplier.

This application note uses the MAX4210E as an example; the MAX4210D and MAX4210F can also be used to build a general-purpose analog multiplier.

In the Figure 1 circuit, the input voltage V1 is converted to a current by the op amp, MOSFET, and R1 resistor; R2 resistor converts it to a smaller voltage. This small voltage is connected to the differential input of the MAX4210E. The maximum input detection voltage allowed by the MAX4210E is 150mV. Based on this, the values ​​of R1 and R2 are selected: R1 = 1kΩ and R2 = 150Ω. The power supply VCC of the entire circuit is 5V; the MAX4210E has a gain of 25V/V. Therefore, the full-scale output voltage is 3.75V.

The op amp should have an input common-mode voltage range that includes ground and better accuracy than the MAX4210E . The total output error of the MAX4210E is less than ±1.5% of the full-scale output (FSO) range at 25°C. The MAX4477 has a pA-level ultra-small bias current, an input voltage offset of less than 350μV, and a CMRR of at least 90dB; therefore, the error introduced is negligible compared to the MAX4210E. Figure 2 shows the first set of measurement results, with input V2 of 0.9V and input V1 increasing in 100mV increments from 0 to 1V.

Figure 2: VOUT vs. V1, V2 = 0.9V.


The calculated gain error is 0.8%, and the total output error is 0.6% of FSO. The gain error is the ratio of the difference between the measured and ideal slopes to the ideal slope, expressed as a percentage. Each slope is obtained by measuring 2 endpoints, assuming linearity. The total output error is the ratio of the maximum difference between the measured and ideal curves to the FSO of 3.75V, expressed as a percentage.


Figure 3 shows another set of measurements with an input V1 of 0.9V and an input V2 of 100mV increments between 0 and 1V. The calculated gain error is 0.81%, and the total output error is 0.58% of FSO.

Figure 3: VOUT vs. V2, V1 = 0.9V.


For both sets of measurements, the gain error and total output error are within the MAX4210 specifications.


Conclusion

For accurate power management, some applications require load power sensing, not just load current sensing. The MAX4210D/E/F can sense both load current and supply voltage, making them ideal for applications powered by batteries or AC adapters. The application note provides a general-purpose analog multiplier using the MAX4210D/E/F that can multiply two 0 to 1V signals for accurate power management.