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Next generation of instruments for radio astronomy will benefit greatly from reflector antenna feeds that demonstrate very wide instantaneous bandwidth and exhibit low noise behavior. Our study focuses on design and measurement of an ultra-wideband inverted conical sinuous antenna and its integration with a low noise pseudo differential amplifier. The self-complementary, frequency independent nature of the planar sinuous geometry results in a nearly constant beam pattern and fixed phase center over more than a 10:1 operating frequency range. In order to eliminate the back-lobe response over such a wide frequency range, we have projected the sinuous pattern onto a cone, and a ground plane is placed directly behind the cone's apex. This inverted, conical geometry assures wide bandwidth operation by locating each sinuous resonator a quarter wavelength above the ground plane. The presence of a ground plane near a self complementary antenna destroys the self complementary nature of the composite structure resulting in frequency dependent impedance variations. We demonstrate, using simulations and measurements, how the return loss can be improved by modifying the sinuous geometry. A physically smaller, laboratory version of the 0.3 to 3 GHz antenna that is truncated to operate from 1 to 3 GHz was fabricated to verify proper LNA-feed integration through careful modeling and measurements. Over this range, a return loss of better than 9 dB is measured while simulations indicate a nearly constant beam pattern. A full decade bandwidth, low noise amplifier was specially designed for noise match to the higher terminal impedance encountered by this antenna yielding an improved sensitivity over what is possible with conventional 50 Ω amplifiers. A measured system noise temperature of less than 100 K is reported. Based on these results, we will increase the bandwidth of the system to 10:1 by simply attaching additional resonators to the sinuous arms.