General Purpose Programs for the Frequency Domain Analysis of Microwave Circuits

This paper presents a state-of-the-art review of the recent advances in computer methods for analysis and design of switched circuits in both time and frequency domains. It also presents new research results on time-domain analysis and sensitivity of switched nonlinear circuits, time- and frequency-domain statistical analysis of switched linear and nonlinear circuits, and efficient modeling and analysis of clock feedthrough and charge injection in switched linear circuits. In time-domain analysis, the modeling of switches and its effect on the simulation of switched circuits are investigated. Formulation methods for these circuits are examined. Inconsistent initial conditions arising from ideal switching are investigated and numerical methods that derive the consistent initial conditions are examined. Sampled-data simulation (SDSIM) of switched linear circuits including clocked sigma-delta modulators is investigated. SDSIM is extended to switched nonlinear circuits. Time-domain sensitivity of switched linear and nonlinear circuits is analyzed using SDSIM. Efficient time-domain statistical analysis of switched linear and nonlinear circuits is introduced, and their effectiveness is assessed using Monte Carlo simulation. Methods that compute the effect of the clock jitter of periodically switched linear (PSL) circuits are examined. Time-domain noise analysis of PSL circuits is investigated. In frequency-domain analysis, exact frequency analysis of multiphase PSL circuits is reviewed. Sensitivity analysis of these circuits is examined in detail. Adjoint network theory and its usefulness in noise and sensitivity analysis of switched linear circuits are studied. Group delay of PSL circuits is investigated briefly. Efficient modeling and analysis of clock feed-though and charge injection of PSL circuits are introduced. Distortion and sensitivity of periodically switched nonlinear circuits with mild nonlinearities are investigated. Finally, frequency-domain noise analysis of PSL circuits is examined.

As a method of evaluating the direction of arrival of conducted interference propagating along a transmission line, a measurement method using coupled transmission lines is investigated. The principle of measurement is the direction selectivity of the coupled transmission lines consisting of two parallel lines. The direction of propagation of the conductive noise is sensed from the difference of the response voltages at the two ends of the coupled transmission line. In the present experiment, a strip line with a characteristic impedance of 50 ohms made of a two-sided substrate of length 12 cm and width 3 cm is used as the coupled line. With this test transmission line, the coupling characteristics of the transmission lines are experimentally confirmed based on a homogeneous transmission line model. With a standard power supply cord as the line under test, the response voltage for the conducted electromagnetic interference generated from a small generator is measured. It is confirmed that the response voltage of the coupled line depends on the direction of propagation of the transient voltage propagating along the transmission line. Hence, it is shown that detection of the direction of propagation of the conducted interference can be carried out easily. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 1, 80(7): 23–31, 1997

With increased wire density of integrated circuits and with increased speed of signal, crosstalks due to couplings of wires and wave distortions due to impedance mismatches have become a problem. For the transient analysis of these signals, using the wave digital filter representation of the wires, simulation methods consider them as coupled transmission lines. However, the existing methods construct a digital model depending on the load of the circuits to be analyzed. This paper represents the loss‐less coupled lines of the circuit to be analyzed by equivalent circuits using ideal transformer interconnections and uncoupled transmission lines. Then its power supply and load, its ideal transformer interconnections and its uncoupled transmission lines are modeled individually by digital filter models thus representing the entire circuit with a wave digital filter. Also, digital models are presented for the cases when coupled transmission lines contain lumped parameter elements and branchings. Furthermore, it is shown that lossy symmetrical coupled lines can be represented by equivalent circuits using ideal transformer interconnections and lossy uncoupled lines, and their wave digital filter representations are given. Finally, a wave digital filter representation of a network containing lossy symmetrical coupled lines is given. It is used as a model for wirings on a GaAs substrate, and examples of its transient response analyses are given.

A computer program is described that performs a Volterra-series analysis of a weakly nonlinear microwave circuit having an arbitrary topology. The program uses the method of nonlinear currents and a nodal formulation. In this approach, each nonlinear circuit element is described as a linear element in parallel with a set of current sources; each current source represents a single order (greater than one) of the mixing products, and its current is a nonlinear function of the node-voltage components at lower-order mixing frequencies. The weakly nonlinear circuit is reduced to a linear circuit, which contains the linear elements and the linear parts of the nonlinear elements, and a set of excitation sources. The program is intended primarily for use in the design of microwave circuits; its catalog of circuit elements includes the distributed elements necessary for such work. Because the program formulates and solves the circuit equations numerically, the user need not simplify either the circuit or the model of the solid-state device, or make any of the other common simplifying assumptions. >

This book is concerned with circuit simulation using National Instruments Multisim. It focuses on the use and comprehension of the working techniques for electrical and electronic circuit simulation. The first chapters are devoted to basic circuit analysis. It starts by describing in detail how to perform a DC analysis using only resistors and independent and controlled sources. Then, it introduces capacitors and inductors to make a transient analysis. In the case of transient analysis, it is possible to have an initial condition either in the capacitor voltage or in the inductor current, or both. Fourier analysis is discussed in the context of transient analysis. Next, we make a treatment of AC analysis to simulate the frequency response of a circuit. Then, we introduce diodes, transistors, and circuits composed by them and perform DC, transient, and AC analyses. The book ends with simulation of digital circuits. A practical approach is followed through the chapters, using step-by-step examples to introduce new Multisim circuit elements, tools, analyses, and virtual instruments for measurement. The examples are clearly commented and illustrated. The different tools available on Multisim are used when appropriate so readers learn which analyses are available to them. This is part of the learning outcomes that should result after each set of end-of-chapter exercises is worked out. Table of Contents: Introduction to Circuit Simulation / Resistive Circuits / Time Domain Analysis -- Transient Analysis / Frequency Domain Analysis -- AC Analysis / Semiconductor Devices / Digital Circuits

Introduction to Circuit Analysis and Design

Coupling capacitors or DC blocks are essential tuning elements in RF/microwave applications. Their role becomes imperative in cascade amplifiers to isolate drain voltages of preceding MMIC from the gate voltage of the following chip where both RF and DC signals are carried through the same line. The purpose of this study is to explain the benefits of a newly designed thin film coupling capacitor called as transmission line metal-insulator-metal capacitor (TL MIM Cap), which serves as a DC block capacitor in microwave circuits. This novel structure provides a unique solution, which cannot be achieved with traditional single layer ceramic capacitor (SLC) structure. It combines two discrete circuit elements into one: “Microstrip transmission line of required length and width” with a “serially attached coupling capacitor”. Thin film capacitive layers ranged from 0.5pF to 50pF, which are typically needed for microwave frequencies within 1–40 GHz, constructed and embedded into 50 Ohm impedance transmission lines in series. Substrates like quartz, glass, or alumina can be used to minimize losses and to achieve higher RF/microwave performance. We used copper traces as conductive layers for optimal conductivity. After manufacturing TL MIM Caps, we tested several capacitance values for 1pF, 5pF, 15pF and 30pF corresponding to a wide frequency range. The RF tests we performed showed that TL MIM Caps exhibited a minimum of 20dB return loss and a maximum of 0.3 dB insertion loss at 1–40GHz range. We also found our technique comes with some workmanship advantages in high frequency circuit assembly as follows: Traditional coupling capacitor attachment with silver epoxy on top of a microstrip transmission line is a manual operation, which requires well trained and experienced technicians. In contrast, using the TL MIM Caps in our high frequency hybrid modules, we found that the process caused errors were eliminated such as the micro short circuit effect caused by conductive epoxy. Therefore we improved yield in assembly stage of the circuits. In addition, improvements are observed in production processes such as less consumption of adhesives (epoxy), no technician failure caused wastes, elimination of extra curing process to attach capacitors, no short circuit inspection, rework, or re-cure operations to fix assembly errors. Last but not least, blocking capacitors are embedded into the microstrip transmission lines in TL MIM Caps. This ensures that having the lowest possible impedance since very short wire bond exists from the bond pad of the TL MIM Cap to the adjacent circuit element.

Coupled transmission lines are experimentally characterised by using 4-port s-parameter measurements in the broad frequency band (up to more than the 20 GHz). The test patterns are designed and fabricated by using a BGA package process. Symmetrical coupled transmission lines are decoupled into two eigen modes that can be readily determined from the measured s-parameters. Then signal transient and crosstalk noise are directly determined from the measured s-parameters. It is shown that not only are the transmission line parameters frequency-variant, but also the frequency-variant effects and non-ideal characteristics of transmission lines have substantial effect on the signal transients and crosstalk noises.

This paper describes a computational model based on lumped elements for the mutual coupling between phases in transmission lines without the explicit use of modal transformation matrices. The self and mutual parameters and the coupling between phases are modeled using modal transformation techniques. The modal representation is developed from the intrinsic consideration of the modal transformation matrix and the resulting system of time-domain differential equations is described as state equations. Thus, a detailed profile ofthe currents and the voltages through the line can be easily calculated using numerical or analytical integration methods. However, the original contribution of the article is the proposal of a time-domain model without the successive phase/mode transformations and a practical implementation based on conventional electrical circuits, without the use of electromagnetic theory to model the coupling between phases.

To simulate or design a reasonably large system, fast and simple models are necessary. To verify the design versus the specifications, more detailed (and costly) calculations can be performed and final adjustments made. In wave propagation problems, circuit analogs provide a powerful, yet simple, means of computing the desired response of the system, such as reflection or transmission coefficients. The reason circuit analog models are good for wave propagation problems, is that they are exact for one-dimensional wave propagation, regardless of whether we consider acoustic or electromagnetic waves. Typically, wave propagation through homogeneous media is modeled as a transmission line with propagation constant β and characteristic impedance Z, whereas obstacles such as thin sheets are modeled as lumped elements. If the sheets are lossless, the circuit models contain only reactive elements such as capacitors and inductors. Modeling complex wave propagation problems with circuit analogs was to a large extent developed in conjunction with the development of radar technology during the Second World War. Many of the results from this very productive era are collected in the Radiation Laboratory Series and related literature, in particular (Collin, 1991; 1992; Marcuvitz, 1951; Schwinger & Saxon, 1968). Further development has been provided by research on frequency selective structures (Munk, 2000; 2003). In recent years, the circuit analogs have even been used in an inverse fashion: by observing that wave propagation through a material with negative refractive index could be modeled as a transmission line with distributed series capacitance and shunt inductance, i.e., the dual of the standard transmission line, the most successful realization of negative refractive index material is actually made by synthesizing this kind of transmission line using lumped elements (Caloz & Itoh, 2004; Eleftheriades et al., 2002). This chapter is organized as follows. In Section 2 we show that propagation of electromagnetic waves in any material, regardless how complicated, boils down to an eigenvalue problem which can be solved analytically for isotropic media, and numerically for arbitrary media. From this eigenvalue problem, the propagation constant and characteristic impedance can be derived, which generates a transmission line model. In Section 3, we show how sheets with or without periodic patterns can be modeled as lumped elements connected by transmission lines representing propagation in the surrounding medium. The lumped elements can be given a firm definition and physical interpretation in the low frequency limit, and in Section 4 we show how these low frequency properties

New types of planar transmission lines employing multilayer structures are proposed for possible applications in microwave and millimeter-wave integrated circuits. Detailed investigations are presented through numerical results calculated using the spectral domain technique. The newly proposed transmission lines have many attractive features such as a large impedance range, flexibility and ability to realize complicated, densely packed integrated circuits, as well as miniaturization through the use of thin dielectric layers. Additionally, they possess all of the inherent advantages of the CPW and microstrip line. Their use in microwave circuits is exemplified through a low-pass filter realized using the new slot-coplanar lines with less than 0.5-dB insertion loss and better than 20-dB return loss. The filter's measured and calculated performances also agree well. >

An overview of standard macromodeling techniques (i.e., employ poles but no phase shifts) for transient simulation of high-speed interconnects is first presented. Then, the limitations of these standard macromodeling techniques (e.g., high model order and slow convergence) are discussed. In order to overcome these limitations, generalized method of characteristics (MoC) techniques include the physical phenomenology of phase shift (time delay) in addition to the system poles, thereby making it possible to model single and coupled transmission lines using far fewer terms than when standard macromodeling techniques are employed. Since MoC techniques incorporate the time delay into the model, causality is also guaranteed. In this paper, the MoC idea is extended by developing a hybrid phase-pole macromodel (HPPM) for the modeling of more complex interconnects with embedded discontinuities. Unlike other generalized MoC techniques that have only been applied to single and coupled transmission lines, the HPPM macromodel can be applied to larger portions of the system that contain multiple cascaded transmission lines and discontinuities. The HPPM parameters can be extracted from either measured or simulated transient data. Comparisons between a standard macromodel and the HPPM show that the HPPM has significant advantages in terms of reduced macromodel orders.

The work presented here introduces lumped elements to an iterative method based on the wave concept combined with the two-dimentional fast Fourrier transformation algorithm known as fast modal transformation (FMT). We extend this method to the analysis of microwave-distributed circuits containing passive or active, linear or nonlinear lumped elements which are characterized by their surface impedance as defined in this article. Simulation results of varactor-tuned filter and phase-shifter circuit examples are compared with the measurement results. Good agreement between simulated and experimental results validates the use of the iterative method for the analysis of planar circuits, including lumped elements. © 2003 Wiley Periodicals, Inc. Int J RF and Microwave CAE 13: 269–275, 2003.

Transmission line port de-embedding is critical in characterization and modeling for high-speed digital systems. De-embedding technique for single-ended transmission lines has been developed and widely used. However, few de-embedding techniques for coupled transmission lines have been reported in the literature. In this paper, a de-embedding technique for coupled transmission lines using a single-ended TRL (Thru-Reflect-Line) calibration pattern is proposed. It is based on directly obtaining VNA (Vector Network Analyzer) error correction data from measurement and post data processing. As accurate de-embedding is related to the equipments used in the measurement, the proposed technique is verified on two different VNAs with different architectures including a three-sampler VNA and a four-sampler VNA. Good agreement of de-embedded mixed-mode S-parameters has been achieved on both VNAs.

In this paper, -15 dB branch-line hybrid was realized. In the case of-15 dB coupling power, the characteristic impedances of transmission lines were 49.20 Omega and 276.689 Omega and it was discussed to realize the high characteristic impedance of 276.689 Omega using coupled transmission lines. Using the method suggested, the problem how to realize the high characteristic impedance of 90deg transmission lines will be solved.