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The grid voltage phase and frequency are crucial information in control of most grid connected power electronic based equipment. Most often, a phase-locked loop (PLL) is employed for this purpose. A PLL is a closed-loop feedback control system that the phase of its output signal is related to the phase of its input signal. Arguably, the simplest PLL is a type-1 PLL. The type-1 PLLs are characterized by having only one integrator in their control loop and therefore having a high stability margin. However, they suffer from a serious drawback: they cannot achieve zero average steady-state phase-error in the presence of frequency drifts. To overcome this drawback of type-1 PLLs, and at the same time, to achieve a fast dynamic response and high filtering capability, a modified PLL structure is proposed in this letter. The proposed PLL has a similar structure to a type-1 PLL, but from the control point of view is a type-2 control system. For this reason, it is called the quasi-type-1 PLL (QT1-PLL). The effectiveness of the proposed PLL is confirmed through simulation and experimental results and comparison with standard PLLs.

Abstract-This paper deals with the accurate and efficient modal analysis of arbitrarily shaped waveguides whose cross section is defined by a combination of straight, circular, and/or elliptical arcs. A novel technique for considering the presence of circular and/or elliptical segments within the frame of the well-known boundary integral-resonant mode expansion (BI-RME) method is proposed. This new extended BI-RME method will allow a more accurate solution of a wider number of hollow conducting waveguides with arbitrary profiles, which are usually present in most modern passive waveguide components. To show the advantages of this new extended technique, the modal chart of canonical (circular and elliptical) waveguides, as well as of irises with great practical interest (i.e., cross-shaped irises with rounded corners) has been first successfully solved. Next, a computer-aided-design software package based on such a novel modal analysis tool has first been validated with the accurate analysis of a referenced complex dual-mode filter, and then applied to the complete design of a novel twist component for -band application based on circular and elliptical waveguides. A prototype of this novel device has been manufactured and measured for verification purposes.