Microwave Three-Dimensional Capacitive Stubs
Introduction. Microstrip filters are widely used in a variety of radio-electronic systems, including telecommunications. Low frequency filters (LPFs) are constructed on the basis of quasi-lumped inductances and capacitances. Quasi-lumped capacitances are performed as microstrip sections with a wide signal conductor or open stubs. Traditional quasi-lumped elements are two-dimensional (2D). Three-dimensional (3D) quasi-lumped elements have 1.5 to 4 times greater reactivity values. The purpose of the paper is to analyze 3D-stubs charateristics. Capacitive 3D-stub transfer characteristic. The 3D-stub is a deaf metalized hole. In the presented paper hole is a square with rounded corners. Dependencies of 1D-model parameters of 3D-stub are shown. From a comparison of 3D- and 1D-transfer characteristics of the 3D-stub it is shown that the 3D-stub in the first approximation can be simulated by a 1D-model in the form of a long line stub. Influence of parasitic inductance on stub notch frequency. For a 1D-model, the stub notch frequency is determined by a quarter-wave condition of it’s length. Stub’s T-junction brings in parasitic reactivities. The parasitic inductance and stub form a series oscillatory circuit. The resonance frequency of this circuit is equal to stub notch frequency. Since traditionally this inductance is negative, the notch frequency increases and stub and LPF transfer characteristics slope decreases. In order to reduce the inductance influence for stub and line contact it is suggested to use a small contact pad. 3D-stub notch frequency and parasitic inductance dependences. The dependences of the notch frequency and parasitic inductance on the 3D-stub heterogeneity depth and contact pad length are analyzed. According to simulation results for a variant with a contact pad inductance values can be not only negative, but also positive. If inductance is positive, notch frequency is less than according to quarter-wave condition. In this case, stub and LPF transfer characteristics slope is higher compared to quarter-wave condition. Discussion of the results. With an increase of the 3D-stub heterogeneity depth from 0.5 to 1 mm, its wave impedance is less in 1.4 ... 3.5 times compared to 2D-stub, and the capacity is greater in 1.6 ... 4.1 times. Contact pad between the stub and line allows to optimize the stub parameters from the condition of the required transfer characteristics slope. Conclusion. 3D-stub has significantly better parameters than 2D-stub. Since the LPF requires the specified capacitance values, depending on the 3D-stub inhomogeneity depth, the area of the 3D-stub is less than 1.6 ... 4.1 times. The 1D-model of the 3D-stub allows to characterize the stub by equivalent wave impedance and relative dielectric permittivity and can be used as the first approximation model for the design and simulating of microstrip LPFs based on capacitive 3D-stubs.
low pass filter; capacitive stub; three-dimensional model; one-dimensional model; stub’s T-junction
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