Equivalent representation of broad-band transmission-line transformer with vector impedances

A method of analyzing broad-band Transmission-line transformers from their open- and short-circuit vector impedances is presented. From a set of open- and short-circuit impedance measurements, the input impedance and insertion loss of the transformer when terminated in any arbitrary load impedance are calculated directly.     

Tapered transmission line computer program using Collin's derivation

Collin's synthesis of the equal ripple transmission line is shown to be computationally identical with Klopfenstein's synthesis. A simple computer program for computing impedance versus length of a tapered line is given, based on Collin's work.     

Series-parallel RLC synthesis without minimisation for a class of biquadratic impedances

A straightforward series-parallel procedure is derived for the transformerless realisation of biquadratic impedances having double zeros and arbitrary, possibly complex, poles; or vice versa. The synthesis avoids the tedious task of previous minimisation, and the appropriate surplus factor is expressed as a simple function of the coefficients of the given biquadratic form.     

Transient analysis of nonuniform, high-pass transmission lines

The transient behavior of nonuniform transmission lines is studied by investigating the step response of a cascaded multiple-section line. The first arriving wave and the transition ripple at the load end are examined in detail. It is found that the characteristic impedances necessary for obtaining the maximum first arriving wave are the same as those of the conventional multiple-section, quarter-wave transformer. The discrete characteristic impedances of the multiple-section line are then extended to a continuously varied impedance function of a tapered line. The high-pass characteristic of the tapered nonuniform line is verified with techniques in the frequency domain     

A Technique for Determination of Filter Insertion Loss as a Function of Arbitrary Generator and Load Impedances

Insertion loss is derived in terms of generator impedance, load impedance, and filter open-circuit and short-circuit impedances. This expression contains a difference term which places great weight on the accuracy with which filter impedances are measured. It is shown that the use of this difference term can be avoided by introducing the filter insertion loss in a circuit with known generator and load impedances. The resulting exact expression contains terms which are easily measurable with sufficient accuracy to provide reliable insertionloss values for the filter for any combination of generator and load impedances. Also shown is a simplified approximate expression for insertion loss which is applicable in a filter attenuation band. A discussion of experimental verification of the expressions is followed by curves showing application of the approximate insertion-loss expression to a particular filter.     

Design of impedance transformers by the method of least squares

The method of least squares is applied to the theory of small reflections of transmission lines to develop numerical algorithms for the design of stepline and tapered line impedance transformers to match two impedances over a frequency band. The transformer characteristic impedance function is expanded by polynomials, pulse functions, approximate operators, and piecewise linear functions to construct an error function for the input reflection coefficient which, after minimization, gives the line impedance and length. The computer programs could be used to design a transformer under the specified conditions and then to optimize the design under the constraints of a problem     

Impedance Transformations For The Generalized Reflection Modulator

A procedure is given for obtaining the impedance transformer which will produce a prescribed pair of phasor reflection coefficients by transformation from a given pair of impedance states terminating the transformer. The transformer may be used in a general two-state reflection modulator: as a phase shifter with phase change at constant amplitude or as an amplitude modulator with level shift at constant or variable phase. The condition governing the reflection coefficients available from a given pair of impedance states is given. Examples and limitations are discussed.     

Exact Design of Stepped-Impedance Transformers (Short Papers)

The exact solutions of the design of stepped-impedance transformers presented until now have been tedious and subject to computational error. We present here an exact synthesis procedure which requires less effort than other exact procedures. In addition, two recurrence formulas are given for determining the characteristic impedances of each section. The coefficients so obtained can be compared to eliminate computational errors.     

Insertion loss concepts

The term "insertion loss" has become such a popular one and is applied to so many different concepts that it is becoming unsuitable for precise use. Certain other concepts connected with insertion loss such as attenuation and mismatch loss, are in need of clarification. A logical set of definitions and equations are presented as a suggested approach to more precise terminology. The effect of complex characteristic impedance on these equations is given in an Appendix. Specific suggestions are given for changes in the usage of terms, which if acceptable and adopted would improve the situation.     

Parallel Wire Susceptibility Testing for Signal Lines

A technique is presented which can be utilized to establish a standardized procedure for performing conducted susceptibility testing on signal lines at the component and/or the subsystem level. Typical military specifications require that the test function be injected to the test lines via a susceptibility transformer, a coupling capacitor, or a standardized network, such as the line stabilization network (LSN). Although these methods may be adequate for testing of power line susceptibility, they present several disadvantages when utilized in signal lines, such as impedance loading, the requirement for physical insertion, and proximity to the load. These disadvantages become more pronounced at RF where the signal developed across the input of the test specimen may be considerably lower than the signal injected at the physical insertion point. A technique that overcomes these deficiencies utilizes a coupling jig that 1) does not require a physical connection, and 2) provides a known coupling across the input impedance of the package being tested-thus simulating, in a very realistic manner, interference coupling as it may occur in a system. A general expression for coupling prediction and a computer solution for various values of load impedances are presented.     

Characterization of On-Chip Transformer Using Microwave Technique

The figure-of-merit of an on-chip transformer is investigated by using a power gain approach in this paper. Adopting a microwave viewpoint, contrary to the lumped-circuit concept, to characterize the on-chip transformer, the transfer power gain between primary and secondary terminals is plotted in the Smith chart by changing the load impedances. Therefore, the peak value of power gain is found at a specific load impedance. To discuss the power loss of two transformers with different metal widths, the device layouts are carefully designed to maintain identical self- and mutual inductances in the transformers' coils. Results show that impedance matching plays a key role in improving the power gain of an on-chip transformer.     

Synthetic Transmission-Line Impedance Transformers (Correspondence)

Somlo has presented a convenient procedure for obtaining the characteristic impedance and length of a single section of lossless transmission line to match two impedances. One impedance and the conjugate of the other are plotted on a circular transmission-line chart, i.e., Smith or Carter chart. A circle is drawn through the two points with its center on the X =0 axis. If the circle does not lie entirely within the R =0 circle, the two impedances cannot be matched with a single section of lossless transmission line with real characteristic impedance. However, if one does not require that the transmission line have a real characteristic impedance, it can be synthesized by a symmetrical T or /spl pi/ network consisting of either lossless inductances or capacitances.     

A Rigorous Solution for Dispersive Microstrip

Closed-form solutions are presented for the frequency-dependent characteristic impedance of microstrip as defined by the ratio of the electromagnetic power to the square of the electric current. The analysis uses the rigorous spectral-domain approach based on the charge-current formulation. Analytical expressions for the impedance solutions show that the frequency dispersion occurring in microstrip is characterized in terms of three different impedances. The characteristic impedance of a TEM line given in the limit as the frequency decreases is derived from one of these impedances, and the other two are involved in expressing the nature of dispersion to vanish in the limit. Conversely, as the frequency increases, these dispersive parts grow rapidly. Some comments are given in conjunction with previous works.     

The Design of Coupled Microstrip Lines

Although graphical results and formulas are available for the design of microstrip couplers, the design procedure is hampered because even- and odd-mode impedances are always expressed in terms of the physical geometry. In practice the designer obtains these impedances and then requires to know the geometry given by them. A new design procedure for coupled parallel microstrip lines is therefore presented. The technique enables the geometry of the coupled lines to be obtained directly from the required even- and odd-mode impedances and uses single microstrip-line geometry as an intermediate step. The results are presented in graphical form using only two universal families of curves. Results are also presented in the form of simple formulas for design programs and also comparisons with practical results are made.     

Analysis of 0° hybrid junction constructed with broad-band transmission-line transformer

A 0° broad-band hybrid constructed with a twisted wire RF transmission-line transformer is analyzed. Simple expressions for isolation, insertion loss, input impedance of various ports, phase unbalance, and amplitude unbalance of the hybrid are derived from the transformer open- and short-circuit impedance parameters and are verified experimentally.     

A New Type of VF Repeater for Two-Wire Transmission Loops

Power loss at voice frequencies in two-wire telephone lines is presently overcome by employing electronic repeaters which produce bidirectional amplification without undue interaction between the outgoing and incoming paths. This isolation between the directional gain elements is achieved by employing balanced transformer windings or negative impedance transformations. Both methods rely heavily on complex line matching circuits to minimize the chance of instability or "singing." This paper describes a simple repeater that achieves bidirectional amplification while using conventional 1:1 line transformers. The obtainable return loss against fixed terminal impedances is only limited by the quality of these transformers. The new device reproduces the action of a hybrid transformer using very simple electronic circuitry and has a potentially wide application both in two-wire systems and in two to four wire conversions.     

Optimum design of a wideband planar N-way fork power divider with arbitrary power division and input-to-output impedance matching

An effective design procedure based on method of least squares is proposed for multi-section and multi-output fork power divider/combiner with arbitrary power division ratios among its outputs in a specified frequency bandwidth together with impedance matching among its arbitrary source/load impedances. Transmission and scattering matrices are obtained for its equivalent circuit. An error function is constructed based on design specifications on its output power division ratios, isolations among output ports, return losses at its input and output ports and source/load impedances in a desired frequency bandwidth. The design procedure is fully developed, which determines the widths and lengths of microstrip line sections and resistor values. A design example is described for unequal power division ratio and unequal input/output impedances. A 3-section and 3-output fork power divider is designed for equal power division and load/source impedances for 2–12 GHz band. It is fabricated and measured. Variations of its transmission coefficients are less than 0.5 dB, isolations at its outputs are better than −15 dB and reflection coefficients at its ports are better than −10 dB. Excellent agreement is observed among the results of the proposed design procedure, full wave computer software and measurement data.     

Synthesis of Reduced Equivalent Circuits for Transmission Lines

This paper presents a method for generating lumped models for symmetrical transmission-line two-ports. These models consist of an ideal transformer and frequency-domain approximations for two physical driving-point impedances. The lumped element values are obtained directly from the distributed parameters or propagation constant and characteristic impedance. The method is applied to dispersive transmission lines, skin effect and waveguides. It is shown that the equivalent circuit is superior in accuracy and number of elements compared to spatial discretizations like ladder approximation.     

宽带Wilkinson 功分器综合公式的缺陷与改进

首先介绍了3 种宽带Wilkinson 功分器的综合方法,重点阐述了最为常用的Cohn 的设计方法,并指出 随着功分器节数的不断增加,在利用Cohn 的设计公式计算隔离电阻阻值时会产生负数的问题。为此,通过引入一 个调整参数改进Cohn 的设计公式,实现了节数更多情况下隔离电阻阻值的准确计算。在计算功分器各级传输线特 性阻抗的过程中,提出了一种基于MATLAB 程序的多项式化简方法,实现了任意带宽的切比雪夫阻抗变换器参数的 快速计算。此外,还给出了一个8 级到15 级的功分器设计参数表格,作为对Cohn 给出的设计表格的扩展。最后,利 用改进后的设计公式,设计了一个1 ~15GHz 的宽带Wilkinson 功分器。仿真和测试结果证明了这种方法的有效性。     

EMI电源滤波器的插入损耗分析

在一般EMI滤波器的共模和差模等效电路的基础上,分析了源阻抗和负载阻抗对滤波器插入损耗的影响.提出了共模插入损耗和差模插入损耗的计算方法,推导了滤波器插入损耗与阻抗关系的表达式,并且对这一关系作了仿真分析,仿真结果验证了理论计算和分析的正确性.