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Rev. 0.1 1/15 Copyright © 2015 by Silicon Laboratories AN442 AN442 Si1102 AND Si1120 D ESIGNER ’S G UIDE 1. Introduction The Si1102 and Si1120 are low-cost, high-performance, ac tive-optical reflectance-based proximity sensors. Both drive an LED to illuminate a target, then measure the reflectance from the target to determine its proximity. Both the Si1102 and Si1120 use short-duration strobe pulses to measure reflectanc e. This keeps the average power consumption in the microwatt range. Both devices cancel background dc ambient before making a reflectance measurement. The reflectance measurement is the difference between the dc ambient and dc ambient plus reflection from the target illuminated by the LED. The Si1102 is a stand-alone, dual-port proximity sensor driving a single LED. It uses an internal analog wakeup controller that is controlled through an external resistor to set the time interval between measurements. The PRX output is maintained between measurements allowing the Si1102 to behave as a proximity on-off function. The Si1102 is well suited for applications , such as electronic toys, powering transmitters for RF alarm sensors, and saving energy in homes or offices. Although the best performance is achieved with 850 nm LEDs, the Si1102 can also be used in short-range applications where red visible LEDs are useful, such as hand washers or paper towel dispensers. The Si1102 sensitivity adjustment se ts a fixed proximity threshold, a re flectance level at which it will detect proximity. This absolute level threshold may drift around 20% or more depending on temperature, LED supply voltage, LED aging, and other environmental factors. Consequently, although it is possible to set a threshold that is less than 10% different than the absolute reflection, it may not be consistent. It is, therefore, good system practice to allow for some system programmability, such as using potentiometers. The Si1120 is designed to operate with a microcontroller. Rather than an on/off output as in the Si1102, the Si1120 encodes the reflectance measurement as a pulse-width-m odulated output where the pulse width is directly proportional to the measured reflectance. Silicon Laboratories offers a wide range of microcontrollers that are well-suited for use with the Si1120. Most Silicon Laboratories microcontrollers offer the PCA (Programmable Counte r Array) that can easily be used to measure the pulse width output. With the addition of a microcontroller, higher level functions can be added. The microcontroller can be used to control multiple LEDs, enabling position determination through triangulation. In addition, unique human interface conc epts, such as gestures, can be implemented to enhance the user interface for your product. Such an interface can provide product differentiation, resulting in additional product revenue. The microcontroller can also be used to control multiple sens ors and a single LED for applications that are particularly power-sensitive. The Si1120 can be programmed to drive a 400 mA or 50 mA pulse. When used with a microcontroller, it is possible to dynamically change the LED current drive to eith er optimize for range or lower overall system power consumption. With the microcontroller, the reflectance measurement frequency can be customized based on the current usage state. Another feature ma de possible by a microcontroller is the abilit y to improve the SNR of the reflectance measurement through pulse averaging. When used with IR f ilters and lenses, it is possible to use the Si1120 and microcontroller to detect human-sized objects one meter away.

Figure 3. Si1102 Circuit

1. Electrical Considerations

The following sections do not need to be read sequentially; it is best to simply reference topics of particular interest. common to both the Si1120 and the Si1102. The principles apply regardless of the peak LED current choice. through VLED, through the RLED resistor. saturation region and no longer sinks the peak 400 mA.

3 TXO

4 DNC

depending on the gain setting; consequently, the pulse width is a linear function of the reflection. increase in ambient from reflection before the SREN circuit times out, then the reflection is below the set threshold. time to overcome the photodiode current. Thus the Si1120 PRX pulse width increases with higher reflectance. absolute reflection operation, TXO current variation of up to 10% from battery fluctuations is usually not critical. variation in TXO current with fluctuations in LED or VDD supplies becomes critical. excessively large CLED capacitors or excessively small RLED resistors should be avoided. use an unregulated voltage rail. Using an unregulated voltage rail (must be < 7 V) is generally the best option. the LED can be powered from either. ripple introduced by the sourcing of the LED current does not affect the rest of the system. Table 1. Recommended RLED and CLED vs. VLED

3.3 V 2  ±5%, 1/16 W 10 µF ±20%

7.0 V 10  ±5%, 1/2 W 10 µF ±20%

6 Rev. 0.1 2.2.2. LED Current Tapped from Regulated Supply Rails The first step is to determine whether the regulated ra il has enough current for the LED. It is best to consider sourcing 2 ms at 400 mA to best assess the supply capability. It is desireab le for the regulator to supply the entire 400 mA. However, it is no cause for alarm if the regulated supply cannot instantaneously supply the full 400 mA for 2 ms. It is still possible to ascertai n feasibility by allowing some of the current to be supplied by capacitors on the voltage rail. Note that this comes at a price; for capacitors to supply current, voltage must drop. The amount of voltage drop is governed by the following equation: Converted to a form we can use for this analysis: This equation determines the voltage drop that occurs at the point of current draw. The voltage drop is directly proportional to the current drawn from the capacitors and the pulse time and is inversely proportional to the capacitance in the system. Finally, approximate the amount of current supplied from the capacitors by subtracting the current that can be supplied by the regulator. Thus, the equation reaches its final form: 2.3. Estimating System Power The system power consumption is dominated by the power delivered to the IR LED. For this reason, the simplest way to estimate system power is to focus on the LED current. The following equation can be used: For example, assume that the LED current is from a 5 V unregulated supply. Also assume that, for the majority of the time, the Si1102 or Si1120 detects nothing (PDETECT = 0). If the conversion frequency is 10 Hz, then: The power drawn by the Si1120 or Si1102 on VDD is small compared to the power used in the LED. For the Si1120, it is recommended that the host firmware keep the Si1120 in its low-power state. Given the same assumptions, the power drawn by the Si1120 when powered at VDD is: iC dv dv dt i C----= dv .002

0.4 I REG–

where: C is the overall capacitance at the VLED rail IREG is the current supplied by the regulator for the LED PLED 1-PercentDetect PNO_DETECT PercentDetect+ PDETECT PNO_DETECT ConvFreq 15 µsec 400 mA VLED PDETECT ConvFreq 1000 µsec 400 mA VLED PLED PNO_DETECT 10 Hz 15 µsec 400 mA 5 V  PLED 300 µW PCHIP ConvFreq 15 µsec 14 mA VDD PCHIP 6.9 µW=

the 400 mA drivers for currents in the LED and ground return paths including the LED decoupling capacitors. LED capacitor to its local ground, and the other loop is formed from the VLED to ground. source approximation of the transistor and a simple constant voltage source model of the LED. Figure 6. Simplified LED Circuit

8 Rev. 0.1 3. Optical Considerations This section contains various light-related topics helpful in understanding the light environment and its effect on the Si1102 and Si1120. In general, the following sections are self-contained and need not be read sequentially. Some of the topics covered are:  Basic reflectance proximity principles  Single port vs. dual port windows  Receiver sensitivity of the Si1102 and Si1120  Light noise  Improved range  LEDs 3.1. Reflectance Proximity Principles Unlike Passive Infrared Receivers (PIR), which detect object motion by sensing changes in illuminated or naturally- emitted infrared, reflec tance proximity devices actively illuminate t he object with an emitter, directly measuring reflectance. However, unlike radar or lidar, which meas ure reflectance transit time to determine distance, reflectance proximity sensors use signal level and optical techniques to de termine range. Because the reflectance from an object falls off with the fourth power of the distance (as with radar), if the object's angle is less than the beam width of the emitter or receiver, the signal level of the reflectance can provide a range estimate typically within a factor of two since an object’s reflectance does not typically vary by more than about ten to one. Although, this same fourth-power response severely lim its range beyond about ½ meter without optical lensing or averaging, it does mean that large or even very reflective objects more than 2x further than the proximity range will not cause spurious detection, unlike PIR devices. 3.2. Single Port vs. Dual Port Single-port operation, where the same window is used for both transmit and receive, creates significant receiver overload issues (even for radar). Single port operation is particularly problematic with non-transit time reflectance- based systems since the reflectance from a common sh ared window for the transmit LED and the receive photodiode produces a very large interfering signal with no way of differentiating the reflection from the window or object (unlike transit time systems). Without some type of optical is olation, a single window will easily have 100x more reflectance from the window than the object being dete cted, even if it is only a few centimeters away. This is also why a camera flash uses an optical path separate from the imaging path (unlike very short-range microscopes, which use the imaging objective to illuminate the object) and why car headlights are not behind the windshield. Dual-Port operation will always give th e best performance. The Si1102 only op erates in dual-port mode requiring very high optical isolation where the leakage coupling from the LED to the IC is always less than the reflectance from an object. However, the Si1120 can be used in either dual-port or single-port mode. In single port mode (PRX50H), the Si1120 requires motion detection signal processing. For long-range proximity sensing (usually over ½ meter), high isolation dual-port operation is no rmally not possible since there are normally many large objects within proximity range, such as walls, desktops, etc. These nearby objects return a large reflectance relative to any moving object that needs to be detected. However, for best performance, it is desirable to minimize optical coupling between the transmitting LED and detector. Excessive coupling increases noise floor and spurious motion detection due to ambient light modulation.

Figure 7. Single Port vs. Dual Port An efficient 850 nm infrared LED emitter driven with 400 mA of peak current might output up to 80 mW of infrared. window. Some light will light-pipe internally, but it is usually low enough to allow 5 to 10 cm response.

10 Rev. 0.1 However, it is important to keep in mind that, due to this same very high dynamic range, high optical loss ports are acceptable. A 30 dB (31.6 to 1 attenuation) loss only results in one third the range (up to 15 cm). This means existing holes in product cases not designed for optical use may be acceptable for short-range proximity sensing; so, the receiving IC might be put next to a speaker or microphone hole that even has a screen over it, and the emitting infrared LED might be placed behind a glass displa y screen. In fact, by atten uating the IC input, there is often not much loss in range over what might arise from worst-case environmental light noise. If given two semi- opaque windows, one of which is more opaque than the ot her, it is best to place the LED under the less opaque location and let the Si1120 or Si1102 be in the more opa que location. This choice will result in a better signal-to- noise ratio. Users are warned that it is possible to adjust the Si11 02 to have high apparent sensitivity where the TX to RX coupling might be as much as 10 to 100 times more than the reflectance from the detected object. This type of adjustment will not be stable since dr ift in the gain or power supply volt age can cause spurious detects or no detects. The LED has a high temperature coefficient of around 0.4%/C. Consequently, a 10 °C change can cause a 4% decrease in signal. If it is unavoidable that a high optical coupling exists between the TX (LED) and RX (Si1120), the Si1120 may still be used for motion detection applications, even under this somewhat difficult co ndition. Essentially, motion detection looks for changes in reflection over the last second or so, ignoring longer-term slower changes. For example, the repetitive pulse width (sampled every 100 ms ) output would be averaged over the last 10 seconds, and a motion detection event is determined to occur if the average pulse width value over the last second has changed by at least 10 µsec. In high-s ensitivity proximity mode (PRX50H), 10 µsec of pulse width corresponds to about 3.3 nW/cm 2 of reflectance change. The Si1120 offers tw o proximity ranges that differ in pulse width sensitivity by 9. The less sensitive range overloads (max imum pulse width) at about t en times higher input levels. In a high-reflectance environment, the lower sensitivity range may need to be used. Although motion detection cannot unambiguously detect t he presence or absence of an object unless it moves, it can estimate object distance and possibly direction of motion when the object moves. Because of the fourth-power effect, a 20% change in distance results in a change in measured reflectance of over two to one. Since any motion- detected object must return a reflectance that is more than the change threshold, this means that we should be able to accurately and easily detect object movement. Direction of motion can be valuable but may require multiple LED sources. If the Si1120 is not used for motion but, rather, as a two-port absolute proximity detector, the calibrate mode (OFC) should be used to maximize performance. This mode is implemented internally in the Si1102, but, in the Si1120, it is provided as a separate mode. The calibration esse ntially measures the zero reflectance value by making proximity measurement with the LED TX driver turned off. If a microcontroller controls mult iple LEDs, it is possible to perform this calibration function by disabling the LED and doing a proximity measurement (in either high or low sensitivity). The calibration function is important since the zero reflection offset value can change by a small but significant amount depending on the dc ambient. Because the dc ambient may be changing rapidly, it is important to perform a calibrate measurement immediately before the proximity measurement without delay between the two measurements. The jitter on the calibration pulse is a measure of noise in the environment and, consequently, can be used to set a minimum detect value; this might be set to one to several times the peak-to-peak jitter value in order to set a robust detect threshold higher than the environmental noise. For motion detection, the calibrate fu nction is usually not necessary since the long-term average provides the reference. On the Si1120, the VIRL Ambient Mode has the same Reflectance-Pulse Width transfer function as the PRX400 or PRX50 Proximity Modes. Therefore, it is possible to use the VIRL Ambient Mode (looking for excessive PRX jitter) as a way of debugging the presence of severe enviro nmental noise when the PRX400 or PRX50 operations result in excessive PRX jitter. In the same way, the VIRH Ambient Mode can be used to debug the PRX50H Proximity Mode.

Rev. 0.1 11 3.4. Light Noise The low-cost silicon photodiode used in the proximity sensor has a peak response in the near infrared but also has a significant response in the visible light region unle ss blocked by a filter. Consequently, both the visible and infrared characteristics of the environment can limit the performance of these proxim ity sensors. Light in the environment is measured in terms of either Lux, which is illuminanc e (visual intensity), or in W/m 2, which is irradiance (power per area). One of the topics relevant to ambient light and noise issues pertaini ng to reflectance proximity sensors is the Luminous Efficacy of Radiation (LER). The LER is the rati o of luminous flux to radiant flux. As a reference, direct sunlight at noon provides about 100 mW/cm 2 of irradiance (received power) or 110 klux of illuminance (visual intensity), usually the maximum continuous light leve l that a proximity se nsor will encounter. Indoor lighting levels are typically less than 1 klux or about 230µW/cm 2 if the light is from efficien t lighting (with no infrared like fluorescent), but, if the 1 klux is from incandescent lig hts, it will produce about 1.5 mW/ cm 2 silicon weighted response (relative to the mW/cm2 for a source at the silicon diode peak response) due to their high infrared output. Sunlight has about one-fourth to one-fifth the silicon diode infrared response per lux as an incandescent bulb. The silicon photodiodes used in the Si1102 and Si1120 tend to have a broad response from about 350 to 1000 nm, with a peak around 830 nm. Light noise in the environment arises principally from shot noise, 120 Hz or 100 Hz ac mains light modulation, and high-frequency electronic ballasts used in fluorescent lights (especially compact fluorescents or CFLs). The behavior of the noise sources is different in the visible versus infrared wavelength bands. Shot noise on a photodiode is proportional to the sq uare root of the current or background ambient level. Generally, the largest shot noise occurs in direct sunlight (~100 mW/cm 2), which, for both devices, is equivalent to an RMS noise of about 3 µW/cm2. A tenfold reduction to 10 mW/cm2 (shade) will reduce this noise to about 1 µW/ cm2. Below 2 mW/cm2, the shot noise is less than the noise floor. Generally, indoor lighting is less than 1 klux and for it to exceed 1.5 mW/cm 2 requires either daylight, window lighting, or bright incandescent lighting. Bright fluorescent lighting is much less than these levels. Consequently, shot noise has little effect on sensitivity for most indoor applications unless the proximity devices are direct ly under strong incandescent lighting. Even in direct sunlight, the increase in noise floor only reduces detection range by less than twofold. The peak-to-peak ripple of incandescent or halogen lig ht sources at 120/100 Hz is about 10% of the average value, but, since incandescent or halogen contains significant power in the infrared region (eight times more infrared than visible light) and since the photodiodes (used for proximity sensing) respond primarily to infrared light, shot noise is a dominant noise source when the proximity detectors are under direct incandescent or halogen light. Fluorescent lights can actually have much higher light ripple percentage than this for both standard ballasts, but virtually the entire ripple is in the visible band. Most high-frequency inverter ballasts filter the input rectified voltage to reduce 120 Hz/100 Hz ripp le or visible flicker but may still have peak-to-peak mains ri pple comparable to incandescent ballasts. Of course, any other type of li ghting powered from the ac mains, whether white LED, industrial sodium lights, mercury vapor, etc., will all typically have these 120/100 Hz components. In addition, the high-frequency ballasts on fluorescen ts typically use 20 kHz (long tubes) to 40 kHz (CFLs) inverters, which generate a triangular current waveform t hat, when folded, causes a 2x frequency light modulation of the ultraviolet light from the mercury vapor plasma discharge. The actual peak-to-peak visible light ripple at 40 kHz or 80 kHz is much less (<5%) than the ultraviolet ripple due to the time constant of the phosphors used on the inside of the tube. Although the mercury plasma mostly generates ultraviolet, it produces a small amount of visible and infrared radiation directly, which can leak past the phosphor. The peak-to-peak percentage modulation of the infrared component can be quite large, although the absolute value is typically low. Without infrared filtering, CFL noise is typically about 5 µW/cm 2 to 10 µW/cm 2 in most CFL illuminated environments. Consequently, for shorter range applications where detect thresholds are above 20 µW/cm2, infrared filtering is not necessary. For best performance, it is recommended that infrared filtering be available for the Si1120 if the ALS function is not used. For the Si1102, infrared filtering is necessary. Although infrared filtering of the receiver IC can remove visible light inverter noise, it gene rally has little effect on shot noise or 12 0/100 Hz infrared from incandescent lights. However, both the Si1102 and Si1120 electrically filter 120/100 Hz noise to reduce its level by 50 dB, or 316 to 1. On the Si1120, 120/100 Hz noise can be mitigated for motion sensing by sampling exactly every 50 ms since there are exactly six cycles of 120 Hz or five cycles of 100 Hz. Similarly, to improve sensitivity and reduce the effects of 120/100 Hz, multi-strobe integration periods should be in exact multiples of 50 ms.

12 Rev. 0.1 3.5. Improving Range As with radar or lidar, beaming of transmit and receive sign als (with dish or directiona l antennas) is important for improved performance. Similarly, for reflectance proximity sensors, lenses that concentrate and beam the reflected light can improve range and more accurately define proximity spaces. Using lenses can increase the range to several meters on both devices. The use of a lens on the receiver increases the signal level and reduces noise pickup from und esirable directions, while a lens on the emitting LED narrows the beam and increases its power angle density in the direction in which it is pointed. The crossover region of the transmit and receive optical beams can provide a proximity detection in space. In addition, multiple, separately-strobed LEDs can be used to define both spec ific proximity region overlaps and relative positions in space, or two LEDs defining different width cones can be used to determine if an object is above or moving directly above a point or off to the side. The main tradeoff in using lenses is th at they tend to make the optical system more “directional”. However, if the goal is to increase the range of detection, it certainly merits consideration. Besides using lenses to improve sensitivity, pulse averaging can also increase range by 3x or more, but this is only viable on the Si1120. Pulse averaging de creases the effects of both internal noise and external noise, typically improving S/N proportional to the square root of th e number of measurement cycles averaged. For example, averaging 10,000 cycles will improve signal- to-noise by a factor of 100, which will typically improve range by a factor of 3. Multiple strobes on the PWM output of the Si1120, can be integrated to improve signal-to-noise. Normally, the signal-to-noise improvement is proportional to the sq uare root of the total number of strobe cycles integrated. For example, if 40,000 strobe cycles are integrated, the signal -to-noise ratio should improve by about 200, which, in turn, will increase pr oximity range by about 3.7 giving a range of two meters without lens. Of course, the total power consumption increases proportionally to the number of strobes. For maximum sampling rate, a dual-port structure should be used in order minimize pulse width by minimizing very near local reflection. However, high- sensitivity integration requires motion detection since, in most applications, at two me ters range, there are fixed weak reflectors closer than two meters, such as walls, floors, ceilings, and doors). If a lens is added on the LED that pr oduces a 10 degree beam width from a 60° arc of the LED, that will increase mw/sr by 6 2 or 36. Similarly, since the active infrared silic on photodiode area on the Si1102 or S1120 is about 1m m2, a lens with 7 mm diameter, will in crease power density in µW/cm 2 by about 38x on the active photodiode. The fourth power of the products of both the TX and rece ive gain is about 6, the increase in proximity range. This illustrates that small lenses can improve range much more than multi-strobe integration. Note that LEDs with built- in lenses are available in the market. Finally, the third basic range-increasing technique is to use safety reflectors or reflective material. These reflectors use the three-surface-corner reflector principle in which light bouncing off the surfaces of the corner of a cube goes directly back to its source. Because the returning light is no t diverging, the reflectance falls off much less than the fourth power; typically, only a few square inches of reflective tape will ea sily double or triple the proximity range. Using all three range extension techniques of reflector ta pe, lenses, and signal integration, an interrupter motion detector with a range of 30 meters may be possible using the Si1120.

Rev. 0.1 13 3.6. LED Parameters and Multiple LED Operation Best performance is generally achieved with the highes t output efficiency 850 nm LEDs. However, 940 nm LEDs can also work. Red LEDs have reduced range but may be suit able in applications where it is desireable to have a visible proximity indicator. White LEDs, which convert blue to white, are not recommended because of the long rise and decay time constant of the phosphors used to broaden or whiten the wavelength. The Si1120 can be used to drive multiple LEDs in conjunction with microcontroller GPIO pins to control multiplexing switches to steer the TXO driver to multiple LEDs. With multiple LEDs, a wide variety of enhanced applications become possible. For example the proximity sensor may be placed on the front of a motorized toy with an LED on each side to allow the toy to sense whether an obstacle is to its left or right and steer away from it or, conversely, to allow a robot doll head to track an object within proximity range by turning its head to keep both reflections at equal amplitude. For human interfaces, multiple appropriately located and lensed LEDs can be used to determine hand gestures laterally, vertically, inward, and ou tward by measuring reflectance and applying suitable algorithms. Simple examples include using hand motion to control the dimming on-off function of a light switch, control picture viewing in an electronic picture frame, or page through documents on e-readers. The proximity sensor can also turn on the picture frame when a viewer's motion is detected nearby and turn it off to save power after the viewer leaves. 3.7. Motion Detection When used with a microcontroller, the Si1120 can be used to implement a simple motion detection system. The simplest motion detection system requires only a single LED. However, if it is desired to cover a larger area, it may be necessary to have multiple LEDs, each targeting a di fferent direction. The number of LEDs used in such a motion detection system is depen dent on the angle co verage. For example, it will ta ke approximately four to five 20° half-angle LEDs to cover 180°. For motion systems, motion sensitivit y is a function of the ti me between samples. Rapid sampling rates will have less difference between adjacent samples. Typically, for human motion detection, sample periods can be anywhere from 10 ms to 1 second between samples. If higher samp ling rates are used to integrate to improve signal-to- noise, moving averages delayed by at least 1 s are us ually required. Of course, motion systems can indicate motion towards or away from, which is sometimes useful. When using motion detection algorithms that detect a ve ry small percentage change in reflection, it is important that the LED driver not saturate but stay in constant current mode in order to minimize the effects of power supply fluctuations on LED TX current, which may cause spur ious motion detection. A few percent variation in LED current from pulse to pulse is not critical. These fluctuations can occur if the LED driver is saturated due to a high LED drop or a series current-limiting resistor and the powe r supply voltage is changing due to other loads or even the LED driver. The 400 mA LED driver is designed to be connected to an independent voltage supply up to 7 V in order to prevent overloadi ng of the regulated Vdd supply. Often, the LED anode supply may have a significant voltage ripple because it is an unregulated battery or input supply with significant wire drop load ripple, etc. Imagine that we have a simple LED circuit with only a resist or and an LED with a 3 V supply. In this case, there is nominally a 2 V constant voltage drop across the LED with only a 1 V drop across the resistor. When there is a 100 mV change on the 3 V supply, this 100 mV change appears primarily across the resistor because the 2 V drop across the resistor is generally constant, due to the na ture of diodes. A 100 mV drop, given an initial resistor voltage of 1 V, translates directly to a 10% drop in current. A 10% drop in current implies a 10% change in total reflectance, and this can easily be 10 times more than the motion change threshold. In order to prevent LED supply modulation, the Si1120 LED TXO driver has been designed to have very high constant current impedance. The 400 mA (or 50 mA) internal current limit has less than a 1% per volt change in current. Consequently, a 100 mV ch ange in LED anode supply will cause less than a 0.1% change in LED intensity, which is much more desirable for sensitive motion detection algorithms. Another source of spurious motion detection can arise fr om dc ambient modulation of the receive gain. On the Si1120, the photodiode and analog front end may have a 1% change in gain over the extremes or dc ambient. This might happen if, in direct sunlight, a shadow falls across the IC receiver. Obviously, if the reflectance is already very high, a 1% change may be more than the motion detection threshold. Again, this is a reason to minimize stray optical coupling for motion detection to keep the ambien t gain modulation below the minimum detection threshold.

a high infrared ambient environment, such as typical outdoor daylight. with the SFH 4650 LED data sheet plot. The mathematical model is shown in Figure 8. Figure 8. Radiant Intensity vs. Angle for the SFH 4650 Model

down to a detector, such as the Si1120 or Si1102. In this simple example, the only source is the SFH 4650 LED. Figure 9. Simple Optical Problem tracing can save computation time. DT is formed. Here, the target is assumed to be a Lambertian diffuse surface. of most objects, including dry skin and clothing. surface, the “brightness” (analogous to radiance) looks the same from all angles; an example is a matte surface.

16 Rev. 0.1 The point is that DT does not have to equal ET, at least not for Lambertian surfaces. What is important is that the target is being illuminated by the LED at an angle of ET. The emitter is an SFH 4650 and is assumed to be a point source. However, it is an unusual point source in that the radiant intensity is a function of ET. For now, we will represent the radiant intensity of the SFH 4650 as: The LED irradiates the surfac e, A. The amount of radiant power at the distance, R E, is essentially the product of the LED radiant intensity and the solid angle that the target intercepts; therefore, the radiant power captured by the target is: The irradiance from the surface is a ratio of the power per unit area; therefore, the surface is irradiance is: Given that the surface is assumed to be Lambertian, it can be shown that the radiance is: This leads to: The Lambertian surface now becomes the light source to the detector. When possible, one should always try to simplify the calculation if assump tions can be made. It is possible to perform an integration of each point on the Lambertian surface and determine how each point contributes to the irradiance at the detector. However, it is best to invoke the "rule of five". The "rule of five" helps determine when a light source can be considered a single point. It is commonly stated that a light source represents 0.03 steradians to the observer; so, if the ratio of the largest dimension of the light source to the distance is less than 1/5, the surface can be considered a point source: From the perspective of the detector, the radiant intensity of the Lambertian surface is: IE f ET units are in W/sr PI E A ETcos RE units are in W ET IE ETcos RE LT ET R ---- where R < 1 LT RE 2   ED IT RD IT LT A DT units are in W sr----- cos=

Rev. 0.1 17 Therefore: and Since the SF 4650 has a mathematical equation: ED from the contribution of that surface can be derived by plugging in the an gles, reflectance R of the surface, the area A, and the distances RE and RD. Note that in Figure 9, the dimension, D, represents the distance of the target to the PCB hosting both the SFH 4650 and the Si1120. As D increases, the ET and ED angles approach 0. Also, the dimensions, R D and R E, get closer to the dimension, D. This simplifies ED: So, it is indeed a fourth root function, as expected for small targets. The analysis can be re peated for as many segments as necessary to cover the entire illuminated surface. As shown, the irradiance, ED, was basically the contribution of a small Lambertian surface irradiated by the SFH 4650. 3.10. Calculating Irradiance from a Specular Surface Reflection When operating in single-port, the window is shared bet ween the detector and the LED. There are actually two reflection coefficients, one for each polari ty. The reflection coefficients are a fu nction of the material differences at the junction and the refractive index, n. Air = 1, and, for a transparent polycarbonate material, it is approximately 1.6. The reflection coefficient is in the neighborhood of 10%, depending on the material. However, whatever R is, the easiest method of calculating the effect of the LED on the detector is to create an image of the specular reflection and then evaluate at twice the distance. In this example, we assume that the LED and the detect or are 2 cm away. Assume that the glass is 1 cm away so that the angles of incidence and reflection are 45°. Using the approximate SFH 4650 mathematical model, the SFH 4650 at 45° has a radiant intensity of 175 mW/sr x 0.137 = 24 mW/sr assuming 400 mA current. The SFH 4650 nominally has a 50 mW/sr at 100 mA, and the derating curve chows that, at 400 mA, there is a 3.5x increase. The equation below is a derived SFH 4650 model that was used to derive this 24 mW/sr result. ED LT A DTcos RD units are in W ED RE 2 RD units are in W IE I0 0.25 1 ET = ED AR I0 D4   IE I0 0.25 1  =

18 Rev. 0.1 It is important to notice that the radiant intensity of the SFH 4650 decreases with increasing . For example, at 60°, the radiant intensity is 0.084 x 50 mW/sr = 14.7 mW/sr, which is around 60% of the radiant intensity at 45°. Returning to the example, the distance is 2.83 cm to the virtual image. Assuming a coefficient of reflection of 10% and applying the inverse square law to the virtual image, the expected irradiance at the detector is 24 mW/sr x 10% / (2.83 cm)2 =3 0 0µ W / c m2. Since an object’s reflectance can be as low as 1 µW/cm 2, this internal reflection represents 300 times that of the object being detected, and this analysis has not yet considered the secondary reflections. It is recommended that optical blocking be used to reduce th is internal reflection. If this is not possible, one should consider the geometry and the LED characteristics in calculating how to reduce the internal reflection. As shown in this example, the incident angle formed at the reflection point is the same angle used in the calculation of the LED radiant intensity. Since the radiant intensity of the LED decreases with increasing incidence angle, we can reduce the amount of unwanted specular reflection by increasing the incident angle. Increasing the incidence angle can be achieved by incr easing the separation between the LED and the detector. The other consequence of moving the detector away from the LED is that the virtual image becomes farther away. Imagine that the separation between the LED and the Si1120 is increased from 2 to 4 cm. This will yield an angle of 63° instead of 45°. This also increases the distance of the virtual image to 3.46 cm. The resulting reflectance is 175 mW/sr x (0.075) x 10% / (3.46 cm)2 = 109 µW/cm2. This is nearly a third of the original 300 µW/cm2 unwanted irradiance. Geometrically speaking, another way of increasing the incidence angle is by moving the window closer to both the IR LED and the Si1120. For example, if the glass is 0.25 cm from the LED and Si1120 instead of 1 cm, the incidence and reflection angles will no longer be 45°, but will now be arctan(1/.25) = 76°. The virtual image is now cm2. Now, consider what happens if the separation is increased while the glass distance is decreased. The angle will become 83°, and the virtual image becomes 4.03 cm distant. 175 mW/sr x (0.0195) x 10% / (4.03 cm) 2 = 21 µW/ cm2; so, doing both methods decreases the unwanted irradiance by an order of magnitude, relative to the original 300 mW/cm2 value. Note that these calculations do not account for secondary reflections and will always be higher. The point being made here is that, in a single-port case, the primary specular reflection can be reduced by increasing the separation between the LED and the Si1120 and by decreasing the distance between the glass and the Si1120 and LED. Another way of looking at this is by relating to human experience. While in broad daylight, or when one tries to look inside a room through a glass window, it is generally di fficult to see anything inside, even though it might be expected that the outside light illuminate the room. The best strategy to see something inside the room is to move closer to the window and apply optical blocking (by using one’s hands) to block the sun's rays.

Figure 10. Specular Reflection

20 Rev. 0.1 3.11. Determining the Reflection Coefficient of a Window This section provides more details on how to calculate the precise reflectance based on Fresnel equations. These can be used to determine the exact coefficient of refl ection based on the incident angle. In prior examples, a reflection coefficient of 10% was assumed. However, this value can be calculated. This information can be found on the on-line encyclopedia, Wikipedia, at http://en.wikipedia.org/wiki/Fresnel_equations. The indices of reflection for the s-polarization and p-polarization are: If, as in most cases, the incident light is of random polarization, the average reflection coefficient can be used. To make matters worse, in our window example, there are actually two surfaces requiring consideration: the inner surface and the outer surface. Both surfaces actually cause reflection. Assuming that interference can be neglected, the combined reflection is: In the case of a single-port design, the n2 > n1, and it can be shown that, at a minimum, the reflection coefficient at small incident angles is: RS n1 icos n 2 1 – – n1 icos n 2 1 – + RP n1 1 – n2 icos– n1 1 – n2 icos+ R RS RP+ R2 R R n1 n2–

Rev. 0.1 21 NOTES:

Silicon Laboratories intends to provide customers with the latest, accurate, and in-depth documentation of all peripherals and modules available for system and software implementers using or intending to use the Silicon Laboratories products. Characterization data, available modules and peripherals, memory sizes and memory addresses refer to each specific device, and "Typical" parameters provided can and do vary in different applications. Application examples described herein are for illustrative purposes only. Silicon Laboratories reserves the right to make changes without further notice and limitation to product information, specifications, and descriptions herein, and does not give warranties as to the accuracy or completeness of the included information. Silicon Laboratories shall have no liability for the consequences of use of the information supplied herein. This document does not imply or express copyright licenses granted hereunder to design or fabricate any integrated circuits. The products must not be used within any Life Support System without the specific written consent of Silicon Laboratories. A "Life Support System" is any product or system intended to support or sustain life and/or health, which, if it fails, can be reasonably expected to result in significant personal injury or death. Silicon Laboratories products are generally not intended for military applications. Silicon Laboratories products shall under no circumstances be used in weapons of mass destruction including (but not limited to) nuclear, biological or chemical weapons, or missiles capable of delivering such weapons. Trademark Information Silicon Laboratories Inc., Silicon Laboratories, Silicon Labs, SiLabs and the Silicon Labs logo, CMEMS®, EFM, EFM32, EFR, Energy Micro, Energy Micro logo and combinations thereof, "the world’s most energy friendly microcontrollers", Ember®, EZLink®, EZMac®, EZRadio®, EZRadioPRO®, DSPLL®, ISOmodem ®, Precision32®, ProSLIC®, SiPHY®, USBXpress® and others are trademarks or registered trademarks of Silicon Laboratories Inc. ARM, CORTEX, Cortex-M3 and THUMB are trademarks or registered trademarks of ARM Holdings. Keil is a registered trademark of ARM Limited. All other products or brand names mentioned herein are trademarks of their respective holders. http://www.silabs.com Silicon Laboratories Inc.

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