Precise measurement of cm wavelength radio back-ground and detection of fine structure spectral distortions in it require an antenna with i) monotonically varying impedance and radiation characteristics, ii) minimum gain towards horizon and iii) low back lobe level. We describe in this paper the design of a sinusoidally profiled planar dipole antenna backed by a log-spiral shaped metallic reflector. It operates in the frequency range of 2–4 GHz and has i) gain less than -20 dB towards horizon, ii) back lobe level less than -35 dB iii) smooth and inflection free impedance characteristics and iv) frequency invariant radiation patterns. The structural parameters have been modeled and optimized using WIPL-D and CST microwave studio electromagnetic simulation software. The design has been validated by constructing a prototype and making field measurements.