Tables for Cascaded Homogeneous Quarter-Wave Transformers (Correction)

Leo Young, the author of "Tables for Cascaded Homogeneous Quarter- Wave Transformers," which appeared on pages 233-237 in the April, 1959 issue of these Transactions, has requested that the following revisions be made in his paper.     

Optimum Quarter-Wave Transformers

The design of uniformly dispersive quarter-wave transformers is a well explored subject. Common examples are rectangular waveguide E-plane transformers, in which the a dimension is kept constant. In this paper, it is shown that the performance of conventional quarter-wave transformers of a single section can always be improved by making the middle section less dispersive than the input and output waveguides, and a formula for the optimum a dimension is given. The theory was verified experimentally. In this instance, the improved transformer measured 50 per cent more bandwidth than did the conventional one, and was 25 per cent shorter besides.     

Inhomogeneous Quarter-Wave Transformers of Two Sections

An inhomogeneous transformer is defined as one in which the guide wavelength is a function of position; for a homogeneous transformer, the guide wavelength is independent of position. A previous paper has dealt with inhomogeneous transformers of one section; the existence of an optimum design (which is never homogeneous) was demonstrated. The mathematical tools for inhomogeneous transformers of two or more sections have been presented in another paper. Our purpose here is to apply these results to the solution of the two-section inhomogeneous transformer. The maximally flat ideal transformer was solved exactly and the design equations verified by subsequent numerical analysis. An approximate procedure to improve the performance over a finite bandwidth (similar to the Tchebycheff response of homogeneous transformers) is also explained.     

General Synthesis of Quarter-Wave Impedance Transformers

This paper presents the general synthesis of a radio frequency impedance transformer of n quarter-wave steps, given an "insertion loss function" of permissible form. This procedure parallels that of Darlington for lumped constant filters by providing the connection between Collin's canonical form for the insertion loss function and Richards' demonstration that a reactance function may always be realized as a cascade of equal length impedance transformers terminated in either a short or open circuit. In particular, it is shown that insertion loss functions of the form selected by Collin are always realizable with positive characteristic impedances, and that the synthesis procedure, for maximally flat and Tchebycheff performance, involves the solution, at most, of quadratic equations. In addition, this procedure permits the proof of Collin's conjecture that, for his insertion loss function, the resulting reflection coefficients are symmetrical. Finally, closed expressions are given for the coefficients of the input impedance of a given n section transformer in terms of the n characteristic impedances and vice versa.     

Ultra-Wideband Bandpass Filters Using Quarter-Wave Short-Circuited Shunt Stubs and Quarter-Wave Series Transformers

This letter introduces a topology of a very wideband filter intended for the use in ultra-wideband 3.1-10.6 GHz applications. Basic filter configuration consists of quarter-wave short-circuited stubs and quarter-wave series transformers. To improve the out-of-band rejection, a low-pass filter is added across the symmetry plane. The proposed component is fabricated in a planar microstrip configuration; however, the topology can be easily adopted for other technologies including those based on surface micromachining. The measurements have shown an insertion loss below 0.86 dB, return loss above 14 dB, group-delay variation under 0.15 ns, and the third harmonic rejection better than 16 dB.     

Application of Quarter-Wave Transformers for Precise Measurement of Complex Microwave Conductivity of Semiconductors (Short Papers)

The utility of a quarter-wave transformer for precise measurement of complex microwave conductivity of semiconductors has been demonstrated. It has been shown for a chosen conductivity of 9 /spl Omega//spl dot/cm that the improvement in measurement accuracy is nearly by a factor of 3 over the conventional reflection measurement using a Teflon transformer.     

Cascaded Multilevel Inverter Employing Three-Phase Transformers and Single DC Input

This paper proposes an isolated cascaded multilevel inverter employing low-frequency three-phase transformers and a single dc input power source. The proposed circuit configuration can reduce a number of transformers compared with traditional three-phase multilevel inverters using single-phase transformers. It controls switching phase angles to obtain an optimal switching pattern identified with the fundamental frequency of the output voltage. Owing to this control strategy, harmonic components of the output voltage and switching losses can be diminished considerably. To verify the performance of the proposed approach, we implemented computer-aided simulations and experiments using a prototype.      

The Synthesis of Quarter-Wave Transformers, Low-Pass and Half-Wave Filters in the Sine Plane (Letters)

This letter presents a method for synthesizing quarter-wave Chebyshev transformers, low-pass and half-wave filters. The method uses sine-plane synthesis which greatly simplifies the numerical calculations and allows one to obtain good numerical accuracy using just a desk calculator. Equations for the transmission coefficient are given in a simplified form.     

Broad-Band Quarter-Wave Plates

Analytical expressions are given for the propagation constant for the two orthogonal dominant modes in a square waveguide loaded with a centered slab of dielectric. These are combined to find the differential phase shift in a loaded section. Solutions of these equations are given for polystyrene which enables one to design broad-band quarter wave plates. The problem of transforming from unloaded to loaded guide is discussed and two solutions are given and another suggested. Experimental results are given and it is found that the work in square guide carries over to circular guide almost intact. It is shown that quarter-wave plates may easily be designed to cover a normal waveguide bandwidth.     

The Quarter-Wave Transformer Prototype Circuit

A quarter-wave transformer not only changes impedance levels, but will also behave as a band-pass filter. In practice, however, band-pass filters are usually required to terminate in equal input and output impedances. They often consist of several direct-coupled cavities, which are similar to transformers whose impedance steps have been replaced by reactive obstacles. It is demonstrated how one can synthesize a quarter-wave transformer, and then "distort" it to obtain a direct coupled cavity filter with a predictable performance. This is illustrated and confirmed by numerical examples. The method is particularly convenient to use in reverse. The quarter-wave transformer prototype is easily derived for a direct-coupled cavity filter which has already been designed by another approximate method, and thus gives an independent evaluation of its performance. If necessary, the filter can then be redesigned, as illustrated in this paper.     

Low-Loss Terahertz Artificial Dielectric Birefringent Quarter-Wave Plates

We have developed anisotropically etched low-loss artificial dielectric birefringent quarter-wave plates (QWPs) for use at 1.5 and 2.8 THz. The grating period for both QWPs is 20 $mu{hbox {m}}$. We etched 46- and 30- $ mu{hbox {m}}$-deep gratings to obtain a $pi /2$ phase retardance between transverse-magnetic and transverse-electric polarization propagating through the QWPs at 1.5 and 2.8 THz, respectively. A SU8 antireflection coating is used to further improve the transmission coefficient by up to 21%. The measured results from Fourier transform infrared spectroscopy show a good agreement with designed specifications.      

Tables for Butterworth-digital-filter design

A method for constructing tables for digital-filter design is described. Filters whose transfer functions are similar to those of Butterworth analogue filters are considered.     

Current Transformers for Inverters

A design method for low frequency current transformers for inverter and motor drive applications is presented. Toroidal and E-I cores based design alternatives are studied and compared.     

基于相位调制和样品摆动的1/4波片相位延迟量测量方法

提出一种基于相位调制和样品摆动的1/4波片相位延迟量测量方法。准直激光束依次通过起偏器、相位调制器、待测1/4波片和检偏器由光电探测器所接收,光信号被转换成电信号后经过放大、滤波以进行数据处理。利用待测1/4波片的摆动可以计算得到与快轴方位角无关的归一化二次谐波分量,在无需知道1/4波片快轴方位角的情况下得到其相位延迟量。实验中对一块石英1/4波片进行了测量,实验结果与现有快轴方向确定条件下的光弹调制测量方法的测量结果一致,某一快轴方位角上多次测量的重复性为0.13°,不同快轴方位角上多次测量的再现性为0.17°。     

Specific Equations for One and Two Section Quarter-Wave Matching Networks for Stub-Resistor Loads

Given a load network consisting of a conductance in parallel with a short-circuited stub, the admittance values of optimum one and two section commensurate transmission line matching networks are derived. These values are expressed in closed form as functions of the bandwidth and ripple level. It is shown that optimum networks have nonzero reflection coefficient minima, as predicted by classical broad-band matching theory.     

Quarter-Wave Compensation of Resonant Discontinuities (Correspondence)

In designing RF transmission line components it is often necessary to place a short-circuited quarter-wavelength stub in parallel with the line or an open-circuited quarter-wavelength stub in series with the line. The stub can be broadbanded by merely changing the characteristic impedance of the line on either side of the stub for a distance of one quarter wavelength.     

Frequency Response of Quarter-Wave Coupled Reciprocal Stripline Junctions

The frequency response of quarter-wave coupled reciprocal 3-port symmetrical junctions for which the reference eigennetwork appears as a short circuit at the reference terminals is presented. The equivalent circuit of such reciprocal junctions is constructed in terms of the reciprocal parts of the split admittance eigenvalues of the ideal 3-port circulator. Since the two circuits are related, the element values selected for the matching networks are the ones which apply to an ideal circulator with an overall Chebyshev response. This is done for n=1, 2, and 3. An important conclusion of this paper is that the design of wideband circulators is closely related to the design of wideband reciprocal 3-port junctions. The paper includes experimental results obtained on a stripline device in its magnetized and demagnetized states.     

Approach for Evaluating Effects of Wall Losses on Quarter-Wave Short-Circuit Impedance Standards

The conservation of energy principle and first-order perturbation theory have been applied to obtain formulas for the physical lengths and reflection coefficient magnitudes of quarter-wave coaxial and rectangular waveguide short-circuit impedance standards. The expressions for the physical lengths ensure zero phase angle at the mating interface when wall losses are present. The method can be extended to include small dielectric and magnetic losses, and requires only knowledge of the loss-free solutions. It can also be applied to other waveguiding structures which support uncoupled modes.