In this continuation of our paper in the last conference proceedings 1 , we consider further developments in the area of Impulse Radiating Antennas (IRAs). First, we consider definitions of gain in the time domain, which are important for optimizing the performance of IRAs. A reasonable definition of gain must be equally valid in transmission as in reception. Such a definition leads naturally to a transient radar equation, which we discuss. Next, we consider how to optimize the feed impedance in a reflector IRA. If we use our simple model of IRA performance, the gain of an IRA is always better at lower impedances. But this implies larger feeds with more aperture blockage. To resolve this, we refine our simple model to account for feed blockage. We also consider the radiation pattern of IRAs, and we provide simple calculations. Finally, we provide a sample experiment which confirms our theory of IRA operation.
I. REVIEW OF IRA DESIGNBy now there exists a considerable body of literature concerning the design of IRA's 1-17 . There are two fundamental types of IRA, the reflector IRA and the lens IRA (Figure 1.1). The reflector IRA consists of a paraboloidal reflector fed by a conical TEM feed and terminated in an impedance that maintains a cardioid pattern at low frequencies. The lens IRA consists of a simple TEM horn with a lens in the aperture for focusing 25,26 . Either design is fed by a voltage source that is ideally shaped like a step function, but is in practice shaped like a fast-risetime impulse with a slower decay. In addition, either design normally has a dielectric lens at the apex to maintain voltage standoff 26,27 . Although there is some feed blockage associated with the reflector design, there is a considerable penalty in weight associated with the lens design. Thus, until lightweight dielectrics (real or artificial) with appropriate loss and dispersion properties are found, lens IRAs will likely be confined to applications with small apertures.The step response of a reflector IRA on boresight consists, to first order, of a prepulse followed by an impulse. The magnitude of the prepulse is determined by transmission line techniques 1,8 , and it lasts for the round-trip transit time of the feed, 2F/c, where F is the focal length of the reflector, and c is the speed of light. The magnitude of the impulse is found by aperture integration 1,5 . The total response iswhere D is the diameter of the reflector, f g = Z feed / Z o , Z o is the impedance of free space, V o is the magnitude of the driving voltage step launched onto the feed, r is the distance away from the antenna on boresight, and u(t) is the Heaviside step function. Furthermore, δ a (t) is the approximate Dirac delta function 3 , which approaches a true Dirac delta function as r approaches infinity. This is a high-impedance approximation based on the aperture integration described by Baum 5 . Later, we provide a correction for lower impedances. Note that the above equation can be expressed in terms of an arbitrary driving voltage as
