Opportunities to achieve a cutoff pattern with the travelling wave antennas of moderate size are discussed. A qualitative model in the form of a parallel plate waveguide with semitransparent endings has been evaluated. A quadrifilar helix antenna with embedded reactances with the length of about 1.5 wavelength has been built. The antenna possesses a smooth pattern in the top semi-sphere with 20 dB drop of the gain (cutoff) while crossing the local horizon. Antenna functionality in applications to positioning with the Global Navigation Satellite Systems has been tested. RMS of positioning error is shown to be of 0.65 mm provided phase noise of the system smoothed out within 1 minute span.