In this article, we provide a comprehensive review of past and present efforts in the field of microwave nonreciprocity with an emphasis on the most commonly used nonreciprocal devices, namely gyrators, isolators, and circulators. After discussing the origin and history of such efforts, we elaborate on the pros and cons of four distinct approaches to break reciprocity which include magnetic biasing of ferrite materials, intrinsic nonreciprocity of solid-state devices, nonlinearities with geometric asymmetries, and finally, periodic spatiotemporal variation. We subsequently pay due attention to the spatiotemporal approach and show that the recently emerging proposals to achieve magnet-free nonreciprocity with linear, periodically time-varying circuits can compete with traditional ferrite devices and even outperform them in several metrics, thus opening the door to exciting venues for miniaturized low-cost and high-performance nonreciprocal devices with numerous applications ranging from full-duplex communications and quantum computing to biomedical imaging and radar systems.

Microwave Nonreciprocity

Generalized thermoelastic infinite medium with voids subjected to a instantaneous heat sources with fractional derivative heat transfer

Numerical inversion of 2-D Laplace transforms applied to fractional diffusion equations

Two-temperature generalized thermoelasticity theory has been applied to determine the conductive and thermodynamic temperature as well as the deformation and stresses in an annular disk The basic equations have been written in the form of a vector-matrix differential equation in the Laplace transform domain and solved for the field variables in closed form Finally, the time variation and space variation of temperatures, deformation and stresses have been estimated by numerical methods and presented in several graphs and the analysis of the results have been made

Eigenvalue Approach to Two-temperature Generalized Thermoelastic Interactions in an Annular Disk

It is assumed that a sinusoidal RC oscillator consists of a linear, passive or active RC network and an amplifier. The properties of such an oscillator are primarily dependent on its open-loop voltage transfer function. A general form of this function is introduced for RC oscillators of the second order, and expressions for the required maintenance gain and the oscillation frequency are derived. It is shown that there exist four distinct types of 2nd-order oscillators. A set of basic building elements for the oscillators is proposed. This consists of some simple RC networks, a voltage divider, a buffer and two amplifiers. The theory and the building elements are used to develop 18 novel oscillator circuits. All these oscillators have either two earthed tuning capacitances or two earthed resistances. It is shown that six of them can be tuned by varying only one capacitance or resistance. Eight of the oscillators are tunable by varying a voltage parameter; in four of these, the voltage-tuning range can be very wide. 14 additional 2nd-order oscillators are suggested. A general 3rd-order RC oscillator is also considered, and it is shown that there exist 15 distinct kinds of this oscillator. The procedure used in the development of the 2nd-order oscillators can also be applied to the design of those of the third order. It is thought that this will lead to a very large number of different oscillator circuits.

An abundance of sinusoidal RC oscillators

A 3-port unit that satisfies the requirements of the circulator concept is realised with a differential-input operational amplifier. It provides, between two of its ports, a direct measure of reflection coefficient at the third port. One unit may be employed as a hybrid transformer; two or more units may be connected in a ring to form an n-port circulator.

Realisation of the circulator concept using differential-input operational amplifiers

A complementary pair of embedding principles for the differential-input earthed-output operational amplifier are combined to obtain a general-purpose resistive embedding which is universal from the strict synthesis point of view in that all four types of controlled source (`transactor´) may be realised with either sign.

Universal active unit for active RC-circuit synthesis

An equivalent circuit of the general 2-port network based on a controlled source having two independent control voltages is derived. A synthesis procedure is given in terms of the transmission-matrix parameters, and it is shown that the network may be realised with only one type of operational amplifier. The method is applied to the ideal transformer, power amplifier and gyrator.

Active nonreciprocal 2-port network synthesis with operational-amplifier realisations

A correspondence is established between a basic operational-amplifier configuration and the ideal transformer with the aid of a hypothetical model of the amplifier. Several related transformer and immittance-convertor circuits are derived. All the given configurations may be obtained by a general synthesis procedure developed in a previous paper and realised with standard earthed differential-input amplifiers.

Ideal-transformer and convertor realisations using operational amplifiers

An investigation is made into the geometrical aspect of the immittance transformation properties of the general 2-port network. Its transmission matrix is decomposed to reveal orthogonal components which represent rotation and/or reflection of the load in the v/t plane, thereby obtaining new insight into the general immittance transformation process.

A.W. Keen

Papers

Realisation of the circulator concept using differential-input operational amplifiers

Universal active unit for active RC-circuit synthesis

Active nonreciprocal 2-port network synthesis with operational-amplifier realisations

Ideal-transformer and convertor realisations using operational amplifiers

Orthogonal decomposition of the 2-port network