A three-stage liquid metal switch employing electrowetting on dielectric (EWOD), including a common EWOD switch 1310 having an input port 1302, a first shared-EWOD-switch output 1336, and a second shared-EWOD-switch output 1338; a first EWOD switch 1340 having a first-EWOD-switch input 1343, a first output port 1304, and a first-EWOD-switch output 1368; and a second EWOD switch 1370 having a second-EWOD-switch input 1373, a second output port 1306, and a second-EWOD-switch output 1398; wherein the first shared-EWOD-switch output 1336 is operably connected to the first-EWOD-switch input 1343, and the second shared-EWOD-switch output 1338 is operably connected to the second-EWOD-switch input 1373.