1 App. Note Code: 3RF -F APPLICATION NOTE The Link Budget and Fade Margin 9/16 Copyright © 2016 Campbell Scientific, Inc.
3 Table of Contents PDF viewers: These page numbers refer to the printed version of this document. Use the PDF reader bookmarks tab for links to specific sections. 1. Introduction ... 1 2. ... 3 Transmit Power 3. System Loss ... 3 4. Antenna Gain ... 5 5. Path Loss ... 5 5.1 Line -of-Sight Path of Propagation ... 5 5.2 Free Space Propagation Model ... 7 ... 5.3 2-Ray Multipath Propagation Model 7 6. ... 10 Received Signal Level Fade Margin ... 11 7. Conclusions ... 13 8. Figures ... System Gain -Loss Profile for a Link Budget 1 1-1. 5-1. ... 5 Optical Horizon vs. RF Horizon 5-2. Path Geometry for 2 -Ray Propagation Model ... 8 Table 3-1. Attenuation Specification for Belden 9914 ... 4 i
5 The Link Budget and Fade Margin 1. Introduction When planning a long road trip to a remote destination, one of the first considerations is the fuel requirement. One considers the storage capacity and rate of consumption to calculate the fuel required to not only reach the destination, but to also arrive with some level of reserve or margin of safety; accounting for the unforeseeable. A very similar process is involved in planning an RF (radio frequency) telemetry link. One begins with the output power capacity of the transmitter and sums the system gains and losses to determine the level of power actually a reliable link, the level of power available delivered to the receiver. To ensure to the receiver should be in excess of that required for a minimum level of performance. gains and losses between the transmitter and the An account of all the various receiver is referred to as the link budget . The system factors involved in this accounting are illustrated in FIGURE 1-1. FIGURE 1-1. System Gain -Loss Profile for a Link Budget 1
6 The Link Budget and Fade Margin Where: P = the transmit power in dBm. TX L ansmitter. = the total system loss in dB at the tr TX G = the antenna gain in dBi at the transmitter. TX L = the total propagation losses in dB between the transmit and receive PATH antennas. G = the antenna gain in dBi at the receiver. RX L = the total system loss in dB at the receiver. RX P = the receive power in dBm. RX The level of received power in excess of that required for a specified minimum level of system performance is referred to as the . So called, fade margin attenuatio because it provides a margin of safety in the event of a temporary n or fading of the received signal power. The minimum required received power level used for the link budget can be totally arbitrary —owing to the designer’s knowledge and experience . —but is most often tied to the receiver’s sensitivity Simply put, the rec eiver’s sensitivity specifies the minimum RF input power required to produce a useable output signal. Typical values for receiver sensitivity fall within the range of – 90 to –120 dBm. Given the following link description: watts (37 dBm); • RF320 radio (both ends): RF outpu t power = 5 s ensitivity = 0.25 μV ( (signal -to-noise - –119 dBm) for 12 dB SINAD -distortion ratio) and ; operating frequency = 170 MHz. • Omnidirectional antenna (both ends) is a n FG1683: gain = 3 dBd (voltage standing wave ratio ) < 2:1. (5.15 dBi); VSWR • The elevation of the transmitting antenna is 30 meters. Transmission line at transmitter: pn • 31332 Surge Suppression Kit (loss ≈ 0.5 dB); 100 ft. of Belden ® 9914 coax ial cable (loss ≈ 1.7 dB @ 170 MHz); miscellaneous connector loss ≈ 0.5 dB. • elevation of the receiving antenna is 10 meters. The Transmission line at r • 31332 Surge Suppression Kit (loss eceiver: pn ≈ 0.5 dB); 50 ft. of Belden 9914 coax ial cable (loss ≈ 0.85 dB @ 170 MHz); miscellaneous connector loss ≈ 0.5 dB. • The path of propagation is an unobstructed line of sight (LOS) over a smooth earth. • The distance between the transmitting and receiving antennas is 20 miles (32.2 km). The link budget input parameters can now be derived. 2
7 The Link Budget and Fade Margin 2. Transmit Power its of The RF320 RF output power is specified in un watts. The following equation is used to convert power in watts to power in dBm: ) ( - ( 2 1 ) + 30 = 푃푃 log 푃푃 10 푑푑푑푑푑푑 푊푊푊푊푊푊푊푊푊푊 The RF output power of the example radio is 5 watts. Therefore: ( ) + = 10 log 5 watts 30 푃푃 푑푑푑푑푑푑 = 37 dBm P TX 3. System Loss plus System loss is the sum of the total insertion loss in the transmission line any loss due to an impedance mismatch with the antenna. Except for the case where an antenna is mated directly to a transceiver’s antenna connector, there will likely exist some combination of coaxial cables, surge suppressors, and possibly even bandpass filters used to connect the transceiver to the antenna. C ollectively, these devices comprise what is termed . the transmission line Each device in the transmission line that does not produce a signal gain (amplifier) will exhibit some degree of signal loss; a decrease in the signal . The datasheet level at its output relative to its input is known as insertion loss for a given device will usually list the insertion loss, and, as with all things “RF”, the value will be frequency dependent. In most cases, the dominant loss will be attributed to the insertion loss of the relatively longer run of cable -mounted antenna. The cable manufacturer’s datasheet will connecting a tower typically specify cable loss in a table listing attenuation in dB per unit of length TABLE 3-1. versus frequency as shown in 3
8 The Link Budget and Fade Margin S 1 . Attenuation - pecification for Belden 9914 TABLE 3 Nom. Attenuation: Freq. (MHz) Attenuation (dB/100 ft) 5 0 .4 10 .5 0 50 1.0 100 1.4 200 1.8 400 2.6 3.6 700 900 4.1 1000 4.4 1500 5.5 1800 6.1 2000 6.5 2500 7.5 3000 8.3 4000 9.9 TABLE Interpolating from 3-1, 100 ft. of 9914 cable will exhibit a loss of approximately 1.7 dB at an operating frequency of 170 Mhz. One should note that this is the loss of the coaxial cable only and does not include t he additional loss of any connectors used to construct a finished cable assembly. For the purposes of a link budget, the insertion loss for connectors can generally be ignored, but for the sake of completeness, an acceptable approximation is 0.1 dB per connector, feed -thru, or adapter. Because maximum power is transferred to the antenna when the output impedance of the transceiver is matched to the input impedances of the transmission line and antenna, a mismatch of impedances will result in a s of radiated power referred to as ismatch loss . It is likely that m relative los each device in the transmission line will exhibit some small deviation from the Ω characteristic impedance , and the net effect is the aggregate of standard 50 owever, for the purposes of a link budget, the these cascading mismatches. H small effects of transmission line devices are negligible and the mismatch specification of the antenna can be assumed to be the dominant factor. The most commonly quoted indicator of impedance mismatch on an antenna datasheet is VSWR and is typically specified as some maximum value over the operational bandwidth; for example , VSWR < 2:1. The following equation is mismatch loss ( ML ) in dB (use only the left -hand used to convert VSWR to value of the ratio). 2 푉푉푉푉푉푉푉푉 − 1 ) (3-1 1 − � 푀푀푀푀 = − 10 log � � � 1 + 푉푉푉푉푉푉푉푉 Therefore, a VSWR of 2:1 equates to a mismatch loss of 0.511 db. 4
9 The Link Budget and Fade Margin Based on the preceding information, we can now calculate the system loss for both ends of the link. L 0.5) + cable ( – 1.7) + connectors ( – 0.5) + mismatch ( – 0.511) ≈ – 3.2 dB – = surge kit ( TX = surge kit ( – 0.5) + cable ( 0.511) ≈ – L 0.85) + connectors ( – 0.5) + mismatch ( – – 2.35 dB RX Antenna Gain 4. By convention, antenna gain figures used in a link budget are expressed in units of dBi; gain relative to a theoretical isotopic radiator. It is not uncommon for a manufacturer’s datasheet to express antenna gain in units of dBd, gain dipole antenna. Relative to an isotropic radiator, a standard relative to an actual half wave vertical dipole antenna will exhibit an intrinsic gain of 2.15 dB in the horizontal. The following equation is used to convert gain in units of dBd to units of dBi: ) 1 - ( 4 푑푑푑푑푑푑 + 2 . 15 푑푑푑푑푑푑 = The FG1683 antenna in the example has a specified gain of 3 dBd. Therefore, to calculate the gain in dBi of the transmitting antenna and the receiving antenna: = 3 + 2.15 G = G TX RX G = G = 5.15 dBi RX TX 5. Path Loss In most cases, path loss is the principal contributor to loss in the link budget. It is the sum of free space loss plus additional losses induced by the interaction of ctions along the EM (electromagnetic) wavefront with the terrain and/or obstru the path of propagation. -of Line 5.1 Path of Propagation -Sight For the majority of RF telemetry links, the primary mode of EM wave propagation is said to be line of sight, a direct, unobstructed path between the transmitting and receiving antennas . Therefore, for a single antenna, the maximum path of propagation is limited by the distance to the RF horizon. As illustrated in FIGURE 5-1, the RF horizon differs from the optical horizon. 5-1. Optical Horizon vs. RF Horizon FIGURE 5
10 The Link Budget and Fade Margin The optical horizon derives from an optical LOS which is a straight, direct path of slant -range distance from the antenna (or eyeball) to a point tangent to the earth’s surface. An RF LOS follows a curved path that is initially parallel to the ace but is progressively bent toward the surface due to the refractive earth’s surf properties of the atmosphere. Therefore, the distanced to the RF horizon will be somewhat (≈7%) greater than the distance to the optical horizon. For a standard atmosphere ( = k = 1.33) over a smooth earth, standard re fraction the distance to the RF horizon is related to the height of the antenna as follows: (5-1 ) √ 124 푑푑 = 4 . ℎ 퐻퐻퐻퐻퐻퐻 Where: d = distance in kilometers to the RF horizon HOR h = the antenna height in meters above a smooth earth h in feet and d in statute miles: For (5-2 ) √ . 414 = ℎ 푑푑 1 퐻퐻퐻퐻퐻퐻 For an RF telemetry link, the maximum line -of-sight path distance is equal to the sum of the RF horizon distance for both the transmitting and receiving antennas: ) (5-3 124 푀푀퐿퐿 푉푉 ℎ + 4 4 124 . ℎ = . � � 푇푇푀푀 퐻퐻푀푀 푀푀푀푀푀푀 Where: LOS = the maximum line -of-sight path distance in kilometers MAX h = height of the transmitting antenna in meters above a smooth earth TX h = height of the receiving antenna in meters above a smooth earth RX For practical, non -smooth earth applications, all heights should be NOTE as mean sea level relative to a common reference elevation such (MSL). Therefore: 푀푀퐿퐿 푉푉 = 4.124 30 + 4.124 10 √ √ 푀푀푀푀푀푀 = 35 .6 km 푀푀퐿퐿 푉푉 푀푀푀푀푀푀 6
11 The Link Budget and Fade Margin -of-sight path of propagation, the For a link to be considered as having a line distance between the transmitting and receiving antennas must be equal to or -of-sight path distance: less than the maximum line ) 4 5 ( - 푀푀퐿퐿 푉푉 ≤ 푑푑 푀푀푀푀푀푀 푃푃푀푀푇푇퐻퐻 (the distance between the transmitting and receiving antennas) is Since 32 km less than the maximum allowable 35.6 km, this link qualifies as a LOS path of propagation. Free Space Propagation Model 5.2 As an EM wave propagates in free space, the power density per unit area he distance traveled. decreases in proportion to the frequency and the square of t These facts give rise to the classic free space loss equation: ( ) ( 5 - 5 ) 퐹퐹푉푉푀푀 푑푑 = + 20 log ( 푓푓 ) 32 . 45 + 20 log 푑푑푑푑 Where: FSL = free space loss in dB dB d = distance in kilometers f = frequency in megahertz For distance in statute miles: ( ) ( 5 - 6 ) ( 푑푑 = 36 + 20 log 퐹퐹푉푉푀푀 푓푓 ) . 58 + 20 log 푑푑푚푚푚푚푚푚푊푊 푑푑푑푑 Therefore, for a distance of 32.2 km and an operating frequency of 170 MHz: FSL = 32.45 + 20 log (32.2) + 20 log (170) dB FSL = 107.2 dB dB While free space loss alone is often used in link budget calculations, it is important to understand that in this context, the term “free space” is meant literally; no atmosphere and no reflective su rfaces or obstructions of any type. This does not represent a realistic environment for earth -based telemetry links and, for many path scenarios, the use of free space loss alone will not result in a realistic link budget. 5.3 2-Ray Multipath Propagation Mode l In the more typical terrestrial setting, the EM wave must propagate through nonhomogeneous atmosphere over a path of often mixed terrain and uneven topography. Additionally, system design constraints may require that a link be established over a path containing unavoidable manmade or natural obstructions. Many of these non -free -space elements in the physical environment can cause the propagating wavefront to be a bsorbed, scattered, refracted, reflected, or diffracted. For a discussion on line -of-sight obstructions, see Line of Sight Obstruction app note. 7
12 The Link Budget and Fade Margin ffect of these propagation mechanisms on the signal level reaching the The net e antenna can be difficult to evaluate analytically and requires a level receiv ing of detailed information typically not available without a precise survey of the intended path. For these reasons, a commercial software application using established empirical propagation models linked to a GIS database is the recommended tool for predicting losses for an obstructed line -of sight path of propagation. A discussion of these tools and their application is beyond the scope of this document. For the purposes of this exercise, a standard atmosphere and an unobstructed line -of-sight (LOS) path over a smooth earth will be assumed. In this context, the term smooth earth refers to the surface of an NOTE idealized spherical earth of constant radius. For even the most benign of LOS scenarios, the signal captured by the receiving antenna is seldom the result of the direct path of propagation alone. In all but the very shortest of path lengths, there will likely be an indirect or reflected signal arriving at the receiving antenna coincident with the direct signal. The resultant signal delivered to the connected receiver will be the vector sum of the relative amplitude and phase of the direct and reflected wavefronts. For an unobstructed LOS path over relatively flat terrain, the primary source of reflections is the earth’s surface. The effect of the ground reflected wavefront on the received signal is largely dependent on the distan ce between the transmitting and receiving antennas, the relative height of the antennas, and the for a 2 reflective properties of the earth’s surface. The path geometry -ray propagation model is illustrated in FIGURE 5-2. 5-2. Path Geometry for 2- Ray Propagation Model FIGURE The reflected wavefront will arrive at the receiving antenna differing in phase and, possibly, amplitude relative to the direct wavefront. The difference in phase is due to a combination of the increased time required to travel the greater distance ( ) and any phase shift induced into the reflected d” wavefront at the point of reflection. For a horizontally polarized wavefront, there will always be a 180° phase shift induced at the point of reflection. For a vertically polarized wavefront, a phase shift in the reflected wavefront only ) of less than 3 0°. The phase shift in a Ɵ occurs for an angle of incidence ( i 8
13 The Link Budget and Fade Margin -reflected, vertically polarized wavefront can approach 180° for very ground small, of incidence. grazing angles Any decrease or attenuation in the amplitude of the reflected wavefront will be partially due to the longer path, but will be largely dependent on the electrical -field polarity of the incident wave, properties of the reflecting surface, the E and the angle of incidence. For a highly conductive surface material such as steel o r sea water, there will be little to no attention of the reflected wavefront. For poorly conductive surfaces such as soil, rock, wood, and fresh water, the amplitude of the reflected wave can vary greatly. interfere irect wavefront either with the d The reflected wavefront will or destructively . Constructive interference occurs when the constructively ). A 0° phase shift with < ±90° 휃휃 wavefronts arrive more or less in phase ( 푑푑푚푚푑푑푑푑 dB gain in rece ived a small difference in amplitude can result in as much as a 6 signal strength relative to the direct wavefront alone. Conversely, destructive interference occurs when the wavefronts arrive more or less out of phase phase difference of 180° and a small difference in ). With a ±90° > ( 휃휃 푑푑푚푚푑푑푑푑 amplitude, the wavef ronts will cancel out , resulting in a null in the received signal level. It should be clear from FIGURE 5-2 that the factors a ffecting path loss are greatly dependent on the relative heights of the antennas and the path distance. When the difference in antenna heights is large and the path distance is less ), the direct and reflected wavefronts will alternate than a critical distance ( d c tive and destructive interference for successive values of (1, between construc d - 2, 3, and so forth) . However, the path loss will, on average, follow the square -distance behavior defined by the free space loss equation. of-the When the path distance is equal to or greater than the critical distance , the and relative antenna heights become very small compared to the path distance, the angle of incidence will approach 0°. For this path geometry, the phase shift contributable to a difference in path lengths becomes very smal l, and the phase shift induced in the reflected wave approaches 180° for both vertical and horizontal polarization. Under these conditions, the power density per unit area will decrease in proportion to the fourth -power of the distance , and the path an be calculated using the following equation: loss c ) ( ( ) = 120 − log 푃푃푀푀 ℎ 20 ℎ log 푑푑 + 40 (5-7 ) 퐻퐻푀푀 2 퐻퐻푊푊푅푅 푇푇푀푀 Where: PL = 2 -ray path loss in dB 2Ray h = height of the transmitting antenna in meters TX h = height of the receiving antenna in meters RX d = distance between antennas in kilometers 9
14 The Link Budget and Fade Margin s: The critical distance is calculated as follow 4 휋휋 ℎ ℎ 푇푇푀푀 퐻퐻푀푀 ) (5-8 = 푑푑 푐푐 휆휆 Where: d = critical distance in meters c h = height of the transmitting antenna in meters TX h = height of the receiving antenna in meters RX λ = wavelength of the propagating EM wave; 1.76 meters @ 170 MHz. Therefore: 10 ∙ 4 ∙휋휋∙ 30 푑푑 = 푐푐 1.76 d = 2.14 kilometers c : calculate path loss using the free space propagation model (Eq. 푑푑 < 푑푑 For 푐푐 5-5). For 푑푑 ≥ 푑푑 : calculate path loss using the 2 -ray propagation model (Eq. 5 -7). 푐푐 Because the distance between antennas is 32.2 kilometers, this example -ray propagation model. requires the 2 Therefore: 푀푀 = 푃푃푀푀 .2) = 120 − 20 ) + (30 ∙ 10 40 log (32 log 2퐻퐻푊푊푅푅 푃푃푀푀푇푇퐻퐻 = 130.8 dB L PATH Received Signal Level 6. Having derived all of the input parameters to the link budget, we can now calculate the power level arriving at the receiver’s input. FIG From URE 1-1: 퐺퐺 + 퐺퐺 = −푀푀 푃푃 + −푀푀 −푀푀 푃푃 퐻퐻푀푀 퐻퐻푀푀 퐻퐻푀푀 푃푃푀푀푇푇퐻퐻 푇푇푀푀 푇푇푀푀 푇푇푀푀 Therefore: – 89 dBm P 2.35 dB = = 37 dBm – 3.2 dB + 5.15 dBi – 130.8 dB + 5.15 dBi – RX 10
15 The Link Budget and Fade Margin 7. Fade Margin By subtracting the receiver’s specified sensitivity from the calculated received signal level, we can determine the extent to which transient path losses or signal fading can be tolerated before system performance is impacted. As has been noted, the receiver’s sensitivity specifies the minimum RF input power required to produce a useable output signal. A point of consternation for the designer is that transceiver manufacturers will often define and quantify “a useable output signal” in differing and sometimes ambiguous ways. Two common methods of specifying receiver sensitivity are: The minimum input signal level required to limit the number of errors • in the received digital data stream to a maximum Bit Error Rate (BER). –4 BER — A t ypical specification would be: – 103 dBm for 1 x 10 meaning, one bit error for every ten thousand bits received. • The minimum input signal level required to produce a minimum SINAD is the ratio, in dB, of SINAD ratio in the demodulated audio. (Signal + Noise + Distortion) to (Noise + Distortion) and is a n expression of audio quality for voice communications. A typical specification would be: 0.28 μV for 12 dB SINAD. A somewhat subjective industry standard specifies a SINAD ratio of 12 dB as the minimum required for intelligible voice communications. The s ensitivity specification for the RF320 series of radios states the RF input level in units of microvolts (μV). For link budget calculations, it is convenient Ω system (the standard to convert units of voltage to units of power. For a 50 for the telecommuni cations industry) , the following equation can be used to convert volts to power in dBm: 6 − 2 ( ) 푉푉 ∙ 10 ) (7-1 = 푃푃 � � + 30 10 log 푑푑푑푑푑푑 50 Where: P = power in dBm dBm = rms voltage in microvolts V Therefore: at 0 Rx Sensitivity .25 uV for 12 dB SINAD 2 −6 ) ( 10 ∙ 0.25 ) = log � 30 + � 10 푉푉푆푆푆푆푆푆푑푑푆푆 푑푑푆푆 푑푑푆푆푆푆 푃푃 푉푉푅푅 ( 푑푑푑푑푑푑 50 119 dBm – Rx Sensitivity = 11
16 The Link Budget and Fade Margin We can now calculate the fade margin for the link. From FIGURE 1-1: 119 dBm) = 30 dB ( – 89 dBm) – = ( Rx Sensitivity – P = Fade Margin – RX Where P , and 10) (p. Rx Received Signal Level , was derived in Section 6 RX was derived earlier in this section. Sensitivity Conclusions 8. A link budget provides a quick, simplistic assessment of a link’s viability and only should only be used as a design tool. The calculations herein provide -world theoretical approximations and do not account for all of the myriad, real variables that can affect system performance. All link budgets should be verified via observed measurements before committing to an installation. e for empirical data. Analysis is no substitut If a highly reliable, mission critical RF telemetry link is required, the design goal should be for a minimum fade margin of 20 to 30 dB. If the link budget calculations or on -site measurements indicate a fade margin of less than 10 d B, one should exercise all possible options to improve upon this figure. Some possible options are: Use an antenna with a higher gain specification on one or both ends of • the link. One should be cognizant of any FCC regulations that may put limits on the m aximum radiated power for given transmitter site. Increase the antenna elevation at one or both ends of the link. If path • obstructions or multipath interference is suspected, even a small nt increase (or decrease) of one- half wavelength could make a significa difference in received signal level. Any increase in system losses due to a longer transmission line are usually more than offset by the decrease in path loss. • Add a repeater site to the path. By far, the largest factor in a link budget is path loss. line calculators and software search will reveal numerous on A quick web products for calculating path loss and link budgets. Some are better than others. At the very least, the exercise outlined in this application note should impart an awareness —of some of the factors involved omplete understanding —if not a c in designing an RF telemetry link. 12
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