Circuits and systems

Drawing on over twenty years of teaching experience, this comprehensive yet self-contained text provides an in-depth introduction to the field of integrated microwave electronics. Ideal for a first course on the subject, it covers essential topics such as passive components and transistors, linear, low-noise and power amplifiers, and microwave measurements. An entire chapter is devoted to CAD techniques for analysis and design, covering examples of easy-to-medium difficulty for both linear and non-linear subsystems, and supported online by ADS and AWR project files. More advanced topics are also covered, providing an up-to-date overview of compound semiconductor technologies and treatment of electromagnetic issues and models. Readers can test their knowledge with end-of-chapter questions and numerical problems, and solutions and lecture slides are available online for instructors. This is essential reading for graduate and senior undergraduate students taking courses in microwave, radio-frequency and high-frequency electronics, as well as professional microwave engineers.

Summary

Modeling of Linear and Nonlinear Blocks

In an integrated microwave circuit, passive devices (such as resistors, inductors, capacitors, transformers, simple and coupled transmission lines) are linear blocks, and can therefore be characterized by linear models. Transistors (field effect or bipolar) and diodes are, instead, nonlinear components also in DC or quasi-static conditions, although they can behave in an approximately linear way under small-signal operation. Linear passive reactive components (such as linear inductors and capacitors) are with memory in the (v, i) port variables; nonlinear reactive elements, like the capacitances of pn or metal-semiconductor junctions, on the other hand are also associated with active components, such as transistors. Thus, MMICs generally include linear and nonlinear elements, memoryless or with memory.

The small-signal approximation, where the transistor characteristics are linearized in the neighborhood of the DC operating point, is well suited to the design of high-gain or low-noise amplifiers; in small signal conditions the active device is approximated as a linear block with memory. The simulation of distortion and power saturation occurring in power amplifiers (but also in low-noise and high-gain amplifiers in the upper limit of their spurious free dynamic range, see Sec. 8.2.3) require instead a nonlinear transistor model, often including linear and nonlinear memory effects.

In analog circuits, linear n-ports are conveniently modeled in the frequency domain, selecting conventional variables (such as voltages and currents) as the component input and output, or exploiting circuit variables that are more suited to the analysis and characterization of microwave circuits, such as the power waves, see Sec. 3.2. A linear n-port can be represented through a linear relationship between input and output variables; if we identify the component status in terms of the Fourier transforms of port voltages and currents, according to the choice of the input and output variable sets we obtain wellknown frequency-domain models such as the series (or current-driven, or impedance) representation and the parallel (or voltage-driven, or admittance) representation [1].

Although a linear element is completely described by a proper set of parameters conveniently sampled over the frequency band of interest, in many cases an equivalent circuit approach is preferred. The equivalent circuit is an approximate model of the component, whose topology and element parameters have to be fitted on measured (or physically simulated) characteristics.

Summary

Introduction

The present chapter describes a set of simulation or design exercises meant to apply, within a microwave Computer-Aided Design CAD environment, the concepts developed in the rest of the book. Each example is, potentially, a CAD laboratory trace. To allow the reader to replicate the examples, additional material is made available online in the form of a project in its specific CAD environment. We chose to develop the project on two well-known and widely used platforms, Microwave Office (MWO) [1] and ADS (Advanced Design Systems) [2]. To keep the presentation within reasonable limits (and also to avoid fast obsolescence due to the evolution of the CAD tool interfaces), for each example only a synthesis is provided with the main results in graphical form.

The examples closely follow the evolution of the text and are intended as short and tutorial in nature. Rather than reporting on full real-word designs, leading to a ready-togo layout, they concentrate on specific aspects that are dealt with in the text on a more theoretical equation-based level. All figures are directly copied (sometimes with minor changes and a conversion to black and white) from the CAD tool user interface, their graphical format being in a way a part of the design experience of the user. Some of the CAD projects actually provide a CAD implementation of numerical examples presented throughout the text.

Microstrip Line and Stub Matching of a Complex Load

The project proposes a CAD implementation of Example 2.5. A line plus stub section (the stub in short circuit) is set up to match to the impedance. The design frequency is chosen as 10 GHz. The electrical line length at 10 GHz is initially set equal to the approximate values found in Example 2.5, and a further optimization is carried out, obtaining slightly different values. Fig. 10.1 shows the resulting input impedance compared to the goal,.

Summary

Transmission Lines

Transmission lines (TXLs), simple or multiconductor, are a key distributed element in microwave circuits. They operate as signal transducers between components but are also the building block for passive distributed elements such as couplers, filters, matching sections, power dividers. In hybrid and monolithic microwave circuits the preferred guiding structures are the so-called TEM or quasi-TEM lines, characterized by broadband behavior and by the absence of a cutoff frequency, that is found in metal waveguides.

From a theoretical standpoint, N metal conductors with a ground plane support N TEM or quasi-TEM propagation modes. In TEM (Transverse ElectroMagnetic) modes, the electric and magnetic fields are transverse with respect to the propagation direction, i.e., orthogonal to the line axis. A purely TEM mode propagates in a line without conductor losses and with a homogeneous cross section, while lossy metal lines and lines with a non-homogeneous cross section support quasi-TEM modes with small longitudinal field components. An example of quasi-TEM line is the microstrip, where the cross section is partly filled by a dielectric, and partly by air. TEM and quasi-TEM lines may also support upper propagation modes with a cutoff frequency; however, the excitation of those modes is to be avoided because they contribute to radiation losses and coupling.

Transmission Line Theory

Transmission lines are a simple but convenient model for one-dimensional wave propagation, serving as a bridge between circuit theory and electromagnetics. Suppose first that the line is made of two lossless parallel conductors, one acting as the signal conductor, the other as the return or ground conductor, surrounded by a homogeneous, lossless medium. Such a structure supports a TEM propagation mode in which the electric and the magnetic fields lie in the line cross section and are orthogonal to the line axis and wave propagation direction; see Fig. 2.1 (a). In a TEM mode the transverse electric field can be derived from a potential function satisfying, in the line cross section, the Laplace equation. This is uniquely determined by the potential of the signal line v(z, t) with respect to the ground line, where the coordinate z is parallel to the line axis and propagation direction. The transverse magnetic field is in turn related to the total current i(z, t) flowing in the signal conductor; −i(z, t) flows instead in the return conductor.

Summary

Radio Frequencies, Microwaves, Millimeter Waves

The meaning of high-speed and high-frequency electronics has changed in a century of technological evolution; see [1]. Radio-frequencies (RF) were at first introduced within the framework of radio broadcasting and point-to-point transmission at the beginning of the twentieth century; however, new applications (such as TV broadcasting and above all the radar around 1940), fostered in turn by the availability of RF signal generators at increasing frequency, caused a gradual explosion of new application fields in the RF, microwave and millimeter wave frequency bands. Before 1970, high-frequency systems were based on vacuum tube generators; in the following decades, solid-state semiconductor devices able to operate above 1 GHz, based both on Silicon and on compound semiconductor technologies, were gradually introduced, leading to a new paradigm, the hybrid and then monolithic Microwave Integrated Circuit, (M)MIC, see, e.g., [1, Ch. 16]. Integration and the resulting downsizing of RF and microwave systems ultimately made microwave electronics, at least in high-volume applications, a low-cost commodity well suited to the consumer market.

For the sake of clarity, let us focus on the meaning of the terms RF, microwaves and millimeter waves and on some of the significant applications in each frequency band:

Summary

Introduction

This chapter aims at providing an overview of the experimental characterization techniques of linear and nonlinear one- and two-ports. After a short review of some basic instrumentation tools (the power meter, the vectorial voltmeter, the spectrum analyzer) in Sec. 9.2, the characterization of linear one- and two-ports, such as passive circuits and linear amplifiers, based on the measurement of power waves (see Sec. 3.2.2) and the related circuit-oriented parameters are discussed. As a first example, one-port measurements are introduced, whose fundamental tool is the so-called reflectometer (Sec. 9.3). The analysis of the reflectometer already allows the main issues involved in microwave measurement set-ups to be discussed, such as: the use of directional couplers to separate incident and reflected waves at the port where the Device Under Test (DUT) is connected; the need to perform measurements at a suitably low Intermediate Frequency (IF) rather than at RF to improve accuracy; the need to calibrate the measurement system to correct for systematic errors in the instrumentation.

In Sec. 9.4 the discussion is extended to the characterization of two-port linear devices adopting the two-port Vector Network Analyzer (VNA), the key instrument for high-frequency characterization first introduced by Hewlett Packard, around 1970 [2, 3]. Downconversion approaches are discussed in Sec. 9.4.1, while a number of calibration strategies are reported in Sec. 9.4.2.

Large-signal rather than linear-only characterizations are fundamental in the experimental assessment of power amplifiers. In Sec. 9.5 the most important aspects related to load-pull measurements are discussed. Sec. 9.6 is devoted to system-level characterization of RF components under modulated signal excitation, with particular attention to power amplifiers. Finally, Sec. 9.7 presents an overview of noise measurement techniques.

Basic Microwave Instrumentation Tools

Microwave measurements exploit a number of tools that are also commonly found in low-frequency electronic or electrical characterizations. Their function and principle of operation will be briefly recalled here.

Power meters are instruments able to measure the power dissipated by a resistive load being part of the meter.

Summary

Introduction

The task of RF amplifiers is to transfer the input signal to the load with an increased power, without overly corrupting the signal through added noise and linear or nonlinear distortion (harmonic or intermodulation). From the energy standpoint, the amplifier converts DC power from the power supply into RF power to the load with a certain efficiency. The output signal should be as faithful as possible a replica of the input signal, or, in a digital context, should replicate with an acceptable error the symbols in the input signal. This requires constant gain over the frequency bandwidth and the input signal dynamic range, linear phase relationship between input and output, and, in general, low enough nonlinear distortion. Such requirements should be satisfied for the whole amplifier frequency bandwidth and for a range of the input signal amplitude defining the amplifier dynamics or Spurious Free Dynamic Range (SFDR); see Sec. 8.2.3. Because of such requirements, amplifiers should behave, within the SFDR, as linear or quasi-linear components, i.e., nonlinearity is a factor that adversely affects the amplifier performance.

As already discussed, three main amplifier classes can be found in transceivers, the Low-Noise Amplifier (LNA) whose main purpose is to amplify weak input signals to the receiver chain with an acceptable compromise between gain and noise; the highgain amplifier (present in the RX and TX stages, often in the IF section), where noise is not the main concern but the primary purpose of design is to maximize the amplifier gain; the Power Amplifier (PA), whose main purpose is to deliver an output signal of the TX chain with a power level adequate for the specific system. The PA maximum power is limited by signal distortion and, ultimately, by power saturation. The maximum power that a transistor can deliver is in fact approximately proportional to the product of the maximum output current and of the breakdown voltage, and distortion increases with increasing output power. Indeed, increasing the transistor periphery or area, thus increasing the saturation power, and keeping the output signal level low with respect to the saturation power (the so-called output backoff, see Chapter 8) is a way to reduce (in class A amplifiers) distortion, and therefore to increase the amplifier dynamics.

Summary

Microwave and millimeter-wave electronics is today far more widespread than it used to be only 20 years ago. Traditional applications based on metal waveguide approaches are still on the market (think about radar systems and some satellite-based systems); however, the introduction of solid-state hybrid and above all monolithic microwave integrated circuits (MMICs) using III-V semiconductors such as gallium arsenide, initially in the low microwave range but now covering frequencies up to millimeter waves, has allowed for a dramatic reduction in the size, weight and cost of many microwave systems in fields ranging from wireless telecommunications to space applications to automotive radars.

Starting from the beginning of this century, a new revolution has taken place in MMICs, with the introduction of RF, microwave and now also mm-wave silicon-based ICs (CMOS but also SiGe). This has finally marked the entrance of microwave systems in the area of low-cost consumer electronics. At the same time, new semiconductor materials for high-power applications (such as gallium nitride) are gradually entering the market of microwave systems, with a promise of size and cost reduction related to the record power densities achievable. And yet, despite the widespread conversion to solid-state electronics, in some areas vacuum tubes are still successfully surviving and expanding their potential, e.g., in the field of THz sources.

The design of microwave circuits is largely based today on Computer-Aided Design (CAD) techniques that have turned the “black magic” associated with the design of distributed (transmission line or waveguide) circuits into a routine that is easily manageable by the designer – of course, provided that he or she has well understood the basics of microwave electronics. Alternative approaches based on lumped parameter components, which make the design of microwave integrated circuits quite similar to that of analog integrated circuits at large, have indeed become increasingly popular in MMICs, at least up to the middle microwave range. On the other hand, high-frequency monolithic and hybrid ICs still have to partly rely on distributed components and the related design styles. In conclusion, today's microwave design is a well-balanced blend of distributed and lumped technological approaches that the designer should be able to master.

Summary

Introduction

Noise is a random unwanted signal, typically of small amplitude, superimposed on the ideal, deterministic voltages and currents of the circuit. In electronics, the term noise has two main interpretations.

Noise can be an interfering signal caused by a set of deterministic signals generated by an external circuit (or by another part of the circuit under consideration). Interference is caused by electromagnetic coupling of the interfering signal source with the circuit interconnects. While this kind of noise has an ultimately deterministic cause, it is often characterized in a statistical way. Electromagnetic compatibility analyzes and models this kind of noise, and develops circuit design approaches having low sensitivity to interferers.

On the other hand, noise (also called intrinsic noise) is a random signal generated by the very elements of the circuit (typically resistors, diodes, transistors; reactive elements are ideally noiseless). Such noise is intrinsically associated with the charge transport and generation-recombination processes in semiconductors and conductors, and cannot be eliminated, though its effect may be, as we shall see, alleviated through proper circuit design. Intrinsic noise is therefore an ultimate limit to the performance of the circuit in dealing with signals of very small amplitude. In fact, when the signal power is comparable with the noise power, the signal over noise ratio (S/N ratio) tends to unity, becoming incompatible with the detection of a signal in the receiver stage.

Due to the presence of intrinsic noise, the open circuit voltage (or short-circuit current) observed at the ports of any electronic device is affected by stochastic fluctuations having zero mean value, but nonzero mean square value (and therefore nonzero available electrical power). Since intrinsic noise is a random phenomenon, it should be characterized as a stochastic process, see Sec. 7.2 for a review.

This chapter is devoted to the basic principles of electrical noise in circuits, to noise device models (active and passive), and to the design of low-noise amplifiers, starting from the analysis of circuits including random noise generators (Sec. 7.3), and including a short discussion on the physical origin of electrical noise (Sec. 7.5). The minimization of the noise figure in a loaded two-port is addressed in Sec. 7.7, while the noise models of passive and active devices are discussed in Sec. 7.6 and Sec. 7.8, respectively.

Summary

Introduction

The purpose of RF and microwave power amplifiers [1, 2, 3] is to obtain, rather than the maximum power gain, the maximum output power compatible with a given device, with acceptable efficiency and linearity. The output power of active devices is, in fact, limited by the maximum voltage and current swing, in turn related to the drain or collector breakdown voltage and to the maximum current, respectively. Moreover, while in small-signal operation the device is approximately linear, power amplifiers, while being ultimately limited by output power saturation, exhibit nonlinear effects (i.e., distortion) that become increasingly important for large input power. Nonlinearities yield signal distortion due to the generation of harmonics and intermodulation products (IMPs); such a nonlinear distortion has to be kept under control to satisfy system requirements.

Power amplifiers are traditionally divided in classes. Class A (Sec. 8.4) amplifiers are quasi-linear since, at least ideally, the device output voltage and current swings corresponding to a single-tone sinusoidal inputs are again single-tone (neglecting distortion). In class B (Sec. 8.6.1) and C (Sec. 8.6.2) amplifiers (to confine ourselves to traditional amplifier classes) the output device current swing corresponding to a sinusoidal input is a set of sine pulses; this harmonic-rich, wideband waveform is converted on the load into a narrowband one through filtering (the so-called tuned load approach).1 The rationale behind introducing strongly nonlinear amplifiers is the increase of the amplifier efficiency, i.e., the ratio between the RF output power and the power from the DC supply (Sec. 8.2.4). Typically, there is a trade-off between efficiency and distortion; in class A amplifiers, low distortion can be achieved by reducing the input and output powers, at the expense of the amplifier efficiency. In traditional amplifier classes, high efficiency can be only achieved at the expense of a large gain penalty.

More advanced amplifier classes, like the harmonic loading amplifiers (class F, Sec. 8.7.1) or the switching amplifiers (e.g., class E, Sec. 8.7.2) are able to achieve a theoretical maximum 100 percent efficiency with acceptable gain. Other strategies (like the Doherty amplifier, Sec. 8.7.3) aim at providing an acceptable efficiency also when the input signal power is not constant, but covers wide dynamics, as needed in many real-life last-generation communication systems. A final issue concerns the efficiency– linearity trade-off.

Bioresorbable electronics that can dissolve away in aqueous environments and generate biologically safe products offer a revolutionary solution to replace the built-to-last electronics predominantly used in implanted devices and electronic gadgets. Their use can reduce the risk of surgical complications by minimizing the number of necessary surgeries, and prevent production of electronic waste by allowing rapid device recycling. This Element presents bioresorbable materials such as metals, polymers, inorganic compounds, and semiconductors that have been used to construct electronic devices, and analyzes their unique dissolution behaviors and biological effects. These materials are combined to yield representative devices including passive and active components and functional systems.

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Microwave Electronics

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4 - Directional Couplers and Power Dividers

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Notation and Symbols

2 - Passive Elements and Circuit Layout

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1 - A System Introduction to Microwave Electronics

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9 - Microwave Measurements

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5 - Active RF and Microwave Semiconductor Devices

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6 - Microwave Linear Amplifiers

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7 - Low-Noise Amplifier Design

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