In this thesis two different research topics are undertaken, both in the area of compact RF/microwave circuits design. The first topic involves the design of a compact circularly polarized (CP) slot-ring antenna. A study of several compact CP microstrip and slotline antennas reported in the past has been carried out. In this research, a method of reducing the size of a printed slot-ring antenna is proposed. The reduction in size is achieved by introducing meandered-slot sections in the ring. Circular polarization is achieved by introducing an asymmetry, also a meandered-slot section, and feeding the antenna at an angle of 45o from the asymmetry using a microstrip feed line. The minimum axial ratio of 0.4 dB is obtained at 2.46 GHz, which is the operating frequency of the antenna. The size of the proposed antenna is reduced by about 50% compared to a conventional CP slot-ring antenna and it displays a CP bandwidth of about 2.5%. The simulated and measured results are presented, and they are in good agreement. The small size of the antenna makes it very suitable for use in modern RF/microwave wireless systems which require compact, low cost, and high performance circuits. Moreover, its CP behavior makes it more attractive for applications such as satellite communications. The second topic in the thesis involves the design of a compact microstrip bandpass filter using triangular open-loop resonators. A new compact three-pole microstrip bandpass filter using four triangular open-loop resonators is presented. A fourth resonator is placed to provide cross-coupling in the structure which gives a better skirt rejection. The measured pass-band center frequency is 2.85 GHz. The filter demonstrates about 7% bandwidth with insertion loss of less than 1 dB in the passband, a return loss of greater than 15 dB and out-of-band rejection of greater than 30 dB. The simulated and measured results are in good agreement. The proposed filter is very attractive for use in modern wireless systems which require bandpass filters having compact size, low insertion loss, high selectivity, and good out-of-band rejection.