  Quantum coherent properties of electrons can be studied in Aharonov-Bohm (AB)
interferometers. We investigate both experimentally and theoretically the
transmission phase evolution in a four-terminal quasi-one-dimensional
AlGaAs/GaAs-based waveguide AB ring. As main control parameter besides the
magnetic field, we tune the Fermi wave number along the pathways using a
top-gate. Our experimental results and theoretical calculations demonstrate the
strong influence of the measurement configuration upon the
AB-resistance-oscillation phase in a four-terminal device. While the non-local
setup displays continuous phase shifts of the AB oscillations, the phase
remains rigid in the local voltage-probe setup. Abrupt phase jumps are found in
all measurement configurations. We analyze the phase shifts as functions of the
magnetic field and the Fermi energy and provide a detailed theoretical model of
the device. Scattering and reflections in the arms of the ring are the source
of abrupt phase jumps by $\pi$.
