812 ieee transactions on antennas and …fig. 2. a normalized far-ﬁeld pattern of an ideal ira...

812 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 54, NO. 3, MARCH 2006

On the Characterization of a Reflector ImpulseRadiating Antenna (IRA): Full-Wave

Analysis and Measured ResultsMajid Manteghi, Member, IEEE, and Yahya Rahmat-Samii, Fellow, IEEE

Abstract—There is a growing demand for impulse radiatingantennas (IRAs) to receive and transmit short pulses. The basicconcepts of IRA are reviewed and the far-field pattern versus fre-quency of an ideal IRA is characterized based on the fundamentalproperties of IRA. It is shown that the transmitted pulse is ideallyin the form of a time derivative of the input pulse. The physicaloptics simulation results show that the far-field characteristicsof a parabolic reflector are very close to an ideal IRA if it isfed properly. The reflector IRA was constructed, analyzed andmeasured at UCLA. The near-field and far-field characteristicsof the reflector IRA are studied using both the method of mo-ments (MoM) full-wave simulations and the frequency domainmeasurements. In this paper, the radiation mechanism of thereflector IRA is studied using a detailed current distributionon the parabolic reflector and the feeding structure at differentfrequencies. Applying either the calculated current distributionon the reflector IRA or the measured near-field results, it is seenthat the aperture field intensity of the parabolic reflector is not thesame in the two principle planes and as a result the beam-widthsin the two principle planes are different. The far-field patterns ofthe antenna are measured and the calculated far-field patternssupport the measured results. The calculated current distributionresults provide a guideline on how to properly change the feedingstructure to achieve a more uniform aperture field and increasethe antenna radiation efficiency.

Index Terms—Antenna measurements, frequency domainanalysis, impulse radiating antenna (IRAs), method of moments(MoM), reflector antenna, ultrawide-band antenna.

I. INTRODUCTION

IMPULSE radiating antenna’s (IRAs) have been used to ra-diate electromagnetic energy in a very short period of time

[1], [2]. Various types of antennas are proposed and tested fordifferent applications. The reflector IRA [3]–[5] and the trans-verse electromagnetic (TEM) horn antenna [6], [7] have beenused extensively for high power applications. The reflector IRA(Fig. 1) consists of a parabolic reflector fed by a self-reciprocalTEM transmission line [8], [9]. The spherical wave that propa-gates through the TEM feed is converted to the plane wave bythe parabolic reflector. Before studying the reflector IRA prop-erties a review of an ideal IRA will be presented.

Manuscript received January 11, 2005; revised August 17, 2005.The authors are with the Antenna Research and Measurements Labo-

ratory, Department of Electrical Engineering, University of California atLos Angeles, Los Angeles, CA 90095-1594 USA (e-mail: [email protected];[email protected]; www.ee.ucla.edu).

Digital Object Identifier 10.1109/TAP.2006.869909

Fig. 1. The 57 cm diameter reflector IRA mounted in the spherical near-fieldchamber at UCLA. A magnified drawing of the feeding structure at the focalpoint is shown in the right corner of this figure.

A. Far-Field Pattern of an Ideal IRA

When an ideal IRA is illuminated with a short pulse planewave in a specific direction and polarization, the open circuitvoltage at the antenna port has the same signal shape as the in-cident wave. The electric field at a reference point of the incidentplane wave, , is related to the open circuit voltage atthe antenna port, , with the effective length of the antenna[10], , as

(1)

To achieve a with the same wave form as the incident wave,, in (1) the effective length of the antenna has to have fre-

quency independent amplitude and linear phase which repre-sents a time delay in the open circuit voltage. Equation (A-6),in Appendix A, shows that for an antenna with ultrawide-band(UWB) matched input, the antenna gain is directly proportionalto the square of the effective length of the antenna and squareof frequency. Because the effective length of an ideal IRA hasto be independent of frequency, gain would be proportional to

0018-926X/$20.00 © 2006 IEEE

MANTEGHI AND RAHMAT-SAMII: ON THE CHARACTERIZATION OF A REFLECTOR IRA 813

Fig. 2. A normalized far-field pattern of an ideal IRA when the H-planebeam-width and the E-plane beam-width are the same. 3 dB beam-width isshown in dashed lines.

the square of frequency, therefore, in the direction that is in-dependent of frequency (usually boresight) the radiated electricfield intensity has to be proportional to frequency

(2)

The solid angle of the antenna is defined as[11] where is the maximum directivity of the antenna. Forsimplicity, assume that the antenna efficiency is 100%, so theantenna directivity is equal to the antenna gain. The IRA gainis proportional to the square of frequency, thus the solid angleis proportional to the inverse of the square of frequency. As aresult, in an ideal case, the beam-width (BW) of the antennacan be approximately related to frequency as

(3)

Equation (3) suggests an expected far-field pattern for an idealIRA. For a typical antenna pattern, the anticipated normalizedfar-field pattern for an ideal IRA versus frequency is shown inFig. 2.

B. Far-Field in Time Domain

For a planar aperture, the far-field at boresight ( or) is related to the tangential electric field, , using

(B-5) in Appendix B, i.e.,

(4)

where and are the aperture area and the speed of light respec-tively. For an antenna with a uniform aperture field the electricfar-field at boresight is

(5)

Equation (5) shows that the electric field in the far zone at bore-sight is proportional to the time derivative of the aperture field.

Fourier transformation of (5) confirms the linear relationship be-tween the far-zone field intensity and frequency as in (2).

Now we can list the properties of an ideal IRA as:

1) Input reflection coefficient is low in an ultrawide fre-quency band;

2) Gain is proportional to the square of frequency;3) The radiated far-field at boresight is proportional to the

time derivative of the aperture field;4) A linear phase relationship exists between the radiated

far-field and the input signal in the entire frequency band.(all frequency components have the same time delay);

5) Direction of the main beam of the radiation pattern doesnot change over the whole frequency band and the beamwidth is proportional to 1/f.

In Section II, first the parabolic reflector is illuminated by afrequency independent spherical wave ideal feed. The scatteredfields are calculated using physical optics technique and it isshown that the far-field patterns demonstrate similar behavioras far-field patterns of an ideal IRA. Then, the reflector IRAwith its TEM feeding structure is studied. A method of momentsbased software, Hybrid electric field integral equation (EFIE)and magnetic field integral equation (MFIE) Iterative (HEMI)[12], is employed to calculate the current distribution on theantenna body as well as the far-field patterns. The antenna ismeasured at the recently constructed spherical near-field mea-surement chamber at UCLA and the experimental results arepresented in Section III. Aperture fields are calculated using theholographic back projection technique and the result are com-pared with the calculated result for the current distribution fromSection II. Furthermore, the far-field patterns calculated usingnear-field measured data are compared with the ones calculatedby full-wave analysis. Conclusion is presented in Section IV.

II. PARABOLIC REFLECTOR

A parabolic reflector antenna with an idealized feeding struc-ture was initially analyzed to compare its performance to that ofan ideal IRA. Due to the massive calculations associated withthe method of moments to sweep in a wide frequency band, weused the frequency domain physical optics (PO) technique [13]for the idealized reflector IRA. Later, HEMI is employed to sim-ulate the Reflector IRA with the actual feeding structure.

A. Idealized Reflector IRA

An infinitely small dipole was used to illuminate a 57 cmparabolic reflector with a focal length to diameter ratioof 0.40. This configuration is simply a parabolic reflector fedby a frequency independent spherical wave illuminator with

and radiation patterns in twoprinciple planes. The frequency domain PO technique is usedto calculate the scattered far-field of the parabolic reflector fora wide frequency band. The calculated far-field pattern in theE-plane is shown in Fig. 3. The far-field pattern in the H-planeis almost the same as the one in the E-plane. Comparing Fig. 3with the expected far-field pattern for an ideal IRA (Fig. 2), onerealizes that the far-field pattern of the parabolic reflector is very


Fig. 3. Calculated scattered E at E-plane (Co-pol.) for the reflector with ashort dipole feed. The fields are normalized to their own maximum for eachfrequency.

close to the far-field pattern of an ideal IRA when it is properlyilluminated.

B. Practical Reflector IRA

A nondispersive TEM feeding structure is employed to illu-minate a parabolic reflector to realize a reflector IRA. The para-bolic reflector converts the spherical TEM mode of the feedingstructure to a uniform phase plane wave at the aperture of thereflector. The conical coplanar plates produce a self-reciprocalstructure with its circle of symmetry usually lying on the rim ofthe reflector [8]. It is shown theoretically that half of the powercarried through the TEM mode by this structure propagates out-side of the circle of symmetry and does not contribute to thehighly directive radiated field by the parabolic reflector [1], [8].

In order to demonstrate the performance of the reflector IRAexperimentally, an antenna was built at UCLA using a 57 cmparabolic reflector with a focal length to diameter ratioof 0.40 and two pairs of conical coplanar plates, which areplaced perpendicular to each other, as the TEM feeding struc-ture (Fig. 1). The size and angles for these plates are chosenin a way to reach characteristic impedance of 400 for eachpair of conical transmission lines and all arms are terminatedto the reflector with their own characteristic impedances loads[14], [15]. There is an analytical method introduced in [3] toanalyze the reflector IRA which gives the radiation fields andthe near-zone fields with a good approximation. In this simplemodel, the interaction between the TEM feeding structure andthe parabolic reflector is not taken into account; therefore, thecalculated radiation field does not contain the correct form ofthe tail waveform [16]. A method of moments based software,Hybrid EFIE and MFIE Iterative (HEMI), is employed tocalculate the antenna surface currents and the far-field char-acteristics. Because the reflector and the feeding structure areincluded in the HEMI model (Fig. 4), the results include theblockage effects of the TEM feeding structure and the inter-action between the reflector and the TEM feeding structure.Furthermore, all current distributions are calculated includingthe total, co-polarization, and cross-polarization currents.

The two perpendicular conical coplanar plates for are con-nected to each other as well as the two in and the gap source

Fig. 4. HEMI mesh model of the reflector IRA. The maximum edge lengthfor the feeding arm is 4 mm and for the parabolic reflector is 10 mm. This onlyshows one quarter of the structure in Fig. 1 due to the symmetry.

is placed between these two so we expect a -polarized radia-tion field. The reflector and its feeding structure have even andodd symmetry with respect to the plane and the plane,respectively. Therefore, one quarter of the antenna is used in thesimulation. A PEC plane and a PMC plane are placed at and

planes, respectively. This reduces the number of unknownsby a factor of four. HEMI uses the RWG [17] basis function. Forthe present application the HEMI mesh model of the reflectorIRA, Fig. 4, the maximum edge length for the feeding arm is4 mm and for the parabolic reflector is 10 mm. Fig. 5 showsthe calculated current distribution on the reflector at three dif-ferent frequencies. These figures show that the current distribu-tion is not uniform and it is more concentrated around theplane (H-plane). Different current distributions along andaxis generates different beam widths in the far zone for the twoprinciple planes which reduces the aperture efficiency. The cur-rent distributions on the TEM feeding structure are calculatedas well (Fig. 6). These figures demonstrate that the current den-sity on the feeding arms decreases with distance from the focalpoint. Also, a standing wave effect at the end of the feeding armscan be seen. In the HEMI model, a wide variety of resistive loadare tried between the feeding arms and the reflector to avoid thestanding waves but they did not disappear. It means that thereis some reactive energy stored in the junction area and a singleresistive load cannot match the feeding arms to the surface ofthe reflector. One may need to use a combination of lumped im-pedances for termination, as mentioned in [18]. Furthermore,the calculated currents show that the current density is higher atthe edges of the feeding arms and has lower density along themiddle of each arm. The points with lowest current density onthe feeding arms are the optimal places for the coaxial cable todetach from the arms. Thus, we can use each one of these armsas an UWB balun [19].

III. EXPERIMENTAL RESULTS

To measure the time domain characteristics of an IRA, onecan use either short pulses and a time-domain measurement


Fig. 5. Calculated y-component (co-pol), and x-component (cross-po.) of thecurrent distribution on the reflector at (a) 1 GHz, (b) 4 GHz, and (c) 6 GHz.

setup or many frequencies in a wide frequency band and use aninverse Fourier transformation to calculate the time-domain re-sults. In this work, we used the frequency domain measurementmethod. The recently constructed spherical near-field measure-ment chamber and the far-field anechoic chamber at UCLA areused to measure the radiation characteristics of the antenna.The measured results presented in the following sections are:A) input impedance, B) holographic images, and C) far-fieldpatterns.

A. Input Impedance

An IRA, at first has to have a low reflection coefficient ina wide frequency band. The conical coplanar TEM transmis-sion line is designed to achieve a 200 input impedance at theantenna port. Fig. 7(a) shows the real part and the imaginarypart of the measured input impedance which is observed at thefocal point. The associated scattering parameter in a 200system is presented in Fig. 7(b). Fig. 7(a) shows that the inputimpedance of the reflector IRA has a low variation about 200in the frequency band between 1.5 to 13 GHz. An HP-8510Bvector network analyzer was used for all measurements and thesweep frequency start from 45 MHz to 13 GHz with 801 points.One can use the inverse Fourier transformation of the reflected

Fig. 6. Calculated current distribution on the TEM feeding structure atdifferent frequencies. (a) 1 GHz, (b) 2 GHz, (c) 4 GHz, (d) 6 GHz.

signal from the antenna port to study some important propertiesof the TEM feeding structure [16]. Fig. 8(a) shows a schematicdrawing of a quarter of the feeding structure with the parabolicreflector. Some of the important points in the reflected signalare indicated with the capital letters as A) the feeding point,B) reflection point at the reflector apex, C) the chip resistorpoint, and D) the connection point between the feeding armand the reflector. The inverse Fourier transformation of the mea-sured reflected signal for different terminations are presented inFig. 8(b). In addition to short-circuit and open-circuit, 100and 200 are examined to study the effect of the terminationon the reflected signal tail. Because the inverse Fourier transfor-mation is applied to the signals with low frequency components,the truncation error generates some variation between the lowfrequency behaviors of the reflected signal tails versus termina-tion loads. This effect appears as a local DC shift in the signalwaveform. There is a differentiated impulse associated with thefeeding point at which is well-matched to the capacitiveproperties of the input impedance shown in Fig. 7(a). Since theinput signal has not seen the termination load at this time, thereis almost no difference between reflected signals for differentterminations.

To look at the reflected signal in more details, Fig. 8(b) ismagnified with horizontal axis in time scale and distance scalein Fig. 8(c) and 8(d) respectively (time is measured for a roundtrip). The next important point in the reflected signal waveform


Fig. 7. (a) Measured real part and imaginary part of the input impedance of the reflector IRA at the focal point. (b) scattering parameter (s ) in a 200 system.

Fig. 8. (a) Schematic drawing of a quarter of the reflector IRA with some of the important points in the reflected signal. (b) The time domain reflected signal fordifferent chip-resistors. (c) A magnified part of the b which shows the reflected signal from different points for different loads. (d) The same figure as c but withthe horizontal axis scaled in distance.

indicates the first reflection from the apex of the parabolic re-flector which is located at ns or .With the exception of the low frequency difference, the reflectedsignal waveform from point does not have an observable vari-ation versus termination loads. Point , located at nsor , is associated with the termination loads. Dif-ferent termination loads have different signature in the reflectedsignals from point . The short-circuit and open-circuit loadsdetermine the upper and lower limits for the reflected signalfrom this point. The feeding arm is connected to the parabolicreflector at point located at ns or . The otherimportant feature which is able to be identified is associ-ated with the second reflection from point and is located at

ns or . There is no feature in the schematicdrawing that can explain the small spike at point ( nsor ). There is a small spike at the point whichwas first identified as an error in the inverse Fourier transfor-mation. Since this signature can be seen in the entire measureddata, there should be a physical explanation. There is a smallpatch on the surface of the parabolic reflector which is locatedexactly at 0.253 m away from the focal point which seems to beassociated with this small spike.

The time domain reflected signals for different terminationloads show that neither the short-circuit nor the open-circuit arethe best termination loads. Furthermore, there is no significantdifference observed between 100 and 200 loads. It means


Fig. 9. Holographic images from measured at (a) 1 GHz, (b) 4 GHz, and (c) 6 GHz for amplitude and phase (unwrapped) of the co-polarization aperture fields.

that there is some reactive energy stored in the arm-reflectorconnection area which can not be reduced using just the resistiveloads. One has to use a combination of resistive and reactiveloads or change the arm-reflector connection to make a bettermatch.

B. Holographic Images

Using the measured spherical near-field data, the holographicimages can be generated for different tangential field at the an-tenna aperture [20]. Fig. 9 shows the co-polarized tangentialmagnetic field (electric current) on a plane located at the re-flector aperture. These figures indicate that the measured fieldintensity is not uniform on the antenna aperture. The measuredfield has higher intensity around the axis in comparison to the

axis area. Also, the co-polarized components have either a rea-sonably constant phase or linear variation phase in those areas

with higher field intensity. The linear phase variation observedin some of the holographic images is because of a slight mis-alignment of the reflector IRA with the measurement system.If the phase-center of the antenna is shifted in plane fromthe center phase of the measurement system a linear variationwill appear in the measured phase in the aperture plane. Theseresults have a good agreement with the calculated current dis-tribution on the antenna surface using HEMI (Fig. 5).

C. Far-Field

Once the tangential near-field distribution over an antennaenclosure or the electric current distribution on the surface ofthe antenna is known, one can calculated the far-field patterns.The calculated far-field from the near-field measured data inazimuth-elevation plane and the calculated far-field from boththe measured data and the HEMI results for two principle planesare presented in Fig. 10.


Fig. 10. Normalized elevation-azimuth measured far-field patterns and a comparison between two principle planes cuts (E and H for the H-plane and E andH for the E-plane) of measured far-field patterns with the calculated ones at (a) 1 GHz, (b) 4 GHz, and (c) 6 GHz.

Both the calculated current distributions illustrated in Fig. 5and the holographic images (Fig. 9) show that the aperture fieldis more concentrated around the -axis. So, the beam-width inthe H-plane is expected to be narrower than the beam-width inthe E-plane. The feeding structure is symmetric in the planeand the symmetry in the plane depends on performance ofthe balun. As seen from these figures, the measured far-field pat-terns at all frequencies are fairly symmetric in the both principleplanes and this confirms the balanced feeding mechanism. TheH-plane and E-plane cuts calculated from near-field measureddata and full-wave analysis (HEMI) for different frequencies arealso presented in Fig. 10. The calculated far-field from full-wavesimulation has a good agreement with the one calculated fromthe near-field measured data.

In Appendix A it is shown that the gain of an ideal IRA hasto increase with square of frequency (A-6). The maximum gainof a parabolic reflector is obtained at boresight , soone has to measure and calculate the far-field of the reflectorIRA at versus frequency. We used the three antenna cal-ibration system to measure the antenna gain versus frequency.The measurement setup consists of two ultra-wideband horn an-tennas, the reflector IRA, and a HP8510B vector network ana-lyzer. The far-field anechoic chamber of UCLA was used for thefar-field measurements. Fig. 11 shows the measured and calcu-lated far-zone frequency response of the antenna at boresight.For the convenience of this study, a ramp function (representinga delay in the time domain) has been subtracted from the phaseof the calculated and measured far-field [Fig. 11(b)]. As one cansee from this figure, the phase has a low variation in the entire


Fig. 11. Calculated and measured far-zone frequency response of the reflector IRA. (a) Calculated and measured amplitude, (b) calculated and measured phase.

Fig. 12. (a) Input differentiated Gaussian pulse. (b) Calculated and measured boresight radiation far-field.

frequency band of operation. Low phase distortion is one of therequirements of the IRAs. The measured far-zone frequency re-sponse of the antenna deviates from the calculated one in somefrequency windows. Some of the reasons can be listed as fol-lows: 1) The frequency cutoff of the UWB standard horn an-tennas is 1.2 GHz so the low frequency results are not valid.2) The far-field anechoic chamber is designed for C-band andX-band and it may affect the measured data at lower frequen-cies. 3) There are some mechanical errors due to the hand-madefeeding structure. Also, the reflector surface has some irregular-ities that contribute to surface errors.

In order to calculate the time-domain radiated far-field atboresight a differentiated Gaussian pulse is used as an ex-ample of the input pulse [Fig. 12(a)] and convolved with theinverse Fourier transformation of the calculated and measuredfrequency response of the antenna [Fig. 12(b)]. Clearly otherforms of the input pulses can also be used [18]. The time domainradiated waveform has a small pulse similar to the input signalwith a minus sign at [point in the Fig. 12(b)]. Thisearly time signal is associated with the radiation from the TEMfeed itself. It has been shown that half of the power acceptedby the reflector IRA radiates directly through the TEM feedingstructure [1], [2]. The current distribution on the reflector IRAand its feeding structure is calculated using HEMI at 4 GHz.

Fig. 13. Far-field pattern of the feeding structure at 4 GHz. It is assumed thatthe feeding structure by itself carries the same current when it is connected tothe parabolic reflector (Fig. 6 at 4 GHz).

Then the radiation patterns of the feeding structure itself whileit is carrying the same current as the complete antenna are cal-culated. Fig. 13 shows a 3-D radiation pattern of the TEM feedat 4 GHz without the parabolic reflector. This figure shows thatthe far-field pattern of the TEM feed has a wide beam-width.


The far-field pattern of the reflector IRA is the superposition ofthe visible part of this pattern and the directed far-field patternof the parabolic reflector. Therefore, the early time radiatedsignal does not change rapidly with variation. It takes almost1.53 ns [point in the Fig. 12(b)] for the excitation waveformto go through a round trip to the reflector and come back tothe focal point. As discussed in the introduction, the radiatedfield from a good IRA aperture has to have a time derivativerelationship with the excitation waveform. Fig. 12(b) showsthat the far zone time domain signal calculated from both themeasured results and the full-wave analysis (HEMI) at pointis the time derivative of the input differentiated Gaussian pulseand it agrees well with the theoretical results.

IV. CONCLUSION

Based on the definition of the gain and effective length ofthe antenna in the frequency domain, the far-field pattern of anideal IRA were determined. It was shown that the far zone fieldstrength and the inverse of the beam-width are proportional tofrequency for an ideal IRA. So, the time domain signal has tohave a time derivative relationship with the excitation wave-form. Also it was shown that a parabolic reflector can func-tion very close to an ideal IRA if it is fed properly. A MoMbased software (HEMI) was employed to calculate the currentdistribution and the far-field characteristics of the reflector IRA.The reflector IRA was constructed and measured in the spher-ical near-field chamber and the far-field anechoic chamber atUCLA.

By taking the inverse Fourier transform of the measured scat-tering parameter, the time domain reflected signal at the antennaport was calculated. It was shown that a resistive terminationload cannot completely match the feeding arm to the parabolicreflector. To avoid the standing wave at the feeding arms one hasto either change the end of the feeding arms in the way to reducethe reactance of the arm-reflector junction or use a combinationof resistive and reactive termination loads.

The full-wave analysis (HEMI) results at different frequen-cies shows that the current density around the axis is strongerthan the current density around -axis. The holographic im-ages were calculated from the near-field measured data con-firm these results too. For that reason the H-plane has to havea narrower beam-width in comparison to the E-plane. The far-field patterns in the azimuth (H-plane) and elevation (E-plane)were calculated from the near-field measured data and presentedfor different frequencies. These figures have a good agreementwith the calculated and measured near-field data. To obtain asymmetric far-field pattern (equal beam width at E-plane andH-plane) one has to change the feeding structure in the way toilluminate the parabolic reflector uniformly.

The calculated and measured far zone frequency responsesof the antenna at boresight were used to calculate the radiatedfield associated with a differentiated Gaussian pulse. The early

Fig. 14. Receiving antenna is connected to a transmission line withcharacteristic impedance Z which is terminated to its match load.

time signal and the time derivative of the input signal can beidentified in both results.

APPENDIX

A. Ideal Aperture in the Frequency Domain

If the receiving antenna with input impedance is con-nected to a transmission line with characteristic impedanceand is terminated to its own matching load (Fig. 14), the max-imum delivered power by the receiving antenna can be calcu-lated from the open circuit voltage, , and effective length, ,as

(A-1)

The maximum delivered power by the receiving antenna also isrelated to the effective aperture by

(A-2)

where is the free space impedance, and gain is defined as

(A-3)

One can calculate the relation between the effective apertureversus effective length of the antenna using (A-1) and (A-2)

(A-4)

Finally, substituting from (A-4) into (A-3), gain of the an-tenna is calculated as a function of the effective length by

(A-5)

which can be simplified to

(A-6)


for an antenna with an input impedance matched to the charac-teristic impedance of the transmission line at entirefrequency range where is the speed of light in free space.

B. Ideal Aperture in the Time Domain

The frequency domain radiated field of a set of arbitrarysources, and , which are limited in a closed volume

in free space is given [10] by

(B-1)

where the observation point is located at , the source point at, , and . One can rewrite this formula

for far-field by substituting by in (B-1)

(B-2)

The time domain electric field in the far zone and in its generalform [21] can be written from (B-2) as

(B-3)where the retarded time, , is defined as

(B-4)

For simplicity, assume the aperture as a planar surface which islocated at . If a PEC is located right behind the aperture

due to the image theory ( andwhere is the tangential electric field in the aperture) we have

(B-5)

where is the area of the aperture.

REFERENCES

[1] R. H. DuHamel et al., “Frequency independent conical feeds for lensand reflectors,” in Proc. IEEE Int. Antennas Propagation. Symp. Dig.,vol. 6, Sep. 1968, pp. 414–418.

[2] C. E. Baum, “Radiation of impulse-like transient fields,” Sensor andSimulation Notes #321, Nov. 1989.

[3] C. E. Baum and E. G. Farr, “Impulse radiating antennas,” in Ultra-Wide-band, Short-Pulse Electromagnetics, H. L. Bertoni, L. Carin, and L. B.Felson, Eds. New York: Plenum, 1993, pp. 131–144.

[4] E. G. Farr, C. E. Baum, and C. J. Buchenauer, “Impulse radiatingantennas, Part II,” in Ultra Wideband/Short-Pulse Electromagnetics 2,L. Carin and L. B. Felsen, Eds. New York: Plenum Press, 1995, pp.159–170.

[5] E. G. Farr and C. E. Baum, “Impulse radiating antennas, part III,” inUltra Wideband/Short-Pulse Electromagnetics 3, C. E. Baum, L. Carin,and A. P. Stone, Eds. New York: Plenum Press, 1997, pp. 43–56.

[6] M. Kanda, “Transients in a resistively loaded linear antenna comparedwith those in a conical antenna and a TEM horn,” IEEE Trans. AntennasPropag., vol. 28, no. 1, pp. 132–136, Jan. 1980.

[7] A. P. Lambert, S. M. Bookers, and P. D. Smith, “Calculation of the char-acteristic impedance of TEM horn antennas using the conformal map-ping approach,” IEEE Trans. Antennas Propag., vol. 43, no. 1, pp. 47–53,Jan. 1995.

[8] C. E. Baum, “Radiation from self reciprocal aperture,” Sensor and Sim-ulation Notes #357, Apr. 1993.

[9] E. G. Farr and C. E. Baum, “Radiation from self-reciprocal aper-ture,” in Electromagnetic Symmetry, C. E. Baum and H. N. Kiritikos,Eds. Bristol, U.K.: Taylor and Francis, 1995, ch. 5.

[10] Antenna Handbook, Y. T. Lo and S. W. Lee, Eds., Van Nostrand Rein-ford, New York, 1988.

[11] W. L. Stutzman and G. A. Thiele, Antenna Theory and Design. NewYork: Wiley, 1998.

[12] R. E. Hodges and Y. Rahmat-Samii, “An iterative current-based hybridmethod for complex structures,” IEEE Trans. Antennas Propag., vol. 45,no. 2, pp. 265–276, Feb. 1997.

[13] Y. Rahmat-Samii, “Reflector antennas,” in Antenna Handbook, Y. T. Loand S. W. Lee, Eds. New York: Van Nostrand Reinford, 1988.

[14] J. S. Tyo, “Optimization of the TEM feed structure for four-arm reflectorimpulse radiating antennas,” IEEE Trans. Antennas Propag., vol. 49, no.4, pp. 607–614, Apr. 2001.

[15] E. G. Farr and C. E. Baum, “Prepulse associated with TEM feed of an im-pulse radiating antenna,” Sensor and Simulation Notes #337, Mar. 1992.

[16] K. Kim and W. R. Scott, “Numerical analysis of the impulse radiatingantenna,” Sensor and Simulation Notes #474, Jun. 2003.

[17] S. Rao, D. Wilton, and A. Glisson, “Electromagnetic scattering by sur-faces of arbitrary shape,” IEEE Trans. Antennas Propag., vol. 30, no. 3,pp. 409–418, May 1982.

[18] D. V. Giri and C. E. Baum, “Temporal and spectral radiation on bore-sight of a reflector type of Impulse Radiating Antenna (IRA),” in UltraWideband/Short-Pulse Electromagnetics 3, C. E. Baum, L. Carin, andA. P. Stone, Eds. New York: Plenum Press, 1997, pp. 65–72.

[19] M. Manteghi and Y. Rahmat-Samii, “A novel UWB feeding mechanismfor the TEM horn antenna, reflector IRA, and the Vivaldi antenna,” IEEEAntennas Propag. Mag., vol. 46, no. 5, pp. 81–87, Oct. 2004.

[20] Y. Rahmat-Samii and J. Lemanczyk, “Application of spherical near-fieldmeasurements to microwave holographic diagnosis of antennas,” IEEETrans. Antennas Propag., vol. 36, no. 6, pp. 869–878, Jun. 1988.

[21] A. Taflove, Ed., Advances in Computational Electrodynamics the Finite-Difference Time-Domain Method. New York: Artech House, 1998, ch.7, p. 410.

Majid Manteghi (S’01–M’05) received B.S. andM.S. degrees from the University of Tehran, Tehran,Iran, in 1994 and 1997, respectively, and the Ph.D.degree in electrical engineering from the Universityof California, Los Angeles (UCLA), in 2005.

He worked as a Research Assistant in theMicrowave Laboratory, University of Tehran, from1994 to 1997, where he designed microstrip patchantennas, arrays, traveling wave antennas, handsetantennas, Base Transceiver Station (BTS) singleand dual polarized antennas, reflector antennas,

and UHF transceiver circuits and systems. From 1997 to 2000, he workedin the telecommunication industry in Tehran where he served as the head ofan RF group for a GSM BTS project. In fall 2000, he joined to the AntennaResearch, Analysis, and Measurement Laboratory (ARAM) of the Universityof California, Los Angeles. He is currently a Research Engineer with theElectrical Engineering Department of UCLA. His research area has includedultrawide-band impulse radiating antennas, miniaturized patch antennas,multiport antennas, dual frequency dual polarized stacked patch array designs,and miniaturized multiband antenna for MIMO applications.


Yahya Rahmat-Samii (S’73–M’75–SM’79–F’85)received the M.S. and Ph.D. degrees in elec-trical engineering from the University of Illinois,Urbana-Champaign.

He was a Guest Professor with the TechnicalUniversity of Denmark (TUD) during summer 1986.He was a Senior Research Scientist at NASA’sJet Propulsion Laboratory, California Institute ofTechnology, Pasadena, before joining the Univer-sity of California, Los Angeles (UCLA) in 1989.Currently, he is a Distinguished Professor and the

Chairman of the Electrical Engineering Department, UCLA. He has also been aConsultant to many aerospace companies. He has been Editor and Guest Editorof many technical journals and book publication entities. He has authored andcoauthored more than 660 technical journal articles and conference papersand has written 20 book chapters. He is the coauthor of Impedance BoundaryConditions in Electromagnetics (Washington, DC: Taylor & Francis, 1995)and Electromagnetic Optimization by Genetic Algorithms (New York: Wiley,1999). He is also the holder of several patents. He has had pioneering researchcontributions in diverse areas of electromagnetics, antennas, measurementand diagnostics techniques, numerical and asymptotic methods, satellite andpersonal communications, human/antenna interactions, frequency selectivesurfaces, electromagnetic bandgap structures and the applications of thegenetic algorithms. On several occasions, his work has made the cover of manymagazines and has been featured on several television newscasts.

Dr. Rahmat-Samii is a Member of Sigma Xi, Eta Kappa Nu, CommissionsA, B, J, and K of the United States National Committee for the InternationalUnion for Radio Science (USNC/URSI), Antennas Measurement TechniquesAssociation (AMTA), and the Electromagnetics Academy. He was elected as aFellow of the Institute of Advances in Engineering (IAE) in 1986. Since 1987,he has been designated every three years as one of the Academy of Science’sResearch Council Representatives to the URSI General Assemblies held in var-ious parts of the world. In 2001, he was elected as the Foreign Member of theRoyal Academy of Belgium for Science and the Arts. He was also a memberof UCLA’s Graduate council for a period of three years. For his contributions,he has received numerous NASA and JPL Certificates of Recognition. In 1984,he received the coveted Henry Booker Award of the URSI which is given tri-ennially to the Most Outstanding Young Radio Scientist in North America. In1992 and 1995, he was the recipient of the Best Application Paper Prize Award(Wheeler Award) for papers published in the 1991 and 1994 IEEE ANTENNAS

AND PROPAGATION. In 1999, he was the recipient of the University of IllinoisECE Distinguished Alumni Award. In 2000, he was the recipient of IEEE ThirdMillennium Medal and AMTA Distinguished Achievement Award. In 2001, hewas the recipient of the Honorary Doctorate in physics from the University ofSantiago de Compostela, Spain. In 2002, he received the Technical ExcellenceAward from JPL. He is the winner of the 2005 URSI Booker Gold Medal tobe presented at the URSI General Assembly. He was also a Member of theStrategic Planning and Review Committee (SPARC) of the IEEE. He was theIEEE AP-S Los Angeles Chapter Chairman (1987–1989) and his chapter wonthe Best Chapter Awards in two consecutive years. He was the elected 1995President and 1994 Vice-President of the IEEE Antennas and Propagation So-ciety. He was one of the Directors and Vice President of the Antennas Measure-ment Techniques Association (AMTA) for three years. He was appointed anIEEE Antennas and Propagation Society Distinguished Lecturer and presentedlectures internationally. He is listed in Who’s Who in America, Who’s Who inFrontiers of Science and Technology, and Who’s Who in Engineering. He is thedesigner of the IEEE Antennas and Propagation Society logo that is displayedon all IEEE ANTENNAS AND PROPAGATION publications.

812 ieee transactions on antennas and …fig. 2. a normalized far-ﬁeld pattern of an ideal ira...

Documents