The most common computer-aided circuit analysis tech- nique is the time-domain transient analysis using the time- marching approach to solve the system of ordinary diﬀer- ential equations (ODEs) that represent the circuit. This ap- proach is used in Spice and many other circuit simulators. Al- though still very useful, this technique presents a number of shortcomings for the analysis of RF and **microwave** **circuits**. Amongst these shortcomings is the huge amount of mem- ory and computation time required for the analysis of cir- cuits with widely separated time scales and/or excitations [1]. This is often the case for mixers, power amplifiers, and oscil- lators. Several techniques have been developed to overcome this problem. Some of them are available in modern circuit simulators and are widely used. In this paper we present an overview of these methods with special attention to the anal- ysis of oscillators.

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Abstract. Field-oriented methods which describe the phys- ical properties of **microwave** **circuits** and optical structures are an indispensable tool to avoid costly and time-consuming redesign cycles. Commonly the electromagnetic characteris- tics of the structures are described by the scattering matrix which is extracted from the orthogonal decomposition of the electric field. The electric field is the solution of an eigen- value and a boundary value problem for Maxwell’s equa- tions in the frequency domain. We discretize the equations with staggered orthogonal grids using the Finite Integration Technique (FIT). Maxwellian grid equations are formulated for staggered nonequidistant rectangular grids and for tetra- hedral nets with corresponding dual Voronoi cells. The in- teresting modes of smallest attenuation are found solving a sequence of eigenvalue problems of modified matrices. To reduce the execution time for high-dimensional problems a coarse and a fine grid is used. The calculations are car- ried out, using two levels of parallelization. The discretized boundary value problem, a large-scale system of linear alge- braic equations with different right-hand sides, is solved by a block Krylov subspace method with various preconditioning techniques. Special attention is paid to the Perfectly Matched Layer boundary condition (PML) which causes non physical modes and a significantly increased number of iterations in the iterative methods.

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In this proposed enhancement to the laser machining prototyping technique, the laser patterning is conducted in two stages; the inner layers are machined as before in the unfired state, whilst the outer layers are patterned post-firing. The minimum strip width and gap on the top layer have been reduced to 30 µm by using this modified technique. The edge definition has also been improved to ±2 µm, meaning that designs with high impedance lines on thin LTCC sheets can be realized, reducing the need for dummy layers. A major limitation in the performance of LTCC **microwave** **circuits** comes from the shrinkage characteristics. The shrinkage of LTCC tape is predictable within a certain margin of error but still leads to unpredictable results, especially for tight coupling structures and filters. By using this two-stage technique, the most critical structures can be made on the outer layers, avoiding the problems of shrinkage and the resulting fabrication tolerance issues. For **microwave** and millimeter-wave **circuits** this is an important improvement because the outer layers can then be used for the more critical components.

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This chapter describes the computer program, CHAIN1, written for the analysis of **microwave** **circuits** using chain matrix analysis as described in section 2 . 2 . The objective of this program was to make the application of the chain matrix analysis more versatile. In previous programs using chain matrix analysis the path structure of the circuit, in terms of cascades of 2 -port networks, always had to be defined in a very precise way in the data. In the CHAIN1 program each 2 -port network in the circuit is connected between two junctions and the networks can be included in the data at any point and in any order. Two junctions must be assigned, in the data, as the input and output ports of the circuit. Loads could be attached to any junction in the circuit but these loads are only included in the analysis if they terminate a branch arm or are connected to the input or output ports of the circuit.

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A preliminary description of this algorithm has already been presented in [13]. However, here a more comprehensive and detailed structured version of the algorithm is presented with a full performance evaluation and a comparative study with other evolutionary algorithms. In particular, this manuscript will give a detailed description on SNO and its operators in Section 2; a preliminary numerical analysis on its performances versus other well-assessed optimization procedures is reported in Section 3, followed by the results of the application of SNO in the optimization of two well known **microwave** **circuits**, namely a wide-band matching circuit and a microstrip line band pass ﬁlter, which will be reported in Section 4.

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Abstract – **Microwave** **circuits** play an important role in wireless communication systems. This paper proposes an efficient technique to design a Destructive/Defected Ground Structure (DGS) based **microwave** **circuits**. A dumbbell shaped DGS is used to design a **microwave** **circuits**. Here, first a Chebyshev type bandpass filter is designed and then a DGS is inserted. Several simulations and comparisons showed the validity of the proposed equivalent circuit model and modeling method. Also, a **microwave** directional coupler is designed and then a dumbbell shaped slotted ground plane is used under the coupled region to minimize the requirement for a narrow slot between the coupled line. The designed **microwave** coupler has a broadband performance and relaxed coupled-line spacing. Simulation result for an optimized DGS based coupler is demonstrated. Finally, a DGS based Phase shifter is designed. These phase shifter gives good characteristic results in terms of insertion loss, return loss and phase shift. Simulation results are well in agreement with theoretical one.

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A novel innovative CRLH TL unit-cell is reported in this paper. This unit-cell is designed based on the concept of WBIDC. This designed unit-cell is having wider frequency band (> 4.00 GHz) of operation as compared to the conventional IDC based unit-cell (< 3.6 GHz). Many of the CRLH TL based **microwave** **circuits** require the frequency of operation more than the 4.00 GHZ in such cases proposed novel unit-cell may be used.

The distributed nature of many **microwave** and millimeter-wave **circuits** ne- cessitates electromagnetic modeling. Thus the full application of computer- aided engineering (CAE) to these **circuits** requires the integration of electro- magnetic models of distributed structures with conventional circuit analysis. In the formative stages of the CAE of **microwave** **circuits**, ports were used in specifying the interconnectivity of networks. The utilization of ports avoided the issue of specifying reference nodes. In analysis, using matrix manipula- tions or signal flow graphs, one of the terminals of a port was used implicitly as a reference node and generally ignored in formulating the mathematical model. The connection of discrete elements is specified nodally but at the highest level of the hierarchy port-based descriptions are used. While it is possible to analyze any circuit with this arrangement it becomes increasingly difficult to specify the connections of large spatially distributed **circuits**, and also to specify and extract desired output quantities. The alternative to using port-only descriptions is to exclusively use the nodal connectivity description, the only method used in general purpose circuit simulators. The conventional nodal specification enables circuit elements to be connected in any possible combination and only one reference node (commonly called the global refer- ence node or simply ground) is used. With spatially distributed **circuits** it is possible to make illegal connections such as connecting a non-spatially dis- tributed element, say a resistor, across a spatially distributed element, e.g. a transmission line. The purpose of this section is to develop and describe the implementation of a scheme for checking the legal connections of a network with mixed spatially distributed and conventional elements.

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currently being studied for the design of tunable RF **circuits** [6]-[16]. Tunable STO characteristics can be obtained only at low temperatures thus allowing the use of high temperature superconductors (HTS) to achieve lower loss. However, since STO exhibit very little tunability at room temperature, they cannot be employed in systems operating at room temperature. BST films can overcome these difficulties. Depending on the specific composition, BST can exhibit paraelectric behavior and making it tunable at room temperature (typically 2:1 or 100% tunabilities are reported). With the recent advances in BST thin film deposition and processing, low loss tunable capacitors, filters, phase shifters and antennas requiring lower drive voltages can be fabricated.

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A mutual drawback for both the stripline and microstrip is that for a given substrate thickness, the line widths cannot be arbitrarily chosen for a certain characteristic impedance. Coplanar waveguide (CPW) of the type shown in Figure 3.2.1(c), on the other hand, offers some degree of freedom as the characteristic impedance is determined by the ratio of strip and gap width and is less dependent on substrate thickness. Therefore, by keeping an appropriate strip-to-gap ratio, different line widths can be chosen for a specific characteristic impedance [74]. As the ground of the CPW structure is in the same plane as the conducting strip, it eliminates the need for via holes during surface mounting of the **microwave** device. In addition, CPW features the lowest cross talk or interference levels from other signals among these three planar transmission lines due to the presence of the ground plane between any two adjacent lines. As a result, CPW **circuits** can be fabricated more compact than microstrip and stripline **circuits**, making it an ideal circuit structure for MIC, as well as MMIC applications.

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In this exercise, you will have the opportunity to represent a real-life inductor and capacitor by equivalent circuit models: more complicated circuit schematics that represent the “real” behavior of the circuit elements. This is an important part of the RF/**microwave** design process, as “real-life” elements contain non-idealities that influence frequency-dependent behavior. Parasitics, as these non-idealities are called, cause the behavior of a circuit element to deviate from its ideal behavior, usually at high frequencies. When the components to be used in building a design are modeled correctly, these non-idealities can be seen before the design is fabricated and necessary adjustments to produce desired circuit behavior can be made.

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As mentioned earlier in Chapter 1, investigating **microwave** properties of superconductors is important in terms of applied superconductivity, development of advanced applications of superconducting materials, as well development of scientific concepts and theories associated with high temperature superconductivity. Limited power handling capabilities of high temperature superconductors (HTS) have narrowed the number of applications of HTS **microwave** devices. For **microwave** HTS filter applications, it is necessary for the HTS filter to be able to operate with relatively high levels of **microwave** power propagating through it. However, it is known that undesirable behaviour can occur at elevated power levels. HTS filter performance can be significantly degraded when internal **microwave** power reaches certain high levels. Other HTS **microwave** devices can also exhibit significant degradation in performance when operating at desired power levels. While the negative impact of high **microwave** power on HTS devices is well documented, there is still no physical theory that explains the link between **microwave** properties and the onset of performance degradation for a given **microwave** power level.

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The basic structure on which we have tested the method was standard 50 Q microstrip transmission line. We have prepared the line by standard litho graphic techniques from a **microwave** PCB of 127 fxm dielectric thickness, the copper strip conductor was 110 //m wide with thickness 17 //m. The signal was coupled from the RF output port of the vector network analyzer, the line was terminated by a 50 load to avoid signal reflection. Figures 7.1 (a), (b) shows the signals acquired by a vertically placed antenna for two different distances of its apex from the sample - 40/im and 60//m, figure (c) shows their difference. We can observe a more narrow field image in (c) indicating the increase of the spatial resolution. The effect of resolution enhancement is even more visible on the figure 7.2 representing the signal distribution across

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28 Chapter 3 Six-Port Network Analyzer Theory It was shown in chapter 2 that if the complex ratio, b3 /b 4 , of two voltage waves emerging from a four-port network can be determined, the[r]

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The design of complex **microwave** **circuits** and systems is mandatory in several important areas for civil and military telecommunication systems, industrial and medical equipments. The conventional **microwave** design techniques are quite effective for the design of basic **microwave** active as well as passive devices [1–4], but these techniques are not able to models the interactions between the different

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In conclusion, we have realized hybrid **microwave** **circuits** made from superconductor-semiconductor NW JEs and characterized them using spectroscopy. NW **circuits** offer several advantages over traditional aluminum **circuits**. First, tuning transitions using the field effect in single NW JE devices offers an alternative to flux biasing of split-junction Al devices, with the potential to reduce on-chip dissipation by eliminating the need for mA-level currents. Second, the hybrid JEs are made exclusively from magnetic-field-compatible materials [38,39]. Magnetic- field-compatible superconductor-semiconductor NW **microwave** **circuits** will open new avenues of research. In particular, very pure solid-state electron spin ensembles (e.g., nitrogen impurities in diamond or phosphorous donors in silicon) could be field polarized to make coherent quantum memories [39,40] for hybrid quantum processors. In addition, hybrid **microwave** quantum **circuits** and the cQED architecture offer a way to study mesoscopic super- conductivity and Andreev bound states [28] in NW JEs and to read out and control Majorana bound states [41,42] in proposed demonstrations of non-Abelian exchange statistics [43–46]. Apart from improving quantum coher- ence, immediate next experiments will therefore focus on the study of these **circuits** in up to ∼0 . 5 T in-plane magnetic fields.

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Haroon Rashid, Designed in 0.18 m CMOS process technology, the simulation results show that the proposed Schmitt trigger circuit’s triggering voltage can be adjusted approximately 0.5 V to 1.2 V. The proposed design is suitable to be implemented in buffers, sub-threshold SRAMs, retinal focal plane sensors, wireless transponders and pulse width modulation **circuits**[1].

The experimental results on calculation of observability estimations on combinational MCNC benchmark **circuits** were performed. Firstly, the initial **circuits** were transformed into ones only with two-input AND gates which may have inverters in its inputs and outputs if necessary. These **circuits** were obtained by the tool ABC [11] as some kind of And-Inverter Graphs (AIGs). The experimental results are presented in Table I. Circuit is the name of an MCNC benchmark circuit, PI/PO/Lines are the number of primary inputs, outputs, and internal lines. Cut is the number of internal lines with

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This current is ________ by the resistance of the first device, the resistance of the second, and the third also, so that the _______________ to current in the circuit is the sum of th[r]

Abstract. Garbled **circuits**, a classical idea rooted in the work of Andrew Yao, have long been understood as a cryptographic technique, not a cryptographic goal. Here we cull out a primitive corresponding to this technique. We call it a garbling scheme. We provide a provable-security treatment for garbling schemes, endowing them with a versatile syntax and multiple security deﬁnitions. The most basic of these, privacy, suﬃces for two- party secure function evaluation (SFE) and private function evaluation (PFE). Starting from a PRF, we provide an eﬃcient garbling scheme achieving privacy and we analyze its concrete security. We next consider obliviousness and authenticity, properties needed for private and veriﬁable outsourcing of computation. We extend our scheme to achieve these ends. We provide highly eﬃcient blockcipher-based instantiations of both schemes. Our treatment of garbling schemes presages more eﬃcient garbling, more rigorous analyses, and more modularly designed higher-level protocols.

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