Operation of Tracking Circulators

The classic two circulation conditions of a junction circulator obtained by setting the imaginary part of the complex gyrator impedance to zero and evaluating the real part does not ensure that the in-phase and counter-rotating eigennetworks are separately idealized. This paper indicates that the physical and magnetic variables of the tracking circulator described by Wu and Rosenbaum coincides with these special boundary conditions. Specifically, the gyrator resistance for this circulator may be calculated at the frequency for which the in-phase eigennetwork exhibits a short-circuit boundary condtion (using the n=0 and +-3 modes) and the counter-rotating eigennetwork modes exhibit complex conjugate immittances (using the n= -1, +2 and n = +1, -2 modes). The paper includes a new formulation for the Q-factor of this type of circulator which is used to calculate that of the tracking circulator.     

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.     

Complex Gyrator Circuits of Planar Circulators Using Higher Order Modes in a Disk Resonator

Tire use of resonators or waveguides utilizing higher order modes is often an attractive solution to the design of millimeter microwave networks. This paper investigates the complex gyrator circuit of a planar junction circulator employing higher order solntions in a disk resonator. The first such solution displays many of the features of weakly magnetized junctions using the dominant mode in a disk resonator, but its loaded Q-factor is incompatible with the realization of quarter-wave coupled devices. Although the second one exhibits more useful equivalent circuits, it requires a relatively large magnetization, which is not altogether practical at millimeter frequencies. A circulator configuration that has a frequency response akin to that of a quarter-wave coupled one is one where the in-phase eigennetwork is degenerate with those of the demagnetized counter-rotating eigennetworks. The degeneracy between the in-phase limit, TM/sub 2, 0, -2/ and the second-order counter-rotating limit, TM/sub 1, 1, -2/ modes, in an oversized irregular hexagonal resonator, is used in this paper to construct such a device.     

The Synthesis of Symmetrical Waveguide Circulators

A method for synthesizing symmetrical waveguide circulators by adjusting the eigenvalues of the scattering matrix is described. This procedure is particularly useful for the design of very compact circulators in the form of waveguide junctions containing ferrite obstacles. Permissible structural symmetries for a circulator are listed, and a standard form for the scattering matrix of a symmetrical circulator is defined. The synthesis procedure is then described in detail, stating the conditions to be imposed on the scattering matrix eigenvalues, and an expression is obtained for the changes in the eigenvalues due to the placing of anisotropic material within the junction. By applying the theory to Allen's 4-port turnstile circulator, it is shown that the use of a matched turnstile junction and a reflectionless Faraday rotator is not essential. The theory is also applied to the design of novel 3- and 4-port circulators, and two 6-port circulators, one of which may be used as a 5-position waveguide switch, are described. Some experimental results are presented for a compact 3-port circulator in the form of an H-plane Y junction, in 1 inch by 1/2 inch waveguide, containing a ferrite post obstacle. This circulator, which operates with a bias field of approximately 25 oersted, has a useful bandwidth of 3 per cent. Greater bandwidths would be expected in a Stripline or a fin-line version of this device.     

The Adjustment of the m-Port Single- Junction Circulator

The purpose of this paper is to present a systematic procedure for the adjustment of the m-port single-junction circulator in terms of the scattering-matrix eigenvalues of the junction. The theory used starts by defining the initial location of the scattering-matrix eigenvalues before any adjustment to the junction is made and also by defining the eigenvalue arrangement of an ideal circulator. The initial set of eigenvalues is then perturbed in a systematic way by adjusting the phases of (m-1) of the eigenvalues one at a time until the final set of eigenvalues is obtained. This procedure leads to (m-1) distinct scattering matrices which can be obtained with (m-1) symmetric perturbations of the junction. This approach also leads to (m-1) distinct boundary-value problems each involving one independent variable instead of the more usual single-boundary problem involving (m-1) independent variables.     

Wideband circulator adjustment using the n = ±1 and n = 0 electromagnetic-field patterns

In its matched condition the scattering-matrix eigenvalues of the 3-port junction circulator lie equally spaced on a unit circle. As the frequency is varied, these eigenvalues rotate in the complex plane at different speeds, and the phase relation between them no longer corresponds to an ideal circulator. This is primarily due to the fact that the reference eigenvalue is normally associated with a nonresonant field pattern and the other two eigenvalues are associated with resonant ones. The purpose of the letter is to describe a new adjustment procedure in which the reference eigenvalue is associated with a resonant field pattern also. If the Q factors of all three field patterns are made the same, the three eigenvalues will all rotate at the same speed, around the unit circle. The bandwidth of the circulator will then be very wide.     

Synthesis of octave-band quarter-wave coupled semi-trackingstripline junction circulators

The complex gyrator circuit of stripline circulators using tracking junctions which satisfy the physical and magnetic variables of the Wu and Rosenbaum boundary conditions, is a nearly frequency independent octave-band resistive network. Such a junction may exhibit two minimas in its reflection coefficient when matched by a two section impedance transformer. However, a third minima may be realised by utilizing a complex rather than a real gyrator circuit. This paper summarises this class of semi-tracking solution in a simple way as a preamble to the design of a degree-3 quarter wave coupled circulator. The overall frequency behaviour of this class of junction has been separately evaluated by combining the electromagnetic and network problems (in conjunction with a two step impedance matching network)     

An Improved Equivalent Circuit for the Thin-Film Lumped-Element Circulator

A program written for the Hewlett-Packard automatic network analyzer permits the S-parameter eigenvalue phases and magnitudes to be displayed. The thus measured eigenvalues of a lumped-element circulator lead to an improved equivalent circuit which explains the observed "double hump" characteristic. The influence of different circuit parameters on the eigenvalues is measured and found in good agreement with the author's previously published theory. It is concluded from this theory and the measurements that, for the lossy circulator in general, maximum isolation, return loss, and minimum forward loss do not occur at the same frequency.     

Field Theory Treatment of H--Plane Waveguide Junction with Triangular Ferrite Post

This paper presents an exact field theory treatment for the H-plane waveguide junction with three-sided ferrite prism. The treatment is general, being independent of the geometrical symmetry of the junction, the number of ports, and the location of the ferrite post inside the junction. The solution of the wave equations in the ferrite post and in the surrounding region is written in the form of an infinite summation of cylindrical modes. The fields at the ferrite-air interface are matched using the point-matching technique. This results in two amplitudes for the cylindrical modes describing the fields in the air region in the form of a matrix. The fields at the arbitrary boundary between the air region and the waveguides are also matched using the point-matching technique. This results in a finite system of nonhomogeneous equations in the field amplitudes. The three-port waveguide junction circulator with central triangular ferrite post is analyzed using this technique. Two specific arrangements are considered. In the first arrangement, the points of the triangles are in the centers of the waveguides, and in the second, the sides of the triangles are in the centers of the waveguides. The method used in this paper can also be applied to study the effect of the ferrite-post geometry on the circulator performance in order to seek the best possible circulator structure. Excellent agreement has been found between published experimental measurements and the numerical results obtained by this technique in the case of a waveguide junction circulator with cylindrical ferrite post.     

Complex Gyrator Circuit of an Evanescent-Mode E-Plane Junction Circulator Using H-Plane Turnstile Resonators

The E-plane circulator is of considerable practical interest but its development has lagged somewhat compared to that of the more common H-plane device. The purpose of this paper is to experimentally investigate the eigenvalue problem and the complex gyrator circuit of an E-plane evanescent-mode junction loaded with one or two H-plane turnstile ferrite resonators symmetrically coupled by three standard rectangular waveguides. The condition for which the eigenvalues of the demagnetized junction are in antiphase has been met with the physical variables at hand, but the more important one for which they are also commensurate has not. A transformer coupled device using quarter-wave-long impedance sections at each port is also described. Its frequency coincides with the even solution of two coupled resonators.     

Synthesis of Quarter-Wave Coupled Circulators with Chebyshev Characteristics (Short Papers)

The purpose of this short paper is to give an exact theory of quarter-wave coupled circulators with Chebyshev characteristics. The synthesis starts by replacing the lumped-element equivalent shunt resonator of the circulator by a distributed one that has the same susceptance slope parameter as the original circuit. In this way the overall network involves commensurate transmission lines only. The bandwidth over which the assumed form of the equivalent circuit applies is carefully discussed in terms of the two split frequencies of the magnetized junction. Tables for the required circulator parameters and transformer admittances for one and two transformer sections as a function of VSWR and bandwidth are included. The realizable solution for the latter arrangement is severely restricted by the equivalent circuit of the basic junction. Experimental results on an octave-band stripline circulator, with a two-section transformer, are also included.     

Synthesis of Transformer Coupled Multiple Frequency Circulators with Chebyshev Characteristics

This paper presents a theory for broad-band matching of stripline junction circulators for operation in two or more frequency bands. In this theory it is assumed that the matching network is composed of cascaded transmission line transformers each of which is an odd multiple of a quarter-wavelength at the center frequencies. The conditions for simultaneous Chebyshev response in multiple frequency bands are determined, and it is investigated to what extent these conditions can be satisfied by stripline circulator junctions. Thus by using a first-order theory, it is shown that if a circulator junction, adjusted for double frequency operation, is matched for Chebyshev response by a transformer of proper length around one of the circulation frequencies then it is also matched for Chebyshev response around the other circulation frequency, provided that the same operation mode is used above and below material resonance. A routine for broad-band multiple frequency matching is proposed for junctions where Chebyshev response is not obtainable. Finally the properties of some externally matched circulators designed according to the theories are shown.     

The Measurement of the Equivalent Admittance of 3-Port Circulators Via an Automated Measurement System (Short Papers)

A derivation of the equivalent admittance of symmetrical 3-port circulators is given which is based on the requirement that the S-matrix eigenvalues be separated by 120/spl deg/ on the unit circle for perfect circulation. This quantity has the property that if a 2-port matching network is found which matches into this admittance, then the same matching network connected in each circulator arm will match the circulator. It was used in conjunction with a computerized measurement system to determine the optimal single-step transformer matching of a stripline 3.7-4.2-GHz circulator and resulted in a device with performance better than 30 dB over this band.     

Circulators Using Planar WYE Resonators

An important class of commercial three-port circulator relies for its operation on a junction resonator consisting of the symmetrical connection of three open-circuited transmission lines. A feature of this resonator is that it may be quarter-wave coupled to form a circulator with a moderate specification (25-percent bandwidth to 25-dB return loss points) and physical dimensions of the order of directly coupled conventional circulators (using a disk resonator). For circulators for which the in-phase eigennetwork may be represented by an ideal short-circuit, the equivalent circuit is a one-port network which may be formed from a characterization of the constituent resonator. This feature is used in this paper to study the equivalent circuit of junction circulators using planar WYE resonators. The derivation of the equivalent circuit parameters is supported with the design of a 4-GHz quarter-wave-coupled stripline circulator.     

Synthesis of Quarter-Wave Coupled Junction Circulators with Degrees 1 and 2 Complex Gyrator Circuits

The complex gyrator immittance of circulators for which the in-phase eigennetwork is commensurate with those of the degenerate counter-rotating ones, and which may be idealized by a frequency-independent open- or short-circuited boundary condition, may be realized as a 1-port STUB-resistor network of degree 1. If the frequency variation of this eigennetwork cannot be neglected compared to those of the other two, the gyrator circuit is of degree 2. There are altogether eight possible complex gyrator circuits, each of which explicitly exhibits the eigennetworks of the device. A knowledge of that, applicable in any given situation, is mandatory for design.     

A Compact Broad-Band Thin-Film Lumped-Element L-Band Circulator

Impedance matrices including magnetic losses are developed for a number of lumped-element ferrite-loaded symmetrical three-port junctions. The scattering matrix eigenvalues corresponding to these matrices are determined as functions of frequency and circuit parameters and are used to analyze these three-ports with emphasis on their properties as circulators. A very compact broad-band thin-film lumped-element circulator is derived from the idealized equivalent circuit. An experimental model approximately represented by this circuit is shown to have a 20-dB isolation bandwidth of greater than 30 percent with an insertion loss of less than 0.6 decibel. A switchable circulator which requires no magnetic-field switching is treated using this same analytical approach. It is suggested that this type of analysis together with additional experimental refinement of equivalent circuits will lead eventually to a computerized design of lumped-element circulators.     

A Finite Element Analysis of Planar Circulators Using Arbitrarily Shaped Resonators

A planar circulator consists, in general, of three transmission tines, connected through suitable matching networks to a magnetized ferrite resonator having three-fold symmetry. This paper describes a finite element analysis which enables the Z-matrix of a planar circulator using arbitrary shaped resonators to be calculated. This technique allows quite general computer programs to be written which permit tables of circulation solutions to be calculated. Results for junctions using disk, triangular, and irregular hexagonal resonators are included in the text. The frequency response of junction circulators using various configurations whose magnetic variables have been chosen so that they operate over the widely used tracking interval has also been evaluated. The optimum response is in each case associated with a unique coupling angle.     

Passivity enforcement via perturbation of Hamiltonian matrices

This paper presents a new technique for the passivity enforcement of linear time-invariant multiport systems in state-space form. This technique is based on a study of the spectral properties of related Hamiltonian matrices. The formulation is applicable in case the system input-output transfer function is in admittance, impedance, hybrid, or scattering form. A standard test for passivity is first performed by checking the existence of imaginary eigenvalues of the associated Hamiltonian matrix. In the presence of imaginary eigenvalues the system is not passive. In such a case, a new result based on first-order perturbation theory is presented for the precise characterization of the frequency bands where passivity violations occur. This characterization is then used for the design of an iterative perturbation scheme of the state matrices, aimed at the displacement of the imaginary eigenvalues of the Hamiltonian matrix. The result is an effective algorithm leading to the compensation of the passivity violations. This procedure is very efficient when the passivity violations are small, so that first-order perturbation is applicable. Several examples illustrate and validate the procedure.     

Mode Chart for E-Plane Circulators (Correspondence)

The mode chart of the E-plane junction circulator is given. The geometry considered consists of two ferrite disks placed against the narrow walls at the plane of symmetry of a symmetrical 3-port E-plane waveguide junction. It is experimentally found to exhibit two modes. One of these modes has a resonant frequency which increases with the spacing between the two ferrite disks. The other mode has a resonant frequency which decreases with the spacing between the disks. Both modes are independent of the disk spacing when the spacing is large. It is also found that the frequency of both modes is proportional to the thickness of the ferrite disks. Finally, circulators obtained by magnetizing each of the two modes circulate in opposite directions. Experimental results on a circulator obtained in this way are included.     

W频段高阶模宽带波导Y结环行器

基于电磁理论计算，发现在Ｗ频段存在环行方向一致的双高阶结谐振模，两模相互邻近，可以用来制成双频环行器，也可以调整环行器参数使两模部分重迭，得到宽带特性．本文给出的实验结果验证了理论预言．双模部分重迭后给出８ＧＨｚ的１８ｄＢ隔离度带宽