A logarithmic reflection chart for presentation of antenna impedance

A logarithmic chart is proposed to offer some advantages over the familiar hemisphere chart of Carter and Smith. On log-log coordinates, the scales are the voltage standing-wave ratio (VSWR), respectively, of impedance variation with zero angle and of angle variation with constant impedance. A locus of constant reflection or VSWR then has two equal diameters but departs from a circle by equal flattening in all quadrants. A locus of impedance variation with frequency has the same shape for any reference value of impedance. The log chart is unbounded so it avoids the crowding near the rim which occurs with extreme values on the hemisphere chart. It is especially useful in presenting the impedance of a small antenna and an associated wide-band matching network.     

Step Response of Lossless Nonuniform Transmission Lines with Power-Law Characteristic Impedance Function (Short Paper)

The step-response waveform of the Iossless nonuniform transmission line possessing a characteristic impedance function Z/sub c/(x)= Z/sub 0/(1 + eta x)/sup 2n/, n = 0,1,2,..., is deduced. The simple and closed-form solutions should be useful for pulse transient analysis involving nonuniform transmission lines.     

Impedance Matching (Correspondence)

Matching an impedance to a transmission line by the use of a cascaded section of line is a well-known process. However, the range of terminating impedance that can be matched by this method, I believe, is not so well-known. Consider a lossless line of characteristic impedance R/sub0/ to which is to be matched an arbitrary impedance /bar Z/ = R + jX by means of another lossless line of lentgh d and characteristic impedance R/sub 1/ cascaded between the first line and the load as shown schematically in Fig. 1. The problem is to determine for what range of values of /bar Z/ a match can be thus obtained for any values of R/sub 1/, and d.     

Quasi-Static Characteristics of Microstrip on an Anisotropic Sapphire Substrate

The well-defined and repeatable electrical properties of single-crystal sapphire make it an attractive substrate material for microstrip, but its dielectric anisotropy constitutes an important design complication. This paper describes investigations into the quasi-static characteristics of single microstrip lines on sapphire substrates cut with a specified orientation. To account for anisotropy, a new permittivity parameter epsilon/sub req/ is introduced, which is a function of the Iinewidth to substrate-height ratio W/h. The variation of epsilon/sub req/ with W/h is derived by finite-difference methods. Universal curves for microstrip on correctly orientated sapphire are presented, showing 1) epsilon/sub req/, 2) the low-frequency limit of effective microstrip permittivity epsilon/sub e0/, and 3) the characteristic impedance of the line Z/sub 0/, all as functions of W/h.     

A fast MoM calculation technique using sinusoidal basis and testing functions for a wire on a dielectric substrate and its application to meander loop and grid array antennas

The input impedance matrix element of the method of moments (MoM) for an arbitrarily shaped wire antenna printed on a dielectric material Z/sub m,n/ is formulated to be composed of three terms Z/sup /spl psi/s//sub m,n/, Z/sup /spl psi///sub m,n/, and /spl Delta/Z/sub m,n/ involving single-, double-, and triple-integral calculations, respectively. The MoM based on the Z/sub m,n/ formulated in this paper (new MoM) is applied to two antennas-a meander loop antenna and a grid array antenna-as well as a simple loop used as a reference antenna. The computation time to obtain the current distribution of each antenna by the new MoM technique is compared with the time required for the conventional MoM, which has an impedance matrix element composed of four terms, all involving triple-integral calculations. It is revealed that the new MoM drastically reduces the computation time: for example, by a factor of 937 for the grid array antenna. In addition, the radiation characteristics of these two antennas are discussed. It is found that a reduced-size meander loop (62% smaller than the simple loop reference) has a radiation pattern similar to the simple loop reference. It is also found that the grid array has an axial beam radiation pattern without side lobes in the principal planes.     

Reflection Charts Relating to Impedance Matching

A reflection chart is some grid of coordinates on which to plot an impedance locus over a frequency range. Taking as a reference a constant real impedance, one may construct contours of the reflection coefficient (or the related VSWR, reflection loss, etc.). The reference may be the wave impedance of a transmission line. This may be a line connecting radio equipment with an antenna or it may be a standard line used in measuring the impedance. The reflection chart in widest use is the so-called "Smith Chart" proposed by Philip H. Smith in 1939. It is one form of the hemisphere chart, which was proposed, also in 1939, by Philip S. Carter. Its properties, uses are described. It has some limitations. A reference value must be assigned, after which the shape of a locus depends on this value. Also, a locus is crowded toward the rim of the chart. A logarithmic reflection chart has recently been proposed by the author, which overcomes these limitations but loses some desirable features of the hemisphere chart.     

Power Waves and the Scattering Matrix

This paper discusses the physical meaning and prop-erties of the waves defined by [Equation], [Equation] where V/sub i/, and Z/sub i/, are the voltage at and the current flowing into the ith port of a junction and Z/sub i/, is the impedance of the circuit connected to the ith port. The square of the magnitude of these waves is directly related to the exchangeable power of a source and the reflected power. For this reason, in this paper, they are called the power waves. For certain applications where the power relations are of main concern, the power waves are more suitable quantities than the conventional traveling waves. The lossless and reciprocal conditions as well as the frequency characteristics of the scattering matrix are presented. Then, the formula is given for a new scattering matrix when the Z/sub i/'s are changed. As an application, the condition under which an amplifier can be matched simultaneously at both input and output ports as well as the condition for the network to be unconditionally stable are given in terms of the scattering matrix components. Also a brief comparison is made between the traveling waves and the power waves.     

The Phase Shift Through Symmetrical 3-Port Circulators (Short Papers)

Simple approximate formulas are derived for the phase shift through matched circulators---with and without transformer coupling---using expressions for the eigenadmittances Y/sub 0/, Y/sub -1/, and Y/sub 1/ which have recently been proposed. These formulas allow one to predict the phase shift from measurements of the VSWR in one case and from a knowledge of the transformer admittance Y in the second. They have been confirmed experimentally for strip-Iine circulators and indicate that in this respect circulators behave like electrically long transmission devices.     

Broad-Band Coupling to High-Q Resonant Loads

Broad-band coupling between a resistive source and a resonant load is considered for coupling networks consisting of a uniform transmission line of impedance Z/sub I/ and length equal to a quarter wavelength at the load resonant frequency. An approximate analysis is used to show that either maximally flat or ripple insertion loss frequency response can be obtained by proper choice of Z/sub I/, and the 3-dB bandwidth obtained in either case is always greater than 1/Q. Depending on the ratio of load and source resistances, the bandwidth may be greater than 1 octave. Network design curves for maximally flat operation with a variety of load parameters are computed without approximation. The design of lumped element approximations for the transmission line network is also described.     

A dual-frequency Wilkinson power divider: for a frequency and its first harmonic

A Wilkinson power divider operating not only at one frequency f/sub 0/, but also at its first harmonic 2f/sub 0/ is presented. This power divider consists of two branches of impedance transformer, each of which consists of two sections of 1/6-wave transmission-line with different characteristic impedance. The two outputs are connected through a resistor, an inductor, and a capacitor. All the features of a conventional Wilkinson power divider, such as an equal power split, impedance matching at all ports, and a good isolation between the two output ports, can be fulfilled at f/sub 0/ and 2f/sub 0/, simultaneously.     

Broadband 180/spl deg/ bit phase shifter using a /spl lambda//2 coupled line and parallel /spl lambda//8 stubs

In this paper, a broadband 180/spl deg/ bit phase shifter using a new switched-network was presented. The new network is composed of a /spl lambda//2 coupled line and parallel /spl lambda//8 open and short stubs, which are shunted at the edge points of a coupled line, respectively. According to a desired phase shift, it provides a controllable phase dispersive characteristic by the proper determination of Z/sub m/,Z/sub s/, and R values. The 180/spl deg/ bit phase shifter operated at 3 GHz was fabricated and experimented using design graphs which provide the required Z/sub m/,Z/sub s/ values, and I/O match and phase bandwidths. The experimental performances showed broadband characteristics.     

Scattering Coefficients for Wall Impedance Changes in Waveguides

The Wiener-Hopf tectilque is used to obtain an exact solution to a two-dimensional scattering problem. In the problem solved, an incident TE/sub 10/ mode, traveling from z= -/spl infin/ in the positive z direction, is confined by infinite bounding planes; these planes have infinite conductivity for z<0 and an impedance Z/sub 1/, for z>0. The scattering from the junction at z=0 gives rise to reflection and transmission coefficients that are exactly determined. An approximate solution for the reflection coefficients is also given when the TE/sub 10/ mode is incident from the opposite direction. Finally, a table is presented which lists some transmission and reflection coefficients for rectangular and circular waveguides with discontinuities in the wall impedances.     

An analysis of base bias current effect on SiGe HBTs

The anomalous dip in scattering parameter S/sub 11/ of SiGe heterojunction bipolar transistors (HBTs) is explained quantitatively for the first time. Our results show that for SiGe HBTs, the input impedance can be represented by a "shifted" series RC circuit at low frequencies and a "shifted" parallel RC circuit at high frequencies very accurately. The appearance of the anomalous dip of S/sub 11/ in a Smith chart is caused by this inherent ambivalent characteristic of the input impedance. In addition, it is found that under constant collector-emitter voltage (V/sub CE/), an increase of base current (which corresponds to a decrease of base-emitter resistance (r/sub /spl pi//) and an increase of transconductance (g/sub m/)) enhances the anomalous dip, which can be explained by our proposed theory.     

磁控管雷基图快速自动测绘技术

本文讨论微波磁控管负载特性曲线即雷基图的快速自动测绘技术。文中提出一种全新的测试原理与方案来实现微波负载阻抗的自动扫描，同时采用了预先设置功率门和频率门的方法实时采集测试数据，使这些数据在等值线生成过程中的利用率达到百分之百，整个测试时间小于８ｍｉｎ。     

The Intrinsic Noise Figure of the MESFET Distributed Amplifier

This paper calculates the intrinsic noise figure of the MESFET distributed amplifier assuming, for simplicity, only the Van der Ziel gate and drain noise sources, and produces an expression for the noise figure of a distributed amplifier containing n identical devices. For large gain and Iarge n, a simple expression exists for the product nZ/sub pi g/, where Z/sub pi g/ is the pi-characteristic impedance of the gate line, which minimizes the overall noise figure of the amplifier. This approximate expression is compared with the corresponding expression for a resonant ampfifier using the same MESFET with the same noise sources and with the optimum source impedance for minimum noise figure. Although the resonant amplifier has a slightly lower noise figure, the need to use a circulator to remove the mismatch associated with the optimum source impedance removes this slight advantage.     

MSTRIP (Parameters of Microstrip) (Computer Program Descriptions)

This program calculates the characteristic impedance, phase velocity, and effective dielectric constant of single or coupled microstrip lines. Parameters to be specified by the user are as follows: range of W/H/sub 1/, S/H/sub 1/, substrate dielectric constant, single or coupled lines with or without an upper ground plane.     

A Logarithmic Transmission Line Chart

A chart is presented which relates the real and imaginary components of the impedanceat any position along a transmission line to the magnitude and location of the standing wave. In the present chart the ordinate is R/Z/sub 0/ plotted logarithmically and the abscissa is a function of X/R. Thus a change in the reference impedance becomes a simple vertical translation of any point. An auxiliary chart permits the direct determination of the length and impedance of transmission line required to match a given impedance.     

Microstrip stepped impedance resonator bandpass filter with an extended optimal rejection bandwidth

Bandpass filters with an optimal rejection bandwidth are designed using parallel-coupled stepped impedance resonators (SIRs). The fundamental (f/sub o/) and higher order resonant harmonics of an SIR are analyzed against the length ratio of the high-Z and low-Z segments. It is found that an optimal length ratio can be obtained for each high-Z to low-Z impedance ratio to maximize the upper rejection bandwidth. A tapped-line input/output structure is exploited to create two extra transmission zeros in the stopband. The singly loaded Q(Q/sub si/) of a tapped SIR is derived. With the aid of Q/sub si/, the two zeros can be independently tuned over a wide frequency range. When the positions of the two zeros are purposely located at the two leading higher order harmonics, the upper rejection band can be greatly extended. Chebyshev bandpass filters with spurious resonances up to 4.4f/sub o/, 6.5f/sub o/, and 8.2f/sub o/ are fabricated and measured to demonstrate the idea.     

Longitudinal Section Mode Analysis of Dielectrically Loaded Rectangular Waveguides with Application to Phase Shifter Design

The structure consisting of an E-plane dielectric slab partially filling a rectangular waveguide is examined with attention on those higher order mode propagation characteristics that are relevant to the design of nonreciprocal remanence ferrite phase shifters. The validity of the model is established by introducing experimental comparison in the form of VSWR measurements for both pure dielectric loading and an actual composite ferrite phase shifter. Emphasis is placed on the consideration of possible mechanisms for the elimination of LSE/sub 11/, LSM/sub 11/, and LSE/sub 12/ modes, since certainly the first, most probably the second, and quite possibly the third will propagate in a practical device. Experimental verification of theoretical predictions is established and phaser design guidelines are drawn. Some additional topics, such as slabcorner chamfering and the effect of the switching wire, are included for completeness.