{"id":401,"date":"2020-03-14T18:09:32","date_gmt":"2020-03-14T18:09:32","guid":{"rendered":"https:\/\/addictek.com\/?p=401"},"modified":"2022-03-16T23:17:55","modified_gmt":"2022-03-16T23:17:55","slug":"low-power-current-sensor","status":"publish","type":"post","link":"https:\/\/addictek.com\/en\/2020\/03\/14\/low-power-current-sensor\/","title":{"rendered":"Low Power Current Sensor"},"content":{"rendered":"\n

\u00a0 <\/p>\n\n\n\n

In this article we will see how realize a current sensor circuit in a device using Arduino or more in general the ATmega328P CPU. The current sensor will leverage the built-in ADC of ATmega328P and few external components. The current sensor will have a good level of accuracy and low power consumption, making the solution applicable even to battery powered devices. Specifically, I realized this solution to measure the charging and discharging current flowing to and from the backup battery used in the remote sensor which is part of the Solar Thermal Controller<\/em> project (see ref. [1<\/a>]). The backup battery is connected to an UPS module to provide continuos power to the the circuit. The UPS module receives input power from a solar cell and provides a 5v regulated power to the output. When the input power is above the load power the backup battery is kept under charge. Charging power is the difference between the available input power and the load power. When the input power is below the load power, the backup battery is used to source the missing power (see Figure 1). <\/p>\n\n\n\n

\"\"
Figure 1. UPS module and backup battery.<\/figcaption><\/figure><\/div>\n\n\n\n

The battery charge\/discharge current along with the battery voltage level are used to determine the state of charge (SoC) of the battery.<\/p>\n\n\n\n

The technique used to measure the current is based on the Ohm’s law. A shunt resistor is connected in series to the battery between the anode and ground.
The current flowing into the battery and resistor are the same, the voltage drop on the shunt resistor is proportional to the intensity of the current.<\/p>\n\n\n\n

\\[
{V_{shunt} = I_{shunt} \\cdot R_{shunt}}
\\]<\/p>\n\n\n\n

For the application scenario, I wanted to sense charging current up to 600mA <\/em>and discharging current up to 150mA<\/em>. With a 0.1\u03a9 shunt resistor, this corresponds to a maximum voltage drop across the resistor of 0.06V<\/em> while charging and -0.015V<\/em> while discharging.<\/p>\n\n\n\n

Wanting to sample this voltage drop directly with ATmega328P built-in ADC (see figure 2), we have two problems: 1) voltage drop is actually too low to be measured with acceptable accuracy. Even having a adequate voltage reference for the ADC, due to the low voltage range, the reading would possibly be affected by eccessive noise, 2) more important the voltage drop changes polarity, being positive during battery charge and negative during battery discharge .<\/p>\n\n\n\n

\"\"
Figure 2. ADC directly sampling the shunt resistor<\/em> drop voltage<\/figcaption><\/figure><\/div>\n\n\n\n

Here is where the use of an instrumentation operational amplifier<\/strong> comes in handy. An instrumentation amplifier is a kind of differential amplifier with additional input buffer stages to easily match the impedance of the amplifier with the preceding stage. Instrumentation amplifiers are commonly used in industrial test and measurement application and has some useful features like low offset voltage, high CMRR (Common mode rejection ratio), high input resistance and high gain.<\/p>\n\n\n\n

For the purpose of the application scenario described here, we need to select a model supporting single power supply and rail-to-rail output operation range. Second, we want it to sink very low current since we don’t want it to affect the measured current and reduce the battery backup time. There are several models that have similar capabilities, one of them is the AD627an by Analog Devices (see ref. [2<\/a>]). The AD627an supports <\/em>85\u03bcA<\/em> maximum supply current, single supply power starting from +2.2V<\/em> and rail-to-rail output swing. As for other instrumentation amplifiers, the gain can be set with one external resistor. Figure 3 shows how the amplifier can be connected between the shunt resistor and ATmega328p for current sensing:<\/p>\n\n\n\n

\"\"
Figure 3. AD627 used to amplify shunt voltage drop before sampling it with the ADC<\/figcaption><\/figure><\/div>\n\n\n\n

Note that the V–<\/sup><\/em> negative input of the amplifier is connected to ground and V<\/em>+<\/sup> to the the other side of the shunt resistor. Having ground as reference, the voltage on V<\/em>+<\/sup> will be positive during battery charge (current flowing like the red arrow in the picture) and negative during battery discharge (current flowing like the blue arrow in the picture).<\/p>\n\n\n\n

From the datasheet we see that the V<\/em>+<\/sup> amplifier input terminal can go from (\u2212VS<\/em>)\u22120.1V<\/em><\/strong> to (+VS<\/em>)\u22121V<\/em>, while the output can go from (\u2212VS<\/em>)+0.1V<\/em> to (+VS<\/em>)\u22120.15V<\/em>. On the V<\/em>+<\/sup> input side, the ability of this amplifier to go 0.1V<\/em> below the negative voltage supply (the ground in our case and hence V<\/em>–<\/sup>) is very important because we need to sense both positive and negative voltage drop accross the shunt resistor. Applying these specifications to the application scenario where \u2212VS<\/em> is 0V<\/em> (GND) and +VS<\/em> is 5V<\/em>, will result in following absolute limits for V<\/em>+<\/sup> input voltage and Vout<\/sub><\/em> output voltage:<\/p>\n\n\n\n

\\[
-0.1V < V^+ < 4V
\\]<\/p>\n\n\n\n

\\[
0.1V \\lt V_{out} \\lt 4.85V
\\]<\/p>\n\n\n\n

As stated above, the shunt resistor voltage drop will be from \u2212<\/em>0.015V<\/em> to 0.06V<\/em> which is well inside the supported range. Now we need to select appropriate values for the gain (G<\/em>) and reference voltage Voff<\/sub><\/em>, the latter being the offset applied to amplifier output. Ideally, the input\/output transfer function of the amplifier is:<\/p>\n\n\n\n

\\[
V_{out} = [(V^+)-(V^-)] \\cdot G + V_{off}
\\]<\/p>\n\n\n\n

Hence, being V– <\/sup>= 0:<\/p>\n\n\n\n

\\[
V_{out} = [(V^+)] \\cdot G + V_{off}
\\]<\/p>\n\n\n\n

However, since the reality is different from theory, in order to stay within the amplifier operating limits, we need to refer to “INPUT RANGE LIMITATIONS IN SINGLE-SUPPLY APPLICATIONS<\/em>” section of the datasheet and select proper gain and offset values.<\/p>\n\n\n\n

The equation in the datasheet on page 16 is used to check the amplifier internal limits and is reported below:<\/p>\n\n\n\n

\\[
V_{A1} = 1.25 \\cdot (V^- + 0.5V) – 0.25 \\cdot V_{off}-\\frac{(V^+ – V^-) \\cdot 25k\\Omega}{R_{G}}
\\]<\/p>\n\n\n\n

In the above equation, RG<\/sub><\/em> is the value of the external resistor used to set the amplifier gain and is calculated according to the following formula:<\/p>\n\n\n\n

\\[
G = 5 + \\frac {200k\\Omega}{R_{G}}
\\]<\/p>\n\n\n\n

\\[
R_{G} = \\frac {200k\\Omega}{G – 5}
\\]<\/p>\n\n\n\n

The datasheet states that VA<\/sub><\/em>1<\/sub> must be in the range from (\u2212VS<\/em>+50mV<\/em>)=50mV <\/em>to (+VS\u2212<\/em>200mV<\/em>)=4.8V<\/em>.<\/p>\n\n\n\n

Setting a gain of 20 (RG<\/sub><\/em>=13.7 k<\/em>\u03a9) and Voff<\/sub><\/em> = 1.235V<\/em>, we have:<\/p>\n\n\n\n

In case of V<\/em>+<\/sup>=-0.015V<\/em>:<\/p>\n\n\n\n

\\[
V_{A1}^{-} = 1.25 \\cdot (0.5V) – 0.25 \\cdot (1.235V) – \\frac{ (-0.015V) \\cdot 25k\\Omega}{13.7k\\Omega} = 0.343V
\\]<\/p>\n\n\n\n

In case of V<\/em>+<\/sup>=0.06V<\/em>:<\/p>\n\n\n\n

\\[
V_{A1}^{+} = 1.25 \\cdot (0.5V) – 0.25 \\cdot (1.235V) – \\frac{ (0.06V) \\cdot 25k\\Omega}{13.7k\\Omega} = 0.207V
\\]<\/p>\n\n\n\n

Both values are well within the admitted range.<\/p>\n\n\n\n

On the output side, minimum and maximum values will be the following:<\/p>\n\n\n\n

\\begin{equation} \\label{eq:voutmin}V_{out}^{-} = V_{ref} + (V^+ – V^-) \\cdot R_{G} = 1.235V-0.015V \\cdot 20 = 0.935V \\end{equation}<\/p>\n\n\n\n

\\begin{equation} \\label{eq:voutmax}V_{out}^{+} = V_{ref} + (V^+ – V^-) \\cdot R_{G} = 1.235V+0.06V \\cdot 20 = 2.435V \\end{equation}<\/p>\n\n\n\n

Again, both values are within the amplifier limits.<\/p>\n\n\n\n

Sampling the amplifier output voltage with ATmega328P ADC, requires setting the proper voltage reference on the Aref<\/sub><\/em> pin. In this case, a +2.5V<\/em> reference will allow the 10 bit ADC to sample the whole amplifier output range. <\/p>\n\n\n\n

The current sensing precision depends on the ADC resolution and corresponds to the minimum change in current that the circuit will be able to sense. The ADC voltage resolution (ADCVres<\/sub><\/em>) is given by:<\/p>\n\n\n\n

\\[
ADC_{Vres} = \\frac {A_{ref}}{2^N}
\\]<\/p>\n\n\n\n

Where N <\/em>is the ADC resolution in bits which equals to 10 in case of ATmega328P. The variation of amplifier output voltage can be written as follows:<\/p>\n\n\n\n

\\[
\\Delta V_{out} = \\Delta (V^+ – V^-) \\cdot G = \\Delta V^+ \\cdot G = R_{shunt} \\cdot \\Delta I_{shunt} \\cdot G
\\]<\/p>\n\n\n\n

So,<\/p>\n\n\n\n

\\[
\\Delta I_{shunt} = \\frac{\\Delta V_{out}}{R_{shunt} \\cdot G}
\\]<\/p>\n\n\n\n

Substituting \u0394Vout<\/sub> <\/em>with the ADC voltage resolution, we get the minimum variation Ishunt<\/sub><\/em> that can be sampled by the ADC, which is:<\/p>\n\n\n\n

\\begin{equation} \\label{eq:1}
I_{res} = \\frac {A_{ref}}{2^N \\cdot R_{shunt} \\cdot G} = \\frac {2.5V}{1024 \\cdot 0.1\\Omega \\cdot 20} = 1.23mA\/unit
\\end{equation}<\/p>\n\n\n\n

The formula to calculate the current flowing on the shunt resistor is the following:<\/p>\n\n\n\n

\\begin{equation} \\label{eq:2}
V_{out}=V^+ \\cdot G + V_{off} = I_{shunt} \\cdot R_{shunt} \\cdot G + V_{off}
\\end{equation}<\/p>\n\n\n\n

The value sampled by the ADC depends on the ADC input voltage (Vout<\/sub><\/em>), the voltage reference value (Aref<\/sub><\/em>) and the ADC bit resolution (N<\/em>) and can be written as follows:<\/p>\n\n\n\n

\\begin{equation} \\label{eq:3}
ADC = \\frac {V_{out} \\cdot 2^N}{A_{ref}}
\\end{equation}<\/p>\n\n\n\n

Getting Vout<\/sub> <\/em>off (\\ref{eq:3}) and substituting in (\\ref{eq:2}) results in:<\/p>\n\n\n\n

\\begin{equation} \\label{eq:4}
\\frac {ADC \\cdot A_{ref}}{2^N} = I_{shunt} \\cdot R_{shunt} \\cdot G + V_{off}
\\end{equation}<\/p>\n\n\n\n

Finally, we can get Ishunt<\/sub><\/em> off (\\ref{eq:3}):<\/p>\n\n\n\n

\\begin{equation} \\label{eq:5}
I_{shunt} = \\frac{\\frac {ADC \\cdot A_{ref}}{2^N}-V_{off}}{R_{shunt} \\cdot G}
\\end{equation}<\/p>\n\n\n\n

Equation (\\ref{eq:5}) can be used in the sample algorithm to calculate the shunt current from the ADC sample value. Ishunt<\/sub><\/em> will be negative if battery is discharging and positive if battery is charging.<\/p>\n\n\n\n

Sampling accuracy considerations<\/h3>\n\n\n\n

There are some principles that is worth taking into account to improve sampling accuracy. Their application is general and not strictly related to the use case described in this article.<\/p>\n\n\n\n

Adjusting the voltage offset<\/h4>\n\n\n\n

You might have noticed in the above description that the sampling interval of the ADC is not fully used. This is because the offset value of the amplifier is almost centered within the ADC sampling interval (1.235V<\/em> vs. [0V<\/em>-2.5V<\/em>]). This is good if the extension of the negative input range of the amplifier is the same as the positive input range. However, in our case, negative range is [-0.015V, 0V] and positive range [0V, +0.06V]. With a centered offset, the amplifier output will never go below 0.935V<\/em> and above 2.435V<\/em> (see (\\ref{eq:voutmin}) and (\\ref{eq:voutmax})) while the ADC will still be able to sample the whole range from 0V<\/em> to Aref<\/em>=2.5V. In other words, we are wasting part of the sample interval which means reducing the practical ADC voltage resolution. Figure 4 shows the amplifier input range vs output range in case of (a) centered voltage offset value (b) adjusted voltage offset value:<\/p>\n\n\n\n

\"\"
Figure 4. Amplifier input range vs output range in case of (a) centered voltage offset value (b) adjusted voltage offset value<\/figcaption><\/figure>\n\n\n\n

Let’s see how to calculate the appropriate voltage offset for the amplifier according to the negative and positive extension of the input range, ADC reference voltage Aref<\/sub><\/em> and shunt resistor value Rshunt<\/sub> <\/em>:<\/p>\n\n\n\n

\"\"
Figure 5. Amplifier input vs. output range <\/em><\/figcaption><\/figure>\n\n\n\n

Being the amplifier input voltage going from -0.015V<\/em> to 0.06V<\/em> the correct voltage offset can be calculated solving the following equality (see Figure 5):<\/p>\n\n\n\n

\\[
(V_{off}-V_{out}^{min}):(V_{out}^{max}-V_{out}^{min}) = (V^+_0-V^+_{min}):(V^+_{max}-V^+_{min})
\\]<\/p>\n\n\n\n

\\[
V_{off} = \\frac {(V_{out}^{max}-V_{out}^{min}) \\cdot (V^+_0-V^+_{min})}{(V^+_{max}-V^+_{min})} + V_{out}^{min}
\\]<\/p>\n\n\n\n

Since amplifier output range must match the ADC sample the interval that is [Vout<\/sub>min<\/sup><\/em>, Vout<\/sub>max<\/sup><\/em>] = [0, Aref<\/sub><\/em>], we get:<\/p>\n\n\n\n

\\[
V_{off} = \\frac {A_{ref} \\cdot (V^+_0-V^+_{min})}{(V^+_{max}-V^+_{min})}
\\]<\/p>\n\n\n\n

Substituting actual values:<\/p>\n\n\n\n

\\[
V_{off} = \\frac {A_{ref} \\cdot 0.015V}{0.075V} = 0.5V
\\]<\/p>\n\n\n\n

Setting the amplifier offset to +0.5V<\/em> would allow us to increase the gain:<\/p>\n\n\n\n

\\[
G = \\frac {V_{out}^{max}-V_{out}^{min}}{V^+_{max}-V^+_{min}} = \\frac {A_{ref}}{V^+_{max}-V^+_{min}} = \\frac {2.5V}{0.075V} = 33
\\]<\/p>\n\n\n\n

Setting the new gain value in equation (\\ref{eq:1}), will give us the updated sampling precision :<\/p>\n\n\n\n

\\[
I_{res} = \\frac {A_{ref}}{2^N \\cdot R_{shunt} \\cdot G} = \\frac {2.5V}{1024 \\cdot 0.1\\Omega \\cdot 33} = 0.75mA\/unit
\\]<\/p>\n\n\n\n

Averaging and Oversampling<\/h4>\n\n\n\n

Signal averaging and oversamplig are common techniques used to increase current sampling accuracy. In order to make these techniques effective we need to make some assumptions:<\/p>\n\n\n\n