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In this note we begin the development of two types of Impulse Radiating Antenna (IRA). o These two designs include a 23 cm diameter reflector IR4, with an F/D of0.38, and a solid dielectric-lens IIU4, or dielectric-immersed lens IIU. This latter design is a Transverse Electromagnetic (TEM) horn immersed in a dielectric, with a prolate spheroidal lens interface to air. The reflector IR4 consists of a paraboloidal reflector, fed by a conical 4-arm feed, whose combined input impedance is 200 Q. The lens IR4 was constructed from a solid block of polyethylene, conical in shape, and capped by a prolate spheroid. It can be short, because of the prolate spheroidal lens. In addition, since the TEM feed is filled with dielectric, it will provide a better match to 50 Q, when compared to an air-filled TEM horn with a lens. Since there are fewer dielectric interfaces with this design, there will also be fewer reflections, which reduces Fresnel loss. The technique for calculating the step response antenna pattern involves calculation of the line integrals of the quasistatic potential over the aperture. The resulting step responses are then convolved with the derivative of the driving voltage to obtain the overall waveshape. The reflector conjuration was calculated using a 4-wire approximation to the aperture. The lens IIU was calculated under the assumption that the aperture was that of a TEM horn built with circular plates. The antenna pattern measurement technique involves using two identical antennas, and we present here the relevant equations for the signal processing. In particular, signal processing techniques are described for extracting the single-antema response from the 2-antema * measurement. The actual measurements will be presented in a later paper, which will be Part II of this note. . I , , L Introduction This report summarizes the design and analysis phase of the development of a Reflector o IRA and a Solid Dielectric Lens IlL4. We consider first the Reflector ~ including design equations, the specific design chose~ boresight and off-boresight radiated field, and received voltage for two identical antennas. Next, we consider the same set of issues concerning the lens Ill& and we also consider the possibility of approximating the elliptical surface with a spherical surface. In addition, we consider adaptive noise filters as a technique to enhance our calculation of the antema step response. Finally, we consider signal propagation through cables, including a simple model of skin effect losses. We begin with the Reflector IIU. IL Reflector IRA We will be building a reflector IRA with a diameter of 23 cm and an F/D ratio of jd = 0.3778. Below we describe the design equations required. A. Design Equations The most interesting portion of the design of the reflector IRA deals with the feed arm angles, as shown in Figure 1.A. 1. The center angle is specified as o P= [ 1 arctan 2~d -1 I (8jd ) ) Furthermore, the feed impedance of TEM feed is [1] fg = ‘(m) K(l -m) (2.A.1) (2.A.2) where K(m) is the complete elliptic integral of the first kind. For the usual case of the feed impedance being 400 Q, we have m=O.565291. Having solved for m and P, one then finds the remaining angles as [1] [ PI = 2 arctan ml/4 tan(p / 2)] P2 [ = 2 arctan m-1’4 tan~ J 2)] (2.A.3) The angles for fd= 0.3778 are now simple to determine. We find fll, P and % are 59.69, 66.99, 74.70 degrees, respectively. *