Antenna Scattering Area

To:   The Microwave Group
From: Dick, K2RIW          23 Apr 2003.
Re:   Antenna Scattering Area, Where Does It Come From; Where Does It Go To?

Comments on Antenna Scattering Area
by Dick Knadle, K2RIW.

INTRODUCTION -- After the series of submittals on the subject of the WA5VJB Sci Am Antenna article, I received a number of replies about Antenna Scattering Area from K3JDC, NU8I, WA5VJB, W6OAL, WA2SAY, and WA1MBA. From these I have formed some further opinions that might help (a little) to clear up this difficult-to-understand subject.

I'm not optimistic that my thoughts will be the definitive answer for the reader; this is a very controversial subject. For at least 30 year's, many articles addressing it have appeared in the IEEE Antennas and Propagation Proceedings, The AP Magazine, among other respected journals. I believe that quite a few of the articles left those readers quite unsatisfied. The syllabus used in the course of many of the respected schools does not seem to cover the subject in a way that allows a student to walk out of the classroom "whistling that tune". I know it is time for a change in the syllabus.

The following is a rather heuristic, slightly visual, and non-mathematical approach. Some readers prefer that approach.

by Dick, K2RIW 4/23/03.

RECIPROCITY -- Every reasonable, low loss, antenna (not containing a circulator or amplifier) obeys the Law of Reciprocity. This means what ever characteristics the antenna displays during transmission (Gain, Pattern, Polarimetry, Side Lobes, Impedance, Main Lobe Efficiency, Radiated Phase (Time Delay), etc.), the antenna will display the same characteristics during reception.

I believe there are virtually no exceptions to this law. However, we often violate this law, in very subtle ways, during our antenna testing procedures. Sometimes that violation is unavoidable without making a very heroic (and expensive) effort. The first "story" will involve a Dipole, and it should make this more clear. The next installment "story" will involve a parabolic dish antenna, and things really get crazy (at first).

THE DIPOLE -- Assume that I'm doing an exhaustive study of all the characteristics of a Half Wave Dipole Antenna, and that I want to pay particular attention to that antenna's Effective Area, and its Scattering Area.

THE TEST -- I'll start out with a well-matched Dipole, that has a good balun attached to it. I'll apply 1 watt of power to it at the proper frequency. I'll carefully measure what happens in all of the three dimensional space in the Dipole's far field, by using well-calibrated instrumentation that performs non-invasive testing, while all the hardware is located on my ideal antenna range (which might be in outer space). My instrumentation will measure the radiated Power Flux Density (PFD), Polarimetry, and Time Delay, over every one of the 41,253 square degrees (4 Pi Steradians) that exists on the "Sphere of Observation" that's located in the Far Field around the Dipole. Assume that Sphere has a radius of 1 km, and that each of my 41,253 measurements are done in such a way that there is no overlap in the measurements (they're all independent).

TRANSMISSION -- During transmission I'll note that the 1 watt of transmitter power was completely absorbed (and supposedly radiated) by the Dipole, and none of it was reflected back to the transmitter (in the steady state). During the Dipole's rise time, there was some reflected energy. I next added up all of the power that was observed over all of the "Sphere of Observation". I was not surprised to find that the cumulative steady state power was exactly 1 watt. The Polarimetry measurements contained no surprises, and the Time Delays (Phase measurements) contained no significant differential delays. The Dipole seems to have a single phase center that emits an Amplitude Pattern that looks like a Donut (with the Dipole through the center), in the usual method of 3D display.

TRANSMISSION ANALYSIS -- Next I'll take all the measured data and convert it into a computer generated 3D animation. The beginning of the slow motion movie will display the instant of transmitter turn-on as a small, spherical, bubble of energy that emerges from near the Dipole, and the bubble's radius expands at the speed of light (which I've slowed down for the movie). (Some pretty strong bubble pattern simplifications are being used in the beginning of this animation). The surface of the first bubble represents the wave front of the first RF cycle emitted by the Dipole. The brightness (or thickness) of various portions of the bubble's surface represents the PFD that's transmitted in the direction of that portion of the bubble.

THE BUBBLE "PATTERN" -- In this animation the Dipole's antenna pattern is represented by a varying bubble thickness (and surface brightness) in the various directions. Broadside to the dipole the bubble is thick and bright. In the direction closer to the ends of the Dipole the bubble is very thin and dim. In exactly the Dipole co-linear direction, the bubble is so thin (and dim) that the bubble appears to have a hole in that direction -- that's the Dipole's null direction (the hole in the donut of the usual kind of 3D pattern display).

CONCENTRIC BUBBLES -- Inside of the first bubble there's a second bubble, one wavelength smaller in radius (the next cycle of energy), that has the identical pattern as the first bubble, but this whole bubble is slightly brighter than the first, because it represents a stronger cycle. The extra strength represents the finite rise time of the Dipole's response since it has approximately a 10% bandwidth. As these bubbles expand there grows a third bubble inside of the pack that's slightly brighter again. Each of the emerging bubbles start out brighter, until the Dipole comes up to steady state response.

100 BUBBLES -- Assume that the dipole is operating at 30 MHz (10 meter wave length), therefore at each instant of time there are 100 concentric, expanding, bubbles located between the emitting Dipole and the "Sphere of Observation" that's located at a radius of 1 km from the Dipole, that's in the center of the sphere.

RECEPTION TEST -- To test the Dipole's reception characteristics, I'll choose one of the pieces of instrumentation that's located on the Equator of the "Sphere of Observation" (broadside to the Dipole) and I'll transmit a 1 watt ERP signal (+30 dBm) from that location toward the dipole. Before the test I calculated that the Free Space attenuation of a 30 MHz signal at a distance of 1 km is -61.99 dB. The Dipole has a calculated Gain of +2.14 dB over isotropic, therefore my calculated reception should +30 -61.99 +2.14 = -29.85 dBm. I performed the reception test and I received exactly -29.85 dBm.

SCATTERING AREA -- At first the test looked great, until later I transmitted brief pulses toward the Dipole to further investigate the Scattering Area. Each of the brief pulses created a spherical wave front that started out from the chosen location on the Equator of the "Sphere of Observation", they progressed toward the Dipole, and eventually exited out the far side of the "Sphere of Observation". Because of the known timing of the wavefront of the transmitted pulses, I could easily differentiate the transmitted pulses from the Dipole's reflected pulses, because of their extra time delay at most of the 41,253 observation points on the "Sphere of Observation". I could also do a steady state test by observing all the PFD's (and phase angles) at the 41,252 reception points, with, and without, the Dipole present, and resolving the PFD differences (by an interferometry extraction technique).

EFFECTIVE AREA EQUALS SCATTERING AREA -- When I added up all of the pulse energy that was scattered by the Dipole, I noticed that it equaled the energy that the Dipole was absorbing. In other words, the Dipole's Effective Area was equal to its Scattering Area. At first, this seems to be a paradox. How can the Dipole have 100% efficiency on transmission (it wasted no energy that was applied to it), yet on reception it seems to have 50% efficiency (it scatters 1/2 of the incident energy that's applied to it). Is this a violation of the Law of Reciprocity? I say no.

RECIPROCITY EXPLANATION -- On transmission, the Dipole emitted spherical wave fronts that had a particular amplitude distribution over the 41,253 square degrees of 3D space. During the reception test we arbitrarily chose to take ONE of those 41,253 square degree locations and use it to send a signal back into the Dipole. From the Dipole's point of view, that's the WRONG AMPLITUDE PATTERN -- 41,252 pieces of the desired pattern are missing. We violated one of the unstated conditions of the Law of Reciprocity -- we didn't reciprocate all of the original conditions.

FULL RECEPTION TEST -- If we had the resources to emit 41,253 signals toward the Dipole, with all had the correct relative amplitude (the original Dipole transmitter pattern), than the Dipole will absorb ALL the reception energy, and the Scattering Area will go to zero.

SPATIAL IMPEDANCE MATCHING -- Up until now, most RF mavens believed that impedance matching of an antenna only concerns what we do at the feed point of the antenna (electronic impedance matching). The second part of "impedance matching" involves "Spatial Impedance Matching", which means creating the correct amplitude pattern (in 3D space), and phase pattern, that the antenna was really designed for. If you mismatch either kind of these "Impedance Matches", then energy will be scattered, and the possible efficiency will be compromised.

SHRINKING BUBBLES -- If we really performed the full Reception Test with the 41,253 properly tuned emitters, analyzed the data, and converted this into a computer generated 3D slow motion animation, what we would see is the same variable brightness areas of the spherical bubbles as during the transmission test, except this time each of the bubbles would be decreasing in radius, and they would each appear to "collapse" on the Dipole. The Dipole would absorb 100% of the energy of each of the bubbles, and there would be no scattered energy. We would have performed a truly Reciprocal Test.

CONCLUSION -- When it's properly used, you could say that a Dipole doesn't have a significant Scattering Area, its Effective Area is proper, and it has 100% Reception Efficiency. Unfortunately, the resources that are required to create a proper Spatial Match to a Dipole are quite heroic, and rarely realized. Therefore, we are forced to live with its detriments, because there are few simplistic antennas that are easier to use.

Many VHF antenna range Gain measurements are referenced to a 1/2 wave Dipole. But, on the range itself, the use of a Dipole as a reference antenna can easily create many multi-path, and reflection problems. There are many other better VHF reference antennas -- such as a well-tuned, and well-calibrated, long Yagi.

NEXT INSTALLMENT -- In the next installment concerning Dish Antennas (in the next few days), we'll need to discuss Structural Scattering (cross section), as well as electronic Scattering Area, and the variation of RCS versus azimuth on all real dish antennas. It's a pattern that looks very different from the antenna's Gain pattern.

by Dick, K2RIW 5/06/03.

INTRODUCTION -- Portions of this memo will be controversial to some readers. The concepts that will be expressed constitute a "Model" that has been created for the purpose of predicting antenna reception characteristics, of both complex and simple antenna types. Although the Model may be flawed, it has done a good job of explaining the phenomena of Aperture Efficiency, and Scattering Area. There probably will be other Microwave Reflector memos that question the concept, or express a different point of view -- I welcome these (within reason). When the smoke settles, I believe we will arrive at a higher understanding of antennas.

In Part 1 (4/23/03), I discussed the Scattering Area and the Reciprocal characteristics of a Dipole antenna. The main point expressed is that there are TWO (2) types of impedance matching that effect the efficiency of the Reciprocity process:

      (1) Electronic Impedance Matching -- That's what you do at the feed point of the antenna to insure that all the transmitter power is absorbed by the antenna (from the feed line).

      (2) Spatial Impedance Matching (Spatial Pattern Matching)-- This addresses how well your Reception Testing Procedure matched the Transmission Characteristics of the antenna-under-test (AUT). Maybe it would be better to call this item Spatial Pattern Matching, or Aperture Distribution Matching; that might give it greater visibility to more readers. But, the bottom line is this: if the total pattern of the energy (signal strength versus azimuth, elevation, and polarimetry) that is presented to the antenna during a Reception Test does not match (by 100%) the COMPLETE pattern that the antenna presented during the Transmission Test, then the antenna will reject a portion of the energy intended for reception, and the magnitude of that rejection can be quantified as the antenna's Scattering Area.

ITEM (2) IS MAJOR -- Most antenna engineers seem to think that Item (1) is the one that causes the magnitude of the Scattering Area that an antenna displays. But, in most circumstances Item (2) has the greatest effect.

The concept within Item (2) seems to create the greatest grief among people studying antennas, so I'll elaborate it. There are two general characteristics by which an Electronically Impedance Matched antenna cannot accept the energy presented to it from space: Polarimetry Error, and Spatial Pattern Error.

POLARIMETRY ERROR -- If I was testing a horizontally polarized antenna and I sent vertically polarized energy toward the antenna during a reception test, few engineers would have any problem accepting the notion that the AUT (Antenna Under test) will have little response to that energy. For most low-mass types of antennas (such as Dipoles and Yagis) the antenna is rather transparent to the cross-polarized energy; that energy will pass through the region of the antenna with little disturbance to the energy. However, for more complex (or massive) types of antennas, such as a Horn or a Dish, the antenna will present a kind of "short circuit" to the cross-polarized energy, and that energy will be reflected, deflected, diffracted, and generally scattered. It will appear as the antenna's Scattering Area.

SPATIAL PATTERN EFFECT, BACK LOBE RESPONSE -- If I was testing a well-tuned Yagi antenna that had a good Front-to-Back ratio, and I was applying the co-polarized reception energy to the back of the antenna, obviously the antenna would have little response. However, in this case the antenna is not transparent to that energy. The Reflector, Driven Element, and nearby Directors are responding to that energy, but their tuning is such that they are presenting an Interferometry Null, or Phasing Null at the Driven Element to the energy that arrives from that direction. A well-constructed Yagi has no lossy properties associated with it, so it can not dissipate this energy. By the Law of Conservation of Energy, this energy must be scattered in some other direction, or it must be generally reflected back in the direction from where it came. I believe that the back of such a Yagi will present a Scattering Area that is at least twice as large as that of a normal Dipole antenna. Under ordinary conditions, a Dipole has a Scattering area that is equal to its Effective Area, but the Dipole that is part of this Yagi's rearward reception has an Effective Area of near zero, therefore its Scattering Area must at least double, because the Dipole and other elements involved.

SPATIAL PATTERN MATCHING, FRONT LOBE -- Many Standard Gain Horn antennas have a gain of about 16 dBi. The Amplitude Distribution across the mouth of the horn has a half SIN-wave-like distribution, with the emitted signal strongest in the center, and near-zero at the vertical edges (vertical polarization is assumed). If I place a pair of identical horns together, mouth-to-mouth, the insertion loss between them will be nearly zero dB (no loss). This condition will persist, even if I create a space between the horns of quite a few wavelengths. This nearly 100% energy transfer between the horns suggests that during this test, each presents an Effective Area of nearly 100% to the other, and a Scattering Area of nearly zero.

NEAR FIELD COUPLING? -- There are antenna engineers who will simply dismiss this test by saying, "the horns are within the Near Field Range of each other, they were reactively coupled, therefore the 100% energy transfer (although accurate) is not relevant". I disagree. There are many situations where one portion of an antenna system is well within the Near Field Range of another portion, and the system performs admirably, and in a predictable manner. Here are a few examples:
      (1) In every Parabolic Dish antenna system, the horn is way inside the Near Field Range of the main parabolic reflector.
      (2) In every Cassegrain antenna system, the sub-reflector is way inside the Near Field Range of the main parabolic reflector, and in most of them the parabolic reflector (and the horn) are inside the Near Field Range of the hyperbolic sub-reflector.
      (3) In many Periscope Antenna Systems, the 45 degree "flyswatter reflector" and the ground-mounted parabolic illuminator are inside the Near Field Range of each other.
      (4) In every optical telescope, all of the individual lenses and mirrors are within the Near Field Range of the other elements, often by a 100,000 to 1 ratio.
      (5) The two 45 degree mirrors that are within a child's optical periscope are within the Near Field Range of each other by a 60,000 to 1 ratio.
      (6) At 10 GHz my 3 foot dish antenna has a calculated Near Field Range of 189 feet. Yet, I can aim a pair of identical dish antennas at each other with a separation of 3 feet, and the insertion loss between them will be nearly zero dB. Each antenna will act like a collimator to the other antenna, each will present the proper Aperture Distribution to the other, and the energy transfer between them will be nearly complete. In that test the apparent Scattering Area between the antennas will seem to be very small. However, in a Far Field reception test, the antenna will experience a uniform Aperture Distribution, and the Scattering Area will be much higher. Which is the real Scattering Area? It seems to be a function of Definition, or of the Testing Procedure (test conditions).

STANDARD GAIN HORN RECEPTION -- If I use one of the Standard Gain Horns in a reception test while receiving a planar wave that was emitted from a long distance, the Standard Gain Horn will have a reception efficiency (Aperture Efficiency) of about 60 to 70%. In other words, the Effective Area (~ 65%) will be larger than the Scattering Area (~ 35%). At first, this may seem to be a paradox. The horn has a radiating efficiency of nearly 100% when it is used for transmitting a signal, yet it has an Aperture Efficiency of about 65% during normal signal reception, and an Aperture Efficiency (Effective Area) of near 100% when receiving the signal from an identical nearby horn.

AMPLITUDE DISTRIBUTION MATCHING -- I say that the reason for this difference is the matching of the Aperture Distribution from the nearby horn (the half SIN-wave-like distribution), versus the mismatch of the far-field spatial signal (it presents a Uniform Distribution). At first, the Uniform Distribution created by the spatial wave sounds like the most desirable one for best reception. However, the horn is not "tuned" for that kind of Aperture Distribution, therefore it cannot accept all of that type of spatial signal. The horn's half SIN-wave-like Aperture Distribution created a particular Antenna Pattern (Spatial Amplitude Pattern over the 4 Pi Steradians of space) when the horn was transmitting. Only when that same (and complete) Antenna Pattern is presented to the horn during a reception test will the horn experience the same half SIN-wave-like Aperture Distribution, and thus be able to accept 100% of the energy being presented to it -- which would be displayed as a 100% Aperture Efficiency. There is a one-to-one Reciprocal Relationship between an antenna's Aperture Distribution, and the Spatial Antenna Pattern it produces while transmitting.

RE-READ? -- I believe that many readers should re-read the last five paragraphs multiple times, in order to absorb the concept. To most technologists who are exposed to this concept for the first time, it sounds crazy. I know of no respected text book that makes this concept clear. Among the antenna engineers who have had 20 to 30 years experience in the field, I believe that fewer than 20% of them understand this concept. Yet, it is a very important concept if one desires to understand the origin of Dish Antenna Aperture Efficiency, or Stealth A/C RCS (Radar Cross Section). For instance, any attempt to create a Low Observable Aircraft (A/C) must entail a thorough understanding of the concept of Antenna Scattering Area. It would be a rather wasteful exercise to put forth a heroic effort to build a stealthy A/C, only to have it become a "Gang Buster" echo on a Radar screen because of the Scattering Area of the antennas that were installed on that A/C -- this has happened many times. There are solutions to this problem, but they are all very difficult to implement, and those solutions would not improve the performance of our amateur microwave antennas.

DISH ANTENNA APERTURE EFFICIENCY -- For most Parabolic Dish Antenna systems a "well-designed feed horn" will present a reflector edge illumination of -10 dB compared to the dish center. This Illumination Taper results in a dish Aperture Efficiency of about 55 to 65%. If it was possible to design an "ideal horn" that presented an Amplitude Taper of 0.0 dB across the reflector, with no wasted edge spill-over energy, then the antenna system could have an Aperture Efficiency of nearly 100%.

60% APERTURE EFFICIENCY? -- Most Microwavers have trouble understanding where the 55 to 65% Aperture Efficiency comes from in a "real" dish antenna system. Often their flawed point of view is the following: "on reception the parabolic reflector brings all the energy to a focus at the center of the feed horn, therefore a good horn has no choice but to accept all that energy." Unfortunately, the horn will not accept all the energy, unless it is presented to the horn with exactly the correct three dimensional amplitude pattern (primary horn pattern), that the horn was designed for.

DISH SPATIAL PATTERN MISS-MATCH -- During boresight reception of a far-off planar wave, the wave presents a Uniform Amplitude Distribution across the parabolic reflector. After reflection, the portion of the wave that hit the dish perimeter region will approach the horn with an almost equal amplitude as the portion of the wave that hit the center of the dish. That total reflected signal now has a nearly uniform signal strength versus angle as it is approaching the horn. The horn will not accept all the energy that has that pattern; it was designed to transmit (or receive) energy that has a -10 dB amplitude taper across the angles of the reflector. The portion of the signal that is not accepted by the horn will be reflected back (scattered) to the parabolic reflector and re-transmitted back into space. This Spatial Pattern miss-match (and reflection [Scattering] ) phenomenon is a three dimensional characteristic of antennas that is quite difficult for many engineers to accept. Therefore, I'll present a pair of two dimensional examples, that may make it clearer.

HYBRID COMPARISON, Example (1) -- Assume that I'm using a Wilkinson Half Hybrid as a power divider. A 50 ohm Wilkinson is the Hybrid that has a pair of 1/4 wave 70 ohm lines connected from the common port to the two output ports, with an internal 100 ohm isolation load resistor between the two output ports. I'll first apply 2 watts to the common port (I'll call this the "transmission" test), and I'll notice that each of the two output ports will display a 1 watt signal, that has a zero degree phase difference between the outputs.

To test the Reciprocity Characteristic, I'll next apply a pair of 1 watt co-phase signals to the two output ports (I'll call this the "reception" test), and I'll notice that the common port now has a 2 watt output. Notice that between "transmission" test and "reception" test I realized 100% efficiency and Reciprocity was demonstrated. However, if during the "reception" test I present a pair of signals that differ in relative amplitude (or phase), than the 100 ohm resistor will experience a differential signal, and signal dissipation will take place. You could say that the Hybrid rejected (or dissipated) the "reception" signals that did not exactly match the "transmission" conditions. You could say that the Wilkinson Hybrid has some similarity to a theoretical Zero dB Taper feed horn.

HYBRID COMPARISON, EXAMPLE (2) -- Assume that I'm using a well-designed coaxial-type -10 dB Directional Coupler as an unequal power divider -- it's somewhat like a -10 dB Taper Feed Horn. During the "transmission" test I'll apply a 10 watt signal to the Common port, and I'll realize a 9 watt signal (with a 90 degree lagging phase shift) at the Straight Through port, and a 1 watt signal (at zero degrees phase shift) at the Directional port. Notice that the efficiency is 100%. During the first "reception" test I'll completely reverse the process by applying a 1 watt signal to the Directional port, and a 9 watt signal (with a 90 degree leading phase angle) to the Straight Through port. At the Common port I'll measure a 10 watt signal (100% efficiency), and most of the Reciprocity process will be demonstrated. But, notice that the phase angle must be reversed during the Reception Test -- both Antennas, Hybrids, and Directional Couplers behave in this way.

During the second "reception" test I'll apply only the 9 watt signal to the Straight Through output port, and no signal to the Directional port. At the Common port I'll measure 8.1 watts (a power loss of 10%, -0.46 dB). Now, the Directional Coupler seems to have gone down from 100% to 90% efficiency because I didn't properly match the "transmission" conditions. Due to the mismatch of the "transmission" conditions, the extra 0.9 watts (-0.46 dB) was lost in the internal 50 ohm termination.

During the first "reception" test, the -0.46 dB of Directional Coupler straight through path insertion loss didn't take place; this can be viewed in at least two ways:

      (1) If all the "transmission" conditions are preserved (with a phase reversal) then Reciprocity will be demonstrated.

      (2) During the first "reception" test the Coupler's internal 50 ohm termination saw a 0.9 watt signal from the 9 watt source, and a 0.9 watt signal from the 1 watt source, but the two 0.9 watt signals were 180 degrees out of phase, thus the termination saw 0.0 volts and no dissipation of energy took place -- one of the benefits of matching the "transmission" conditions.

ANTENNA-HYBRID ANALOGY -- In both the Antenna and the Hybrid examples, power will be "wasted" if the "transmission" conditions (amplitudes at the Hybrid ports, or amplitudes at the various Antenna angles) are not 100% duplicated during a "reception" test. The only difference between them is where the "wasted" power goes. The "wasted" power becomes scattered in the case of an antenna Spatial Pattern Mismatch. In a Hybrid mismatched "reception" test the "wasted" power becomes dissipated in the Hybrid's internal termination. There have been some "simplified" Hybrids that do not have an internal termination (such as the 4:1 power divider that amateurs use to feed 4 antennas), these will Scatter the mismatched "reception" power back to the antennas. Similarly the Hybrids in the previous examples would scatter the mismatched "reception" energy back to the sources, if their internal terminations were removed. Well designed antennas have no lossy elements associated with them, therefore they Scatter (and do not dissipate) the Spatial Pattern Mismatched energy that is presented to them.

ANTENNA/HYBRID DIFFERENCES -- In the previous example a -10 dB Directional Coupler was being compared to a -10 dB Illumination Taper Feed Horn. When the -10 dB signal (the 1 watt signal) was omitted during the "reception" test, the Coupler's efficiency decreased from 100% to 90% (-0.46 dB). However, in a Parabolic Dish Antenna, the -10 dB illuminated area at the dish perimeter has much more area that the 0.0 dB illuminated area near the center, thus it includes a substantial amount of the dish "transmitting" energy. This would be equivalent to using a Directional Coupler that had a number of -10 dB output ports (each with an internal 50 ohm termination). If the "reception" signals were omitted from all the -10 dB Coupler ports, the impact on the Coupler's efficiency would be a decrease to 60% (-2.2 dB); this would be similar to the dish Aperture Efficiency of 60% that occurs during the reception of the Far Field wave that has the "mismatched" Uniform Distribution signal that creates the Spatial Pattern Mismatch at the feed horn.

PRELIMINARY CONCLUSION -- The concept expressed within this memo may seem quite radical to many readers, and maybe the concept contains errors. However, over the years a good number of technically-savvy people have come to accept the concept as being real. I have used the concept to explain the measurements that I and my colleagues have experienced while using an Instrumentation Radar to measure the Scattering Area of various antennas under various conditions. As stated earlier, the Model may be flawed, but it has (thus far) done an excellent job of explaining the observed measurements.

BORESIGHT ONLY -- Most of the main lobe Aperture Efficiencies and Scattering Areas that have been discussed only apply to the antenna's boresight response. Beginning at angles that are slightly off of boresight, some very different phenomena begins to happen; it's called Structural Scattering. These characteristics, and some Scattering Area surprises, will be discussed in a subsequent memo (next week).

by Dick, K2RIW 5/14/03.

INTRODUCTION -- I have often been asked, "how big is the Scattering Area" of certain antennas. Many amateurs and engineers think the Scattering Area is usually quite small, and only of academic interest. As you are about to see, it can sometimes be VERY LARGE. I'm about to describe the biggest one I've ever measured, and I'll discuss the internal "war" that persisted within a company (for 6 months) because of a technical difference of opinion on this subject. I believe this incident can be quite educational concerning: Scattering Area and RCS measurement, and a characteristic of human nature that can hinder a project when a strong difference of opinion occurs. But first, a few definitions are required.

RADAR CROSS SECTION (RCS) -- In the Radar world, RCS is defined by the "Projected Area" of a perfectly conducting sphere, and the signal level that such a sphere will reflect back to the Radar. For instance, a metal sphere that has a diameter of 1.128 meters has a Projected Area of one square meter -- meaning that it will project a shadow of one square meter on the ground at High Noon on a sunny day. That metal sphere could be used as a one square meter (0.0 dBsm), Standard Radar Target, for the purpose of calibrating the sensitivity of a Radar system.

RCS ASSUMPTIONS -- The first assumption is that the projected area of the sphere will cause it to intercept a predictable amount of the Radar signal -- one square meter's worth. The second assumption is that the sphere will then scatter that signal energy (equally) in all directions of free space. In reality, the sphere slightly favors the Retro-Direction, but this difference is small, and usually ignored.

RCS CALCULATION -- The hard part to understand is that many objects can have an RCS that is MUCH LARGER (in RCS square meters) than their physical area (in real square meters). This is particularly true for a Corner Reflector, or a flat metal plate at its normal angle. For each of these the:

Maximum RCS = (4 * Pi * A^2)/(Lambda^2).


  • A equals the Projected Area of the plate (or Corner Reflector) at its favored angle.
  • Lambda is the wavelength (in the same units).

  • Here is an interesting example. By using the above formula, at 1.0 GHz a one square meter of flat sheet metal has a Maximum RCS of 139.6 square meters (+21.4 dBsm). That's because the sheet of metal (at the best angle) can be very efficient at reflecting the signal back to the Radar. It would take a round metal sphere of 13.33 meters in diameter (43.7 feet), to have a Projected Area of 139.6 square meters, and to give the same echo power -- that's quite a contrast.

    ANTENNA SCATTERING AREA -- During a test of the reception characteristics of almost any antenna, a portion of the energy that is presented to the antenna will not be absorbed. That portion is sometimes quantified by the parameter called Scattering Area. For instance, if a Parabolic Dish Antenna has a surface area of 100 square feet, and if during a Far-Field boresight-angle reception test it displayed a measured Aperture Efficiency of 60% (an Effective Area of 60 square feet), then most likely that antenna has a Scattering Area slightly above 40 square feet. The extra Scattering Area is due to the fringing effect that occurs around the perimeter of the antenna, and the scattering of other structural parts. That scattered signal energy is usually scattered (to some degree) in all the three dimensional directions around the antenna (almost isotropically).

    SCATTERING AREA VERSUS RCS -- A portion of the scattered energy is scattered back in the direction from where it came; this retro-directed energy would be available for reception at a Mono-Static Radar system. That portion could become the target's Mono-Static Radar Cross Section (RCS), after a conversion factor that normalized the range and the Radar's ERP. In general, the RCS energy is less than the Scattering Area energy, since it only involves the energy that is scattered in a particular direction (back to the Radar). However, a target's RCS rating (in square meters) can be much larger than the Scattering Area (in square meters) because of the peculiar definition of RCS, and its relationship to the projected area of a metal sphere that displays the same echo power.

    THE "RCS PROJECT" PROBLEM -- About 15 years ago I worked on an Independent Research and Development (IRAD) project that had to estimate the Boresight RCS of a particular Parabolic Dish Antenna (that was unavailable to us), and the RCS had to be estimated at a frequency that was far removed (much higher) than the antenna's normal operating frequency. My colleagues and I came up with an estimated RCS number that was strongly challenged (by over 10,000:1) by the project manager. The technical difference of opinion persisted for over 6 months. This created some very frayed nerves among the affected individuals. In order to resolve the dispute, the company's Chief Scientist decided that a Proof-of-Concept measurement would have to be made on a surrogate, real operating antenna system.

    THE TARGET -- The chosen surrogate target was the antenna of an FAA ASR-8 Radar System that was located at the local airport. It operated at 2.8 GHz, and we were going to make an RCS measurement at 16.25 GHz (5.8 times higher in frequency), at the frequency of a portable (Man-Pack) Radar system. The RCS measurement was going to take place from the balcony of a 10th floor hotel room that was located 5 miles away. It had a line-of-sight path to the airport radar.

    PERMISSIONS & SAFETY REQUIREMENTS -- The FAA gave us permission for the test, and they had our telephone number to cancel the test if any interference appeared on their Radar screen. The company's Safety Department tested the Biohazard characteristics of the portable Radar and declared it to be safe in the manner in which we intended to use it. The hotel manager gave us permission to rent the room and run the test, particularly because it was an off season, and the top few floors of the hotel were empty.

    THE CANCELED TEST -- The project manager developed a strong opposition to the test. He convinced the company vice president to order a cancellation of the Proof-of-Concept test by declaring that the measurement was a waste of company resources because there would be too little echo power to measure, and there was a chance that the portable Radar would cause an interruption of a hotel patron's heart pacer, and the company would be sued. Thus, the project manager had succeeded in getting the whole project canceled for the third time. This greatly frustrated the involved employees.

    THE "K2RIW RADAR" MEASUREMENT -- Because of my faith in the project I decided to proceed on my own time. I prepared and calibrated a pair of 300 milliwatt 10.368 GHz "White Boxes" with the 29" dishes as a CW Radar. I and two fellow employees went to the hotel on a weekend with about 500 pounds of test equipment and we made the RCS measurement of the FAA Radar by using my Ham Radio license to legalize the transmission. That "flee powered CW Radar" made a measurement that demonstrated significant 10.368 GHz echo power from the FAA Radar antenna, and this result was reported to the company's Chief Scientist.

    THE RESCHEDULED MEASUREMENT -- Based on the encouraging measurement with the "K2RIW CW Radar" the Chief Scientist decided to take over the management of the project, and he re-opened the project for the 4th time. We were now authorized to use one of the company's portable Radars, and a more formal Proof-of-Concept test was scheduled to take place at a US Military Base (with their permission) that had both a FAA ASR-8 Radar and a nearby mountain about 3 miles away. By locating the portable radar at various points along the road that was on the nearby mountain, the RCS measurement of the FAA Radar could be made at various elevation angles to the FAA Radar.

    THE RCS MEASUREMENT PROCEDURE -- I was using a Man Pack AN/PPS-5 portable Radar that put out 1 KW pulses at 16.25 GHz into a 42 by 14 inch Bat Wing antenna (38 dB gain). This is a battery-powered transistorized Radar with a Magnetron final transmitter that puts out 100 nanosecond pulses at a PRF of 10 kHz (an average of one watt output). I found the correct altitude along the road on the mountain (690 feet) that put me in the peak of the 2.8 GHz beam from the FAA Radar (at +2.5 degrees elevation). I found that I had to put a 20 dB pad in front of the PPS-5 Radar receiver to keep it from saturating from the 16.25 GHz echo power I was getting from the 2.8 GHz FAA Radar antenna, when its rotating dish was aimed at me.

    RADAR CALIBRATION FOR RCS MEASUREMENT -- I rechecked the RCS Measuring Calibration of the PPS-5 Radar by performing three tests: a calibrated corner reflector RCS test, a signal generator receiver response test, and a directional coupler plus Spectrum Analyzer transmitter power output test. During the RCS measurements, the strength of specific echoes were measured by using a pulsed signal generator to inject (with a calibrated directional coupler) equal-amplitude pulses (at almost the same range) into the portable Radar's receiver. The receiver responses were being observed on an oscilloscope (an A-scope display).

    HOW BIG WAS IT? -- After the on-site calibration tests, I confirmed that the FAA Radar (at its boresight angle) was generating a 16.25 GHs RCS of 57,500 square meters (+47.6 dBsm), with a pair of brief peaks (on each rotation) that were even higher. There are very few Radar discrete targets on Planet Earth that are much larger than that. That's almost the RCS you will observe from a full-sized Aircraft Carrier at a broadside angle. It would take a metal sphere 271 meters high (888 feet) to equal the same Radar echo power.

    WHY THE >>BIG<< DISAGREEMENT? -- The original project manager considered himself to be a "Radar expert"; this caused him to arrive at the following three (3) conclusions. He had heard that parabolic dish antennas are capable of creating big echoes. Therefore, a few years earlier he had ordered the testing of some of the parabolic dish reflectors that were in the company's warehouse. (1) The feed horns were not present (he didn't think that mattered), and thus the measured echoes were very small. (2) He reasoned that the expanded aluminum mesh that made up the parabolic reflector of the 2.8 GHz FAA Radar antenna would allow most of the 16.25 GHz signal to pass through without substantial focusing, or reflection. (3) He further reasoned that the FAA Radar's 2.8 GHz feed horn would not respond to the 16.25 GHz signal. He was extremely wrong on all three assumptions.

    WHAT HAPPENED NEXT -- The project proceeded to the next steps toward developing a product. The original project manager had earlier told many company officials that the employees on this project (particularly Dick, K2RIW) were very foolish to believe that a large echo would be realized. He lost much of his credibility after the Proof-of-Concept measurement was finally made. Soon after the measurement he resigned from the company (after 20 years of employment); many believe that the embarrassment of this incident was a contributing factor.

    NEW RESPECT? -- For the next 5 years my pronouncements and estimations (concerning RF and radio matters) went unchallenged. It is nice to be respected and appreciated, and I received some company (and IEEE) awards because of the results of this and two similar projects. But, I could no longer obtain an objective opinion when I asked my fellow employees for a confirmation of my speculative ideas -- they were afraid to challenge me. They sometimes gave me credit for knowledge I did not have.

    WHAT MADE THE HUGE RCS? -- When a pulse from the 16.25 GHz portable Radar arrived at the boresight angle of the antenna of the FAA Radar, the 15 foot wide dish reflector (with 100 square feet of area) experienced a nearly uniform Amplitude Distribution. Despite its expanded aluminum surface (with some energy feeding through the surface) and surface roughness, it focused a certain portion of that energy at the center of the antenna's 2.8 GHz feed horn. The horn was not "tuned" for that Amplitude Distribution (particularly not at 16.25 GHz) and it rejected a good portion of the focused energy. The rejected energy then become scattered by the horn, and a good portion of that scattered energy was reflected back to the parabolic reflector. The reflector "refocused" that energy back into a beam that was directed at my portable Radar.

    THE HORN CREATES MOST OF THE ECHO -- If the Radar's 2.8 GHz feed horn had not been present, then the 16.25 GHz focused energy would have simply passed through the focal point, and been dispersed into space over the very wide angles that the parabolic reflector subtends (from the viewpoint of the feed horn). You could say that the feed horn created the Scattering Area that, ultimately, resulted in the large RCS, because without it the maximum RCS would have been over 1,000 times smaller.

    EVEN STRONGER RCS? -- As the FAA Radar antenna rotated, the 16.25 GHz signal that was focused by FAA Radar's parabolic reflector would sweep across the region of the 2.8 GHz feed horn. At the proper boresight angle, the focused 16.25 GHz signal would be located at the center of the 2.8 GHz feed horn, and a certain portion of that signal would proceed down the horn, and be propagated by the 2.8 GHz wave guide to the Radar's receiver (where much of it would be absorbed). However, at the two times during each rotation that the antenna was aimed slightly to the left or right of the boresight angle to the portable Radar, the 16.25 GHz signal would be focused on the outer edges of the 2.8 GHz feed horn. At these times the feed horn could accept none of the focused energy, thus it was all scattered. During these two very brief periods, the RCS was considerably greater than the recorded value (57,500 square meters). The instrumentation that I was using was not able to catch and record the value of the two peaks; it is possible that they were almost 10 dB stronger. Thus, a graph of the 16.25 GHz echo power versus antenna rotation would display a pair of "rabbit ears".

    CONCLUSION -- I hope the Microwaver's find this saga to be educational, and maybe they can use the information in some of their future projects.

        73 es Good VHF/UHF/SHF/EHF Optical DX,
        Dick K2RIW.
        Grid FN30HT84DC27