Equivalent length design equations for right-angled microstrip bends

For printed antenna systems, microstrip feeding networks may become quite complex, including several right-angled bends. In designing feed networks we have to consider reflection levels at and electrical lengths of the bends. Removing a part of the area of metallization in the bend's corner can compensate for the excess capacitance and reduce the reflection level of the bend. Full wave simulations have been performed for unmitered and (50%) mitered right-angled bends in microstrip on FR4 and FR4 -like substrates in the frequency range 868MHz - 60GHz. The simulations revealed that for reflection levels below -15dB, up to 10GHz mitering is unnecessary. For reflection levels below -20dB, mitering must be applied for frequencies in excess of 2.5GHz. A slight modification of the centreline approach for unmitered bends leads to an equivalent electrical length for unmitered bends with an absolute accuracy of less than one degree for all frequencies and substrates, where the reference planes may be brought back all the way to the bend. Applying this modification to 50%-mitered bends, having the reference planes at 0.2 λg distance from the bend, λg being the wavelength in the substrate, leads to an absolute error in electrical length of less than two and a half degrees for all frequencies and substrates