designfeature By Charles Capps, Delphi Automotive Systems HOW DO WE DEFINE THE FAR FIELD OF AN ANTENNA SYSTEM, AND WHAT CRITERIA DEFINE THE BOUNDARY BETWEEN IT AND THE NEAR FIELD? THE ANSWER DEPENDS ON YOUR PERSPECTIVE AND YOUR DESIGN’S TOLERANCES. Near field or far field? everal engineers, including myself, were many definitions,” and “why is it so important to sitting around talking one day when the ques- know about the far field in the first place?” To begin Stion arose, “When does a product find itself in to answer these questions, start with some basic in- the far field of a radiation source?” One of the engi- formation. neers, an automotive antenna expert, immediately Because the far field exists, logic suggests the ex- stated that the far field began at a distance of 3l from istence of a close, or near, field. The terms “far field” the source, with l being the radiation wavelength. and “near field” describe the fields around an an- The EMC (electromagnetic-compatibility) engineer tenna or, more generally, any electromagnetic-radi- challenged this statement, claiming that “everyone ation source. The names imply that two regions with knows” that the far field begins at a boundary between them exist around an antenna. Actually, as many as three regions and two bound- . aries exist. These boundaries are not fixed in space. Instead, A visiting engineer working on precision anten- the boundaries move closer to or farther from an an- nas got his 2 cents in with, “The far field begins at tenna, depending on both the radiation frequency and the amount of error an application can toler- , ate. To talk about these quantities, you need a way to describe these regions and boundaries. A brief where D is the largest dimension antenna.” I hap- scan of reference literature yields the terminology in pened to know the “correct” answer is Figure 1. The terms apply to the two- and three-re- gion models. USING AN ELEMENTAL DIPOLE’S FIELD All of these guys are good engineers, and, as the For a first attempt at defining a near-field/far-field debate went on, I wondered how such a seemingly boundary, use a strictly algebraic approach.You need simple question could have so many answers. After equations that describe two important concepts: the the discussion ran its course, we tried to make some fields from an elemental—that is, small—electric di- sense of it. Could all of the answers be correct? This pole antenna and from an elemental magnetic loop question led to several others, such as “where have antenna. SK Schelkunoff derived these equations us- all these definitions come from,”“why do we need so ing Maxwell’s equations. You can represent an ideal THREE-REGION MODEL TWO-REGION MODEL DOMINANT TERMS 1 1 1 1 1 1 , IN THE REGION r r2 r3 r2 r3 r FAR FIELD NEAR FIELD NEAR FIELD FAR FIELD FRAUNHOFER ZONE TRANSITION ZONE FRENEL ZONE FRENEL ZONE FRAUNHOFER ZONE Figure 1 FAR FIELD INDUCTION FIELD STATIC FIELD REACTIVE FIELD FAR FIELD FAR RADIATION FIELD NEAR RADIATION FIELD REACTIVE FIELD INDUCTION ZONE RADIATION ZONE QUASISTATIONARY STATIC OR FAR FIELD TRANSITION REGION FAR FIELD REGION QUASISTATIC FIELD Two- and three-region models describe the regions around an electromagnetic source. www.ednmag.com August 16, 2001 | edn 95 designfeature Near and far field h electric dipole antenna by a short uni- ters; and 0 is the free-space impedance, ward. Examine Table 1, which contains form current element of a certain length, or 376.7V. a large set of far-field definitions from the l. The fields from an electric dipole are: Equations 1 through 6 contain terms literature. It’s disconcerting to first make in 1/r, 1/r2, and 1/r3. In the near field, the a point with a simple mathematical der- 1/r3 terms dominate the equations.As ivation, only to have reality disprove the the distance increases, the1/r3 and 1/r2 theory. (1) terms attenuate rapidly and, as a result, Therefore, examine the boundary the 1/r term dominates in the far field. To from two other viewpoints. First, find the , define the boundary between the fields, boundary as the wave impedance examine the point at which the last two changes with distance from a source, be- terms are equal. This is the point where cause this phenomenon is important to the effect of the second term wanes and shield designers. Then, look at how dis- (2) the last term begins to dominate the tance from an antenna affects the phase equations. Setting the magnitude of the of launched waves, because this phe- , terms in Equation 2 equal to one anoth- nomenon is important to antenna de- and er, along with employing some algebra, signers. you get r, the boundary for which you are searching: WAVE IMPEDANCE Defining the boundary through wave (3) , impedance involves determining where an electromagnetic wave becomes “con- and stant.”(The equations show that the val- . ue never reaches a constant, but the val- . h 5 V The fields for a magnetic dipole loop ue 0 377 is close enough.) Because are: the ratio of a shield’s impedance to the Note that the equations define the field’s impedance determines how much boundary in wavelengths, implying that protection a shield affords, designing a the boundary moves in space with the shield requires knowledge of the imped- (4) frequency of the antenna’s emissions. ance of the wave striking the shield. Judging from available literature, the dis- If you calculate the ratio of the elec- tance where the 1/r and 1/r2 terms are tric and magnetic fields of an antenna, , equal is the most commonly quoted you can derive the impedance of the near-field/far-field boundary. This result wave. The equations in Figure 2 compute may seem to wrap up the problem rather the impedance of the electric and mag- nicely. Unfortunately, the boundary def- netic dipoles, where ZE is the ratio of the (5) inition in reality isn’t this straightfor- solution of Equation 1 to the solution of , and (6) , where I is the wire current in amps; l is the wire length in meters; b is the elec- trical length per meter of wavelength, or v/c, 2*p/l; v is the angular frequency in p e radians per second, or 2* *f; 0 is the permittivity of free space, or 1/36* p 29 m *10 F/m; 0 is the permeability of free space, or 4*p*10-7 H/m; u is the angle be- tween the zenith’s wire axis and Figure 2 the observation point; f is the fre- quency in hertz; c is the speed of light, or 3*108m/sec; r is the distance from the source to the observation point in me- Equations and impedance plots describe elemental dipole and loop antennas. 96 edn | August 16, 2001 www.ednmag.com designfeature Near and far field Equation 2, and Z is the ratio of the so- creases, the ratio becomes constant, de- real-world problem: how to define the H 5h 5 V lution of Equation 4 to the solution of fined as ZE 0 377 . boundary. The problem can change the Equation 5. The constants cancel each This equation calculates the intrinsic boundary location, and the shield de- other out, leaving: impedance of free space. From the graph, signer has to define the location. you can see that the distance at which the intrinsic impedance occurs is approxi- ANTENNAS AND THE BOUNDARY mately 5*l/2*p, with l/2*p a close run- An antenna designer would examine ner-up. Note that at l/2*p, a local mini- the boundary location with the parame- mum (maximum) for an electric (mag- ters of a dipole antenna determining the netic) wave exists whose value is not 377V. A more detailed way of de- P , scribing the change in Figure 3 z impedance is to iden- r tify three regions and two U9 and boundaries. Here, the bound- r9 aries come from eyeballing the impedance curves. The choic- I/2 z es are close to what boundaries U and regions appear in the liter- y ature. They are the near field, z cos U that is, the distance, (a) . , z the transition region, r Figure 2 also presents a MathCAD U9 TO A POINT P, VERY FAR AWAY graph of the magnitudes of these two , equations. The selected values for the I/2 wavelength, l, and the step size, r, pres- and the far field, z r9 ent the relevant data on the graph. Con- U . y sidering just the electric-field impedance z cos U in the near field, that is, r*b,,1, Equa- tion 7 simplifies to: So, where is the boundary? In this case, you can’t nail it (b) . down as precisely as you had previously. With this line of A geometry for an antenna and a receiver are “close” (a) as As the distance from the source in- reasoning, you encounter a well as “far away” (b) from one another. TABLE 1—DEFINITIONS OF THE NEAR-FIELD/FAR-FIELD BOUNDARY Definition Remarks Reference for shielding l/2p 1/r terms dominant Ott, White 5l/2p Wave impedance=377V Kaiser For antennas l/2p 1/r terms dominant Krause 3l D not >>l Fricitti, White, Mil-STD-449C l/16 Measurement error<0.1 dB Krause, White l/8 Measurement error<0.3 dB Krause, White l/4 Measurement error<1 dB Krause, White l/2p Satisfies the Rayleigh criteria Berkowitz l/2p For antennas with D<<l and printed-wiring-board traces White, Mardiguian 2D2/l For antennas with D>>l White, Mardiguian 2D2/l If transmitting antenna has less than 0.4D of the receiving antenna MIL-STD 462 (d+D)2/l If d>0.4D MIL-STD 462 4D2/l For high-accuracy antennas Kaiser 50D2/l For high-accuracy antennas Kaiser 3l/16 For dipoles White (D2+d2)/l If transmitting antenna is 10 times more powerful than receiving antenna, D MIL-STD-449D 98 edn | August 16, 2001 www.ednmag.com designfeature Near and far field boundary and as the phase front of a z*cos(u) to P with respect to a wave from from an antenna.