Implementation and Investigation of a Compact Circular Wide Slot UWB Antenna with Dual Notched Band Characteristics using Stepped Impedance Resonators

A coplanar waveguide (CPW) fed ultra-wideband (UWB) antenna with dual notched band characteristics is presented in this paper. The circular wide slot and circular radiation patch are utilized to broaden the impedance bandwidth of the UWB antenna. The dual notched band functions are achieved by employing two stepped impedance resonators (SIRs) which etched on the circular radiation patch and CPW excitation line, respectively. The two notched bands can be controlled by adjusting the dimensions of the two stepped impedance resonators which give tunable notched band functions. The proposed dual notched band UWB antenna has been designed in details and optimized by means of HFSS. Experimental and numerical results show that the proposed antenna with compact size of 32 × 24 mm2, has an impedance bandwidth range from 2.8 GHz to 13.5 Hz for voltage standing-wave ratio (VSWR) less than 2, except the notch bands 5.0 GHz - 6.2 GHz for HIPERLAN/2 and IEEE 802.11a (5.1 GHz - 5.9 GHz) and 8.0 GHz - 9.3 GHz for satellite and military applications

Average-Case Complexity of Shellsort

We prove a general lower bound on the average-case complexity of Shellsort: the average number of data-movements (and comparisons) made by a $p$-pass Shellsort for any incremental sequence is \Omega (pn^{1 + 1/p) for all $p \leq \log n$. Using similar arguments, we analyze the average-case complexity of several other sorting algorithms.Comment: 11 pages. Submitted to ICALP'9