This paper demonstrates a high-Q broad-band active inductor and its application to a low-loss analog phase shifter. The proposed high-Q broad-band active inductor utilizes frequencyinsensitive negative resistance to compensate constant internal losses caused by the drain-to-source conductance of the fieldeffect transistors (FET's), the dc bias circuit, and several other factors. The measured frequency range of the fabricated In- AlAsnnGaAsRnP HEMT active inductor is 6 to 20 GHz for Q values greater than 100, and 7 to 15 GHz for Q values greater than 1000. A low-loss analog phase shifter is also fabricated at Cband. This is constructed with the active inductors, the varactor diodes and the low-loss multilayer broad-side coupler in a MIC structure. Since the constant negative resistance of the active inductors also compensates the line loss of the coupler and the varactor diodes' series resistance, the measured results show a good insertion loss performance with a large phase shift. A phase shift of more than 225" within a 0.8 dB insertion loss from 4.7 to 6.7 GHz, another of more than 180" within 1.3 dB insertion loss from 3.7 to 8.5 GHz, and one more of more than 90" within 1.4 dB insertion loss from 3.5 to 10.6 GHz were obtained.