STL Path Planning James W. Pollock, P.E. [email protected] This is a planning guide, as well as a check list, for those looking at the path requirements for an UHF or Microwave STL (Studio Transmitter Link). The companion spread sheet is designed to be a straight-forward and intuitive resource. It is organized in accordance to the major block functions and their components. There are factors to consider in implementing an STL link. Studio-Transmitter Path. With the assistance of Google Earth or a current topographical map, draw the desired path from source to destination. • Identify elevations (ASL) of the source (studio) and the destination. • Identify the highest elevation between the two points. • Determine the path distance. • Determine the First Fresnel Zone clearance. • Examine the path for obstructions such as buildings, hills, and electric switch yards. • The ideal situation is a straight, clear-shot, free space path. Tx Antenna Fresnel Ellipsoid Rx Antenna Studio, Offices Transmitter Building Obstacle STL Path with a Fresnel Clearance Fresnel Zones. A successful project depends on taking Fresnel Zones into account. The maximum Fresnel radius occurs at the path mid-point of the path. This means that the STL path should clear an obstruction by at least the first Fresnel radius. An encroachment of 20% into the first Fresnel zone is allowed. The Fresnel zone radii are at their minimum at the antenna aperture. The Fresnel zones are a family of concentric ellipsoids that surround the STL path, and their radii are independent of antenna gain. The Fresnel zone is the surface of an ellipse generated by revolving the ellipse along its major axis. The surface of the ellipse defined by the locus of points whose sum of Page 1 of 9 January 01, 2010 . The “odd” Fresnel radii are beneficial in the sense that a reflection from the roof of an obstruction will arrive in phase with the main beam at the receiver.2. jim@jimpollock. 0. Signal path and reflections show signal reinforcement.3. 2010 . Signals tend to reinforce. (:=) means “defined as” 1st Fresnel Zone: Signal path and reflection phase differential is 0o to 90o. Pollock. Signal path and reflection phase differential is 270o to 450o Signals reinforce. Fresnel radius (Fn) in meters Fn D 2 n d( 1 d) n = Fresnel Zone Number..net distances from the focal points are a constant value. Even Fresnel Zone... The focal points represent the parabolic antennas. P. Such a serendipitous event would add 3 db of an apparent “free” gain. Page 2 of 9 January 01. Signal path and reflections show cancellation interference. 3rd Fresnel Zone. Signal path reflection phase differential is 90o to 270o Signals tend to cancel. 2nd Fresnel Zone. In the first Fresnel zone. Simplified Formula for the Path Midpoint: Rn n D 8 note: The operator.STL Path Planning James W. the difference between the direct and reflected paths are 90o to -90o. 1.5 for the midpoint D = End to end length of the path in meters.6 of the first Fresnel clearance gives 3 db gain. which reduces to 0 db at 1. This is when the path difference is an odd multiple of quarter-wavelengths. d = 0.0 Fresnel. Encroachment by an obstacle is recommended to be no more than 40% of the zone radius.E. The “even” Fresnel radii will impose anti-phase interference if they are reflected off the roof of an obstruction. l = Wavelength in meters d = Proportion of “D” from either end of the path.. Odd Fresnel Zone. STL Path Planning James W. don't forget precise antenna alignment. It is analogous to a light bulb illuminating the inside of a sphere.5 o with respect to the center of the path. but you may have to pay penalties in regard to transmitter output power and/or cable sizing in order to compensate for other path losses. As when the radius of the sphere is doubled. the area of the sphere is multiplied four-fold. If the antennas at each end are as much as 8. the narrower the 3db beam-width. Also. and use the minimum amount of cable connectors.E. You may have to enlist the assistance of a land surveyor to align the antennas. Page 3 of 9 January 01. Thus the variables induced by practical antennas do not affect the path loss. or at least provide sighting markers to which you aim the antenna. The best situation is that the cables should be home runs from the antenna to the equipment transient grounding panel. which is not captured.3 meter diameter dish antenna with 20 dbi gain has a 3 db beamwidth of about 17 degrees at 950 MHz. 2010 .5o off center alignment. Power density decreases in proportion to the square of distance from the source. an unexpected loss of 6 db is added to the path. The energy. Antenna alignment with respect to the path thus becomes quite tedious. and the illumination density on the interior surface is one fourth of its former value. The calculations are based the inverse square law. Consider beam-width when chosing an antenna. High gain antennas demand a stable. continues on into free space or is absorbed by the landscape. Path Loss Path loss is calculated with respect to theoretical unity gain antennas with an aperture efficiency of 100% . A given path has a certain loss attributes which are completely independent of the antenna. The energy does not disappear. Approximate 3db (Half Power Beam Width) beam width for a parabolic dish:[1] HPBW = l*70o/D D = Diameter (meters) l = Wavelength (meters) System Losses. P.net Antennas. Lower gain antennas are less demanding. It just becomes less and less dense as it travels away from its source at the speed of light. It is irrelevant as to what antenna is used. Path loss is actually a measure of the energy that has not cannot be captured by a practical antenna. Each 6 db of loss is equivalent to doubling the length of the STL path. This is a +/. Pollock. A 1.8. The higher the antenna gain. Use the best cable that you can afford. rock solid mounting and support system. jim@jimpollock. The path does not care about antennas. will produce an output of 1 watt in a field power density of 1w/m2. 2010 (4) .net For the purposes of the subject at hand. GT = Power Gain of Transmitter Antenna For simplification. and current distribution in the target dipole.55. the antenna gains are set to unity gain (0db). Pollock. [4] g = 4*p* A*(h) l2 (1) The effective area is the physical area multiplied by the efficiency factor (h) for the antenna. [email protected] Path Planning James W. A = l2/(4*p*h) (3) Power Density Power Density at a point which is on a sphere at a distance of “r” from the source is equal to the effective radiated power transmitted divided by the area of the sphere: [5] PD = PT *GT/(4*p*r2) PD = Power density. Typically. the reflectivity of the reflector. The gain (g) is related to the area (A) and efficiency factor (h). Power (PR) received by the receiving antenna is the product of Power Desnity (PD) and the effective Page 4 of 9 January 01. Corrections for gain other than unity and efficiency factor (h) of less than 100% will be addressed. P. Ae = A*h (2) [3] Typical efficiency (h) factor for a parabolic reflector anetnna is 0. The theoretical receive antenna which captures the radiation is assigned a power gain of unity. power density is expressed as watts-per-square meter (w/m2). and are assumed to be 100% efficient. This may seem a bit low.E. a a half wavelength dipole is at the focal point in a parabolic antenna. but the efficiency depends on materials. For our reference receive antenna with a unity (0 db) gain. watts/m2 PT = Transmitter Power in watts. An antenna with an effective capture area of 1 m2. [2]. equation (1) must solved for the required physical area by setting the gain (g) to 1. Pathdb = 20*log(l/(4*p*r)) (9) Page 5 of 9 January 01.STL Path Planning James W. P.E. hR = efficiency factors of the receive antenna. By substituting equation (3) for Ae in equation (5).net phyical area (A) of the receiver antenna. PR = A*hR*PT/(4*p*r2) (5) A = Physical area of the receive antenna. PR = Power received. PR = l2/(4*p)*PT/(4*p*r2) Grouping like terms and simplifying: PR = (l/(4*p*r)2*PT (7) (6) The ratio of power received (PR) and power transmitted (PT) is the attenuation ratio. Path = *(l/(4*p*r))2 (8) In terms of loss in “db” the Path gain (-loss) for the far field is. Pollock. 2010 . jim@jimpollock. PT = Transmitted Effective Radiated Power in watts. STL Path Planning James W. jim@jimpollock. r = Path distance in kilometers l = Wavelength in meters Pathdb = 20*log(l) – 20*log(r) -82.E. Pollock. P.net The Final Path Equation Expansion of Equation (9): Pathdb = 20*log(l) – 20*log(r) –20*log(4*p)-60. (11) (10) Page 6 of 9 January 01. 2010 . 2010 .5*D)2 + R2 = (0.net Fresnel S. D + ¼l. (0. Under this construct.5*D + DD where DD for each leg is n/8 l. It is only SMOG (Simple Matter Of Geometry) Let us make an assumption that the midpoint of a VHF-UHF radio link path can be modeled as an isosceles triangle.O. The Fresnel Zone radius is maximum at the path midpoint.G. the reflected signal traveling along the interfering path arrives 90O out of phase with the primary signal. P. the interfering path length from “Tx” to “Rx” is therefore.E. Page 7 of 9 January 01. Pollock.STL Path Planning James W.5*D + DD)2 Side Side Hypotenuse Upon expanding both sides and solving for R2. [email protected]. Fresnel zone definitions: n=1 0-90o path phase difference n=2 90o-270o path phase difference n=3 270o-270o path phase difference What we have here is the Pythagorean Theorem for a “right” angle triangle: The square of the hypotenuse is equal to sums of the squares of the remaining two sides. The direct path is of length “D” (meters) and each interfering path leg has a length of 0. Thus. the interference path is constructive.STL Path Planning James W. P. jim@jimpollock. the interference path is destructive Page 8 of 9 January 01. 2010 . The radius of the first zone at the path midpoint is: R2 = (0.125*n*D*l) ½ “n” is the Fresnel index. This simplifies the expression. Pollock. DD2 becomes minuscule when compared to “D*DD”.25*D2 + D*DD + DD2 By combining terms.125*D*l ) ½ To generalize The Fresnel Radius at the path midpoint. Rn = (0. For “Even” values of n.125* D*l) R = (0. R2 = D*DD For the case where DD is 1/8 l. and it can be ignored. Summary For “Odd” values of n.E. The term. R2 = D*DD + DD2 For cases where D>>DD.25*D2 + 0.net R2 = -0. August 1997 pg 28 equation #5 OET Bulletin 65 pg. Office of Engineering and Technology. P. Pollock. Page 9 of 9 January 01.STL Path Planning James W. Descriptions of Fresnel zone properties added. pg 44 OET Bulletin 65. Edition 97-1. McGraw-Hill. 2010 . Simplified formula offered. Document paging refreshed in order to accommodate the text added on page 2. Page 2-33.8. Thomas Milligan McGraw Hill New York 1985. Johnson and Jasik. Milligan pg 7 Milligan. Revisions: Jan 01. Handbook of Antenna Engineering.net References [1] [2] [3] [4] [5] [6] Modern Antenna Design. 2010 Page 2 Fresnel Radius formula corrected. 19 equation #3. Federal Communications Commission. 9 Geometry for the STL path midpoint explained. Pg 44.E. jim@jimpollock. Pages 7 .