Derivative Integration Algorithm for Proximity Sensing

Proximity sensing applications requires the detection of small changes in capacitance (typically on the order of a few femtofarads) around the noise floor. There are many ways to process the data to determine whether a target was detected or not. So how do you choose? This application note describes a simple algorithm that can be used for proximity sensing or capacitive touch button applications that does not require significant processing overhead. 1 Basic Concept To detect a change in capacitance for proximity sensing applications, a baseline measurement (no target in the sensing area) and a detection threshold above/below the baseline measurement is required to determine whether a target is within close proximity to the sensor. The minimum system sensitivity is set by the noise floor of the sensor and any external interference. The detection threshold must be set at or above this noise floor. Figure 1 illustrates the operation of the detection threshold concept. Figure 1. Signal and Noise Consideration for Determining Detection Threshold There are several issues that arise with this basic idea. For example, if the baseline is not inherently stable or constant and a capacitance drift becomes noticeable, the algorithm will need to track a slow moving average of the baseline and compare that to the actual signal. This can be robust but not efficient. A more efficient and effective way to process the data is to look at the rate of change with a derivative integration algorithm. All trademarks are the property of their respective owners. 1 SNOA939–September 2015 Derivative Integration Algorithm for Proximity Sensing Submit Documentation Feedback Copyright © 2015, Texas Instruments Incorporated X[i-1] = X[0] I[i-1] = 0 Loop1: D[i] = X[i] X[i-1] Is (ABS(D[i]) greater than DT)? true: I[i] = I[i-1] + D[i] else: I[i] = I[i-1] Is (I[i] H /d) true: Object detected I[i-1] = I[i] else: Object not detected I[i-1] = I[i]*L Parameters IT = Integration threshold DT = Derivative threshold L = Leakage factor X[i] = Current sample point X[i-1] = Previous sample point D[i] = Derivative I[i] = Integral of derivative I[i-1] = Previous integral of derivative Derivative Integration Algorithm www.ti.com 2 Derivative Integration Algorithm A derivative integration algorithm (pseudo code shown in Figure 2) is a simple and robust way to process the data. It can be used for both proximity sensing and capacitive touch buttons; the only difference between the two would be the derivative and integration thresholds for each sensor to obtain a robust and highly sensitive response. This algorithm tracks the rate of change or derivative (D[i]) between the current measurement (X[i]) and previous measurement (X[i-1]). Proximity sensing applications require the detection of small capacitance changes (on the order of fF). This requires the derivative threshold (DT) to be very low. As the derivative value passes the threshold, a variable that tracks the integral or sum of the derivative differences accumulate until it passes an integral threshold (IT). Once IT is reached, an object has been officially detected. Changes in capacitance due to noise can be a severe problem, especially if the DT is very low. The integral of the derivative (I[i]) can start to accumulate and falsely trigger as aa detection. Random noise should stabilize the integral value so that the mean is zero (no capacitance drift occurs), but a high integration threshold (IT) can allow enough noise margin for non-random noise. The leakage factor (L) is a value between 0 (instant dissipation) and 1 (no dissipation). It is typically set at 0.99 to represent that the algorithm has some memory and information on past values to determine where the detection boundary occurs. Various leakage factors can be used for a faster recovery time if the integral swings too far positive. This causes temporary sensitivity reduction until the integral can stabilize near zero. Figure 2. Pseudo Code for the Derivative Integration Algorithm As a visual example, once the human hand approaches the sensing area, the integration value starts to accumulate as along as the derivative of the measurements hit the derivative threshold. If the hand has been “detected” by the device (integral value goes above IT) and stops in the sensing area, the derivative flattens out and the integral stops accumulating. As the hand moves away from the sensor, the integral recedes until it goes below the threshold. This indicates the target object is outside of the intended sensing range. For capacitive touch button applications, a low derivative threshold is not required. The integration threshold can be optimized based on the desired button response. Multiple derivative and integration thresholds can be implemented to filter out any high frequency noise seen in the sampled measurements and increase the sensitivity response. Figure 3 shows an example of the raw code waveform with a target in proximity to the sensor using the FDC2214. Figure 4 corresponds to the derivative of the raw code and Figure 5 corresponds to the integral count. As the derivative becomes more negative (object approaching closer to the proximity sensor), the integral count matches the raw code signal as expected. The thresholds can also be optimized to be robust against any slow moving drift that occurs. Figure 6 shows how a drift in the raw code is compensated in the integral count. The signal is preserved without any distortions due to the slow upward drift. 2 Derivative Integration Algorithm for Proximity Sensing SNOA939–September 2015 Submit Documentation Feedback Copyright © 2015, Texas Instruments Incorporated Sample In te gr al C ou nt 0 50 100 150 200 250 300 350 400 450 -2000 -1750 -1500 -1250 -1000 -750 -500 -250 0 250 500 750 D003 Sample D er iv at iv e C ap ac ita nc e C ha ng e 0 50 100 150 200 250 300 350 400 450 -120 -90 -60 -30 0 30 60 90 120 150 180 D002 Sample P ro xi m ity R aw C od e 0 50 100 150 200 250 300 350 400 450 34216500 34217000 34217500 34218000 34218500 34219000 34219500 34220000 D001 www.ti.com Derivative Integration Algorithm Figure 3. Proximity Raw Code Example 1 Figure 4. Proximity Derivative Code Example 1 Figure 5. Proximity Integral Example 1 3 SNOA939–September 2015 Derivative Integration Algorithm for Proximity Sensing Submit Documentation Feedback Copyright © 2015, Texas Instruments Incorporated Sample P ro xi m ity R aw C od e 0 200 400 600 80