Now we begin the study of transistor circuits. Transistors have three terminals. Usually one of the terminals is the input, another is the output, and the third is a common connection that is shared between the input and the output. Transistor circuits can increase the power of a signal. For this they require an additional DC power source. Circuits that increase power are called active circuits. By comparison, a passive circuit has loss. The filters we covered in the earlier chapters are examples of passive circuits. We will study several different active circuits. An amplifier increases the power of a signal without changing the frequency. In an oscillator, an output sine wave is generated without any input signal. Transistors can also be used in passive circuits. In Problem 5, we saw that a transistor could act as a fast switch, with either a low resistance between the output terminals or a high resistance, depending on the input voltage. We will also use a transistor as a variable attenuator to control the signal level.

Manufacturers can combine many transistors on one chip of silicon. These circuits are called integrated circuits, or ICs. Many thousands of different integrated circuits are available. One common type of IC includes several amplifiers cascaded one after another, so that the output signal is much larger than the input. These circuits are called op amps, short for operational amplifiers.

Introduction

This chapter discusses the use of superconductors in the construction of microwave filters. Superconductors can help in two ways. Firstly, the performance of a filter is improved by the use of superconductors in the sense that the insertion loss can be significantly reduced, as well as improving the filter roll off and reducing its bandwidth. Secondly, filters can be miniaturised. The improvement in the performance of filters is generally achieved by using fairly conventional design techniques, and improvement arises due to the reduced dissipation owing to the low surface resistance. However, miniaturisation usually requires a change in the geometry of filters and therefore entirely new types of filter become possible when superconducting materials are used in their construction. Improved performance and miniaturisation are complementary and reducing the size of a filter generally leads to reduced performance, although superconductors allow a much larger reduction in size, when compared with normal metals, whilst still giving improved performance. A third possible reason for using superconductors is to use their special properties such as the change in internal (or kinetic) inductance with microwave power or temperature, or to use their switching capabilities. These functions are discussed further later in this chapter. This chapter is organised under the theme of miniaturisation, where most of the interesting novel work has been in HTS filter development. All the filters discussed, especially those only having a modest amount of miniaturisation, are superior in performance to conventional filters made from normal metals.

Introduction

This chapter is mainly concerned with the measurement of the microwave response of a circuit. The equipment that performs these measurements is discussed briefly in Section 4.1, which reviews the capabilities of the network analyser. Following this section a detailed description is given on how to extract the unloaded quality factor of a cavity or resonator from measurements taken on a network analyser. It is well known that the unloaded quality factor can be estimated by simply taking the ratio of the centre frequency to the 3 dB bandwidth of the transmission response of a resonator, and the unloaded Q can be calculated by simply using the insertion loss measured at resonance. However, although this may be adequate for many situations, greater accuracy may be required or reflection measurements from the cavity may only be available. Calculations are therefore given for both one- and two-port measurements. For the two-port case both symmetrical and asymmetrical coupling are considered. Throughout the discussion, indications of how the accuracy of quality factor measurements may be improved are given. The final section of this chapter deals with power dependent measurements. The calculation of the energy stored in a cavity or the current on a resonant transmission line from S (scattering) parameter measurements is given.

Measurement system

Modern microwave measurement equipment, although expensive, allows accurate measurements to be made with the minimum of effort.

A revolution in the field of superconductivity occurred in 1986 with the discovery of superconductors with a transition temperature greater than the boiling point of liquid nitrogen, and many laboratories around the world began the exciting work of developing these materials. This book stems from one such laboratory, which has been looking at the microwave aspects of these materials, not only from a basic science view point, but also from a desire to demonstrate their potential for new applications. The development of microwave applications has proceeded very rapidly, and in less than ten years superconducting communication and signal processing systems are being flown in space, with many other microwave devices and systems to be found in the market place. This book essentially charts this development from the basic fundamental considerations of superconductors in high-frequency fields to the use of superconductors in microwave passive applications.

The book should be suitable as a basic introduction to the microwave applications of superconductors, and can be read independently of any previous knowledge of superconductors. However, the reader is recommended to consult one of the many texts about superconductivity in general in order to obtain a balanced view of the subject. It is expected that a number of different groups will find this book of interest. It could form the text for a specialized undergraduate course or be used in a more general course on microwaves.

Introduction

Two tables are given in this appendix. Table A3.1.1 gives a summary of some of the expressions for various parameters of a plane wave in conductors, superconductors and dielectric materials, with the various approximations applied in their derivation. The derivation and description of these expressions are given in Chapter 1. Table A3.1.2 gives a summary of some useful fundamental physical constants.

Substrate requirements

Superconducting films have to be grown on some sort of substrate which must be inert, compatible with both the growth of a good quality film and also have appropriate microwave properties for application purposes. From the microwave point of view, a high dielectric constant of well-known value is good for miniaturising components, as discussed in chapter 5. However, for higher frequencies this miniaturisation may be a problem in that the size of the circuit may be reduced considerably and the size reduction may make it difficult to produce the device. The design of devices is simplified if the dielectric constant is isotropic in the plane of the film and has a low dispersion for wide band devices, although compensation can be built into the device design if the parameters are sufficiently well characterised. It is also more convenient if the dielectric constant does not change much with temperature, improving the temperature stability of the final application. Whatever the dielectric constant, it must be reproducible and not change appreciably from batch to batch. For many of the devices discussed in this text a low dielectric loss tangent is of fundamental importance, especially on high-Q filters or resonators or long delay lines. If the loss tangent is not low enough, then the advantage of using a superconductor can be negated.

Introduction

Delay lines are an important application of superconductors and one in which they have a distinct advantage over other technologies. A delay line consists of a long transmission line, usually microstrip, stripline or coplanar line, which is deposited on to one or more substrates. This chapter is split into two main sections. Section 6.3 discusses delay lines which just delay the signal over a wide bandwidth; in principle the output should be a replica of the input signal but delayed by a certain time. However, the more interesting aspect of delay line technology is discussed in Section 6.5 and the following sections. Here, delay lines are described which perform a filtering or signal processing function and have applications both in electronic warfare and communications.

An idea of the capabilities of superconducting delay lines can be gained by considering the wide microstrip. Figure 6.1.1 shows the attenuation of a wide microstrip calculated from Equation (2.3.6), together with a number of other methods of delaying a signal. It can be seen that it is possible to obtain hundreds of nanoseconds of delay for only several decibels of loss for a superconducting wide microstrip at 10 GHz. Superconducting delay lines offer one of the lowest loss transmission media, even approaching the attenuation of the atmosphere. The transmission along optical fibre is also very low loss and in fact a whole technology related to signal processing using optical fibre has been developed.

Introduction

This appendix looks briefly at the microwave properties of superconducting materials and how these properties vary with external influences. It looks briefly at some of the issues affecting these properties and comments on reasons for specific trends. Its primary motivation is to provide typical values of these properties for the microwave design engineer. Although there are many hundreds of high-temperature superconductors with varying transition temperatures, YBa2Cu3O7−x (YBCO), with a transition temperature of about 92 K, is by far the most popular. The reason for this is historical, but the surface impedance of any of the HTS materials does not improve significantly over YBCO, even though the transition temperature may be higher. As more materials are investigated in detail, with greater emphasis being placed on the optimisation of the surface impedance, the dominance of YBCO may recede. This appendix thus mainly discusses the microwave properties of YBCO, although a brief mention is made of some of the thallium-based superconductors, which have also been studied in the context of microwave engineering. The majority of measurements presented have been made using the coplanar resonator, described in Section 3.8, at The University of Birmingham. The films tested are state-of-the-art and come from a variety of sources. Since the coplanar resonator is used, the results given are therefore taken on a structure which is close to the final application, and includes any effects due to film patterning.

Introduction

Antennas can benefit in a number of ways when superconductors are used in their fabrication. This chapter describes areas where superconductors are useful, and in which applications the greatest improvement can be obtained. The obvious application is in the improvement of the radiation efficiency of small antennas and superdirectional arrays. Antennas which are around the size of one wavelength are normally fairly efficient and superconductors cannot help. However, as the size of the antenna is reduced the efficiency reduces due to the increasing dominance of the ohmic losses. In this case superconductors reduce the losses and maintain a reasonable efficiency as the antenna shrinks in size. In principle, it is possible to obtain any directivity from any size of antenna array, and small directive antennas are called superdirective antennas. Again, superdirective antennas are very inefficient and superconductors help to make these a practical proposition, albeit with only a moderate superdirective capability. In addition to the reduction in efficiency, reducing the size of antennas and superdirective antenna arrays also makes matching to a reasonable system impedance increasingly difficult. High-Q matching networks are required, where superconductors also help considerably in performance improvement. As both these antenna types shrink, the Q also increases, restricting the bandwidth over which they can operate, and this now remains the practical limitation to their usefulness. For application purposes, the balance between efficiency or gain and Q needs to be assessed and this chapter addresses this problem in both a general way and also for some specific antennas.

Introduction

In 1947 Pippard pointed out that a wave would be slowed when it propagated along a superconducting transmission line. This effect is due to the increase in inductance of the transmission line because of the penetration of the external magnetic field into the superconductor. The effect increases as the proportion of the magnetic field inside the superconductor increases relative to the proportion of the external magnetic field. This is not the only effect of using superconductors in transmission lines. Provided the transmission line propagates in a TEM mode, a superconducting transmission line is dispersionless, due to the penetration depth not varying with frequency. This is in contrast with a normal conductor where the skin depth is a function of frequency, and increasing the frequency has the effect of reducing the skin depth and hence increasing the velocity due to the decrease of internal inductance. However, for application purposes the most important effect of using superconductors is the very low loss of the transmission line.

This chapter looks at superconducting transmission lines in some detail. Section 2.2 considers the wide microstrip or parallel plate superconducting transmission line. This transmission line is one of the simplest and is close to the type of transmission line used in many applications. Because of its simple nature, the wide microstrip can be analysed and considerable understanding of the effects of using superconductors can be gained.

Introduction

A cavity resonator is any structure which is able to contain an oscillating electromagnetic field. In general, it has a number of distinct resonant frequencies which are dependent upon the geometry of the cavity. If an oscillating field is set up within a cavity it will gradually decay because of losses. These losses may be due to a number of phenomena but are mainly due to (i) the finite conductivity of the walls of the cavity, (ii) losses in any dielectric material within the cavity or (iii) radiation out of any apertures in the walls. The main reason for using superconductors in the construction of a cavity is to reduce the conduction loss and reduce this decay to a minimum. The decay of the oscillating field is inversely proportional to the quality factor of the cavity, and is discussed extensively below for the characterisation of cavities.

Cavities are of interest for a number of reasons. By producing a superconducting sample part of a cavity resonator the losses in the superconductor can be deduced. Cavities also form the main functional part of many microwave filters. By coupling a number of cavities together, a filter can be constructed. A high-Q cavity also forms the main feedback element in a microwave oscillator. In fact, cavity resonators form the most fundamental building block in the majority of microwave circuits and hence will be discussed in some detail in this chapter.

Introduction

This first chapter deals with some fundamental aspects of how superconductors interact with high-frequency fields, and discusses the theoretical tools available for the solution of problems. Although superconductors were discovered in 1911 by H. Kamerlingh Onnes, it was not until the early 1930s that significant consideration was given to high-frequency effects. The thermal properties of superconductors were investigated by Gorter and Casimir in 1934, and they predicted a temperature dependence of superconducting carriers by minimising the Helmholtz free energy. To do this the carriers within a superconductor were assumed to consist of both superconducting and normal carriers whose relative densities changed as a function of temperature. This two-fluid model was taken further by the London brothers in 1934 to account for the high-frequency properties of superconductors. Their contribution is outlined in Section 1.2. The London equations can be used in conjunction with Maxwell's equations in order to allow them to be applicable to superconductors. Complex conductivity also follows from the two-fluid model. This simplifies the problem in that the normal conductivity σ can be replaced by a complex conductivity σ1 – jσ2, which accounts for superconducting phenomena. Heinz London also produced some early measurements on the surface resistance of tin, during which he discovered the anomalous skin effect, and Fritz London was the first to suggest that flux in a superconductor is quantised.