INTRODUCTIONNowadays, as the operating frequencies of microwave and RF transceivers are trending to shift to higher frequencies, local oscillators play an important role in communication systems.Ž . Phase-locked oscillators PLOs are commonly used in the systems, but they contain many components such as VCOs, phase detectors, and frequency dividers, resulting in a high cost. On the other hand, ILOs are simple, low cost, and millimeter-wave possible, but relatively do not have enough w x of a locking range 1, 2 .In this paper, we analyze an ILO in terms of feedback signal into the active device and a fictitious internal source generated by the nonlinear characteristics of the active device, and then propose a systematic design procedure to enhance the locking range of the ILO. Frequency doublers are designed for this procedure using the impedance substi-Ž . tute method Fig. 1 . Through this method, oscillators can be designed as amplifiers. That is, the feedback signals of the oscillators can be viewed as the input signals of the amplifiers with the same output powers. Therefore, the feedback signal levels into the transistors and the harmonic terminations maximizing the fictitious internal source can be determined easily in the design process. Compared with the conventional design procedure, this approach results in a wide locking range of the ILO. Figure 1 shows the impedance substitution method of the Ž . oscillator. jX , jX , and Z in Figure 1 a represent the gate, Ž . drain impedance, respectively. Also, P , P repre- DESIGN APPROACH FOR ILOsent the oscillation feedback signal into the gate and the external source, respectively. The three-port ILO can be Ž . Ž . impedance is Z as in Figure 2 b , where P is a out s fictitious internal source generated in the transistor. Ž . If the ILO is applied to the multiplier, the P is s composed of the subharmonic component of the external source and the intermodulation components of two tones: the external signal and the feedback signal. In the case of a frequency doubler, the second subharmonic component of Ž . the external signal is the dominant component in P . locking condition is satisfied as such:This equation is re-expressed by free-running frequency terms:Ž . where ⌬ P , ⌬⌫ , and ⌬⌫ are deviations of P , ⌫ , Ž . Equation 3 is approximated asŽ . In Eq. 4 , the locking range of the ILO can be estimated because it is generally proportional to ⌬ P . The first term in f the parentheses is related to the output power, the second to the Q of the circuit, and the last term means the nonlinear characteristics of the active device. They are similar to the w x well-known Adler's equation 3 . Therefore, in the case of constant Q, increasing the internal source and decreasing the feedback signal level can enhance the locking range. But the small feedback signal level in the design process lowers the output power. DESIGN OF ILOFirst, determination of the feedback signal level P is considf ered with respect to the output power and locking range because the output po...
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