Active devices are important elements in RF systems where they perform functions such as amplification, mixing and rectification. For mixing and rectification, the non-linear properties of the device are of paramount importance. In the case of amplification, however, the non-linear properties can have a damaging effect upon performance. This chapter concentrates on small signal amplifiers for which it is possible to select conditions such that there is, effectively, linear amplification. Amplifiers based on both bipolar junction and field effect transistors are considered and the chapter includes some revision concerning their characteristics and biasing. The high frequency performance of transistor amplifiers is limited by what is known as the Miller effect and a large part of the chapter is devoted to techniques for overcoming this phenomenon.

The semiconductor diode

The semiconductor diode is a device that allows a current flow, but for which the magnitude of the flow depends in a non-linear fashion upon the applied voltage. Many varieties of diode are manufactured by forming junctions out of p- and n-type semiconductors. There are, however, several important diode varieties that have other types of junction (the semiconductor to metal junction of a Schottky diode for example). A p-type semiconductor can be formed by introducing a small amount of indium into silicon. This creates a structure that allows electrons to flow at energy levels slightly above those of the bound electrons. An n-type semiconductor can be formed by introducing a small amount of arsenic into the silicon.

Semiconductor devices will always have some form of non-linearity in their characteristics and this can be both an advantage and a disadvantage. For amplifiers, non-linearity is clearly a disadvantage in that the amplified signal will not be a faithful reproduction of the input signal. Mixers, however, provide an example of the advantages of non-linear behaviour in semiconductor devices. An ideal mixer is a device for which the output is the product of two input signals. For purely sinusoidal inputs, this will imply outputs at the sum and difference frequencies. Mixers are essential for operations such as frequency translation, modulation and detection. As a consequence, they are an important building block for both transmitters and receivers. The current chapter considers the operation of a variety of mixers and their application to modulation and demodulation. In addition, the chapter considers some modulation and demodulation processes that do not involve mixing.

Diode mixers

Diode mixers are important because of their low noise characteristics. Whilst single diode mixers are not normally used at frequencies below 1 GHz, their analysis provides some useful insight into the operation of mixers in general. It should be noted that diode capacitance can have a detrimental effect upon mixer performance and low capacitance devices, such as the Schottky barrier diode, will normally be required for operation at higher frequencies.

The circuit in Figure 4.1 shows a single diode mixer that converts an RF input signal at frequency ωRF into an intermediate frequency (IF) signal at frequency ωIF = |ωRF − ωLO| by mixing it with a local oscillator (LO) signal at frequency ωLO.

Antennas are the means by which electromagnetic wave energy is fed into, and extracted from, the propagation medium. They are a key element in RF systems and their design and analysis constitutes a very important area of RF engineering. The problems of antenna design are many and varied. Modern spread spectrum systems will require antennas that are capable of operating over a wide range of frequencies. Mobile communications have a requirement for small efficient antennas that radiate over a wide arc. Radar, on the other hand, requires antennas that illuminate only a narrow arc, but can be steered over a wide region. In many systems, the requirements turn out to be conflicting and it is important for the designer to understand the practical constraints in order to achieve the best compromise solution. The present chapter seeks to introduce the most fundamental concepts of antenna engineering and to describe some important varieties of antenna.

Dipole antennas

Broadly speaking, an antenna is a device that transforms wave propagation down a transmission line (a physically narrow channel) into wave propagation through free space (a physically wide channel) and vice versa. If we consider a parallel wire transmission line, we could conceive of opening it out at its end to better couple the waves into free space. The opened out section would then correspond to a dipole antenna. In its unopened state, the transmission line will reflect back to the source almost all of the energy that reaches its end.

RF signals will often need to be transmitted with considerable power if they are to survive propagation with adequate signal level. As a consequence, we will need to consider amplifiers that can operate at large signal levels. Up to this point, we have concentrated on small signal amplifiers for which efficiency and linearity have not been a major problem. These aspects, however, require careful consideration in the case of RF amplifiers operating at large signal levels. Small signal amplifiers are typically of the class A variety and highly linear. Whilst class A amplifiers are sometimes used at high power levels, they do not represent an efficient use of the d.c. energy that is supplied to the amplifier. Class B, AB, C and E amplifiers are far more efficient, but have the disadvantage that they are highly non-linear and hence create considerable harmonics. These harmonics can be troublesome and require specialised techniques, or filtering, for them to be brought down to an acceptable level. The following chapter considers power amplifiers in the class range from A to E. It concentrates on BJT amplifiers, but the same principles can be applied to FET amplifiers.

Class A

Class A amplifiers attempt to operate over that part of the transistor characteristic for which there is linear translation of the input signal to the output. For a BJT, a typical configuration is shown in Figure 7.1.

Frequency selective circuits are extremely important elements of an RF system. They often consist of a combination of inductors and capacitors that achieves maximum power transfer at a particular frequency or range of frequencies. Since there will be maximum power transfer to a load when its source has conjugate impedance, such combinations will often be designed to achieve an impedance match at the frequencies to be selected. Frequency selective circuits need not be restricted to combinations of inductors and capacitors, but can also consist of lengths of transmission line or electromechanical devices such as quartz crystals. In the current chapter, we will concentrate on combinations of inductors and capacitors that have maximum transfer at a particular frequency, leaving broadband and transmission line circuits to later chapters.

Fundamental to selective circuits is the concept of resonance. That is, if a circuit is driven by an oscillatory stimulus, there will be a frequency, or frequencies, at which the circuit response peaks. We start the chapter by investigating this concept.

Series resonant circuits

For an inductor and capacitor in series, there will be a frequency (the resonant frequency) at which the reactance of the capacitor will cancel that of the inductor (i.e., the combination will behave as a short circuit at this frequency). Below the resonant frequency, the combination will have a capacitive reactance whose magnitude increases with decreasing frequency. Above the resonant frequency, the combination will have an inductive reactance that increases with frequency.

INTRODUCTION

The subject of CMOS RF integrated circuit design resides at the convergence of two very different engineering traditions. The design of microwave circuits and systems has its origins in an era where devices and interconnect were usually too large to allow a lumped description. Furthermore, the lack of suitably detailed models and compatible computational tools forced engineers to treat systems as two-port “black boxes” with frequency-domain graphical methods. The IC design community, on the other hand, has relied on the development of detailed device models for use with simulation tools that allow both frequency- and time-domain analysis. As a consequence, engineers who work with traditional RF design techniques and those schooled in conventional IC design often find it difficult to converse. Clearly, a synthesis of these two traditions is required.

Analog IC designers accustomed to working with lower-frequency circuits tend to have, at best, only a passing familiarity with two staples of traditional RF design: Smith charts and S-parameters (“scattering” parameters). Although Smith charts today are less relevant as a computational aid than they once were, RF instrumentation continues to present data in Smith-chart form. Furthermore, these data are often S-parameter characterizations of two-ports, so it is important, even in the “modern” era, to know something about Smith charts and S-parameters. This chapter thus provides a brief derivation of the Smith chart, along with an explanation of why S-parameters won out over other parameter sets (e.g., impedance or admittance) to describe microwave two-ports.

INTRODUCTION

Phase-locked loops (PLLs) have become ubiquitous in modern communications systems because of their remarkable versatility. As one important example, a PLL may be used to generate an output signal whose frequency is a programmable, rational multiple of a fixed input frequency. The output of such frequency synthesizers may be used as the local oscillator signal in superheterodyne transceivers. Phase-locked loops may also be used to perform frequency modulation and demodulation, as well as to regenerate the carrier from an input signal in which the carrier has been suppressed. Their versatility extends to purely digital systems as well, where PLLs are indispensable in skew compensation, clock recovery, and the generation of clock signals.

To understand in detail how PLLs may perform such a vast array of functions, we will need to develop linearized models of these feedback systems. But first, of course, we begin with a little history to put this subject in its proper context.

A SHORT HISTORY OF PLLS

The earliest description of what is now known as a PLL was provided by H. de Bellescize in 1932. This early work offered an alternative architecture for receiving and demodulating AM signals, using the degenerate case of a superheterodyne receiver in which the intermediate frequency is zero. With this choice, there is no image to reject, and all processing downstream of the frequency conversion takes place in the audio range.

INTRODUCTION

Given the effort expended in avoiding instability in most feedback systems, it would seem trivial to construct oscillators. However, simply generating some periodic output is not sufficient for modern high-performance RF receivers and transmitters. Issues of spectral purity and amplitude stability must be addressed.

In this chapter, we consider several aspects of oscillator design. First, we show why purely linear oscillators are a practical impossibility. We then present a linearization technique that uses describing functions to develop insight into how nonlinearities affect oscillator performance, with a particular emphasis on predicting the amplitude of oscillation.

A survey of resonator technologies is included, and we also revisit PLLs, this time in the context of frequency synthesizers. We conclude this chapter with a survey of oscillator architectures. The important issue of phase noise is considered in detail in Chapter 18.

THE PROBLEM WITH PURELY LINEAR OSCILLATORS

In negative feedback systems, we aim for large positive phase margins to avoid instability. To make an oscillator, then, it might seem that all we have to do is shoot for zero or negative phase margins. Let's examine this notion more carefully, using the root locus for positive feedback sketched in Figure 17.1.

This locus recurs frequently in oscillator design because it applies to a two-pole bandpass resonator with feedback. As seen in the locus, the closed-loop poles lie exactly on the imaginary axis for some particular value of loop transmission magnitude.

INTRODUCTION

The first stage of a receiver is typically a low-noise amplifier (LNA), whose main function is to provide enough gain to overcome the noise of subsequent stages (such as a mixer). Aside from providing this gain while adding as little noise as possible, an LNA should accommodate large signals without distortion, and frequently must also present a specific impedance, such as 50 Ω, to the input source. This last consideration is particularly important if a passive filter precedes the LNA, since the transfer characteristics of many filters are quite sensitive to the quality of the termination.

In principle, one can obtain the minimum noise figure from a given device by using the optimum source impedance defined by the four noise parameters: Gc, Bc, Rn, and Gu. This classical approach has important shortcomings, however, as described in the previous chapter. For example, the source impedance that minimizes the noise figure generally differs, perhaps considerably, from that which maximizes the power gain. Hence, it is possible for poor gain and a bad input match to accompany a good noise figure. Additionally, power consumption is an important consideration in many applications, but classical noise optimization simply ignores power consumption altogether. Finally, such an approach presumes that one is given a device with fixed characteristics, and thus offers no explicit guidance on how best to exercise the IC designer's freedom to tailor device geometries.

INTRODUCTION

We asserted in the previous chapter that tuned oscillators produce outputs with higher spectral purity than relaxation oscillators. One straightforward reason is simply that a high-Q resonator attenuates spectral components removed from the center frequency. As a consequence, distortion is suppressed, and the waveform of a well-designed tuned oscillator is typically sinusoidal to an excellent approximation.

In addition to suppressing distortion products, a resonator also attenuates spectral components contributed by sources such as the thermal noise associated with finite resonator Q, or by the active element(s) present in all oscillators. Because amplitude fluctuations are usually greatly attenuated as a result of the amplitude stabilization mechanisms present in every practical oscillator, phase noise generally dominates – at least at frequencies not far removed from the carrier. Thus, even though it is possible to design oscillators in which amplitude noise is significant, we focus primarily on phase noise here. We show later that a simple modification of the theory allows the accommodation of amplitude noise as well, permitting the accurate computation of output spectrum at frequencies well removed from the carrier.

Aside from aesthetics, the reason we care about phase noise is to minimize the problem of reciprocal mixing. If a superheterodyne receiver's local oscillator is completely noise-free, then two closely-spaced RF signals will simply translate downward in frequency together. However, the LO spectrum is not an impulse and so, to be realistic, we must evaluate the consequences of an impure LO spectrum.

INTRODUCTION

Because of its high performance, the superheterodyne is the only basic architecture presently in use for both receivers and transmitters. One should not then infer, however, that all receivers and transmitters are therefore topologically identical, for there are many variations on a basic theme. For example, we will see that it may be desirable to use more than one intermediate frequency to aid the rejection of certain signals, leading to a question of how many IFs there should be, and what frequencies they should have. Answering those questions is known as frequency planning, and converging on an acceptable frequency plan generally involves a substantial amount of iteration.

An important constraint is that on-chip energy storage elements generally consume significant die area. Furthermore, they tend not to scale gracefully (if at all) as technology improves. Hence, the “ideal” integrated architecture should require the minimum number of energy storage elements, and there are continuing efforts even to eliminate the need for high-quality filters through architectural means. Complete success has been elusive, though, and one must accept that the desired performance frequently may be achieved only if external filters are used. It is not too much of an exaggeration to assert that architectures are essentially determined by available filter technology.

Once a basic architecture and its associated frequency plan have been chosen, other key considerations include how best to distribute the huge power gain (typically 120–140 dB for receivers) among the various stages.

INTRODUCTION

The previous chapter on amplifier design generally ignored the issue of generating suitable bias voltages or currents. This neglect was by conscious design in order to minimize clutter in the circuit diagrams. In this chapter we finally take up the study of this important topic, focusing on a variety of ways to generate voltages and currents that are relatively independent of supply voltage and temperature. Because CMOS offers relatively limited options for realizing bias circuits, we'll see that some of the most useful biasing idioms are actually those based on bipolar circuits. A parasitic bipolar device exists in every CMOS technology and may be used, for example, in a bandgap voltage reference. Even though the characteristics of parasitic transistors are far from ideal, the performance of bias circuits made with such devices is frequently vastly superior to that of “pure” CMOS bias circuits.

In what follows, it is worthwhile to keep in mind that any voltage we produce must depend on some collection of parameters that ultimately have the dimensions of a voltage (such as kT/q, for example). Similarly, any current we produce must depend on parameters that ultimately have the dimensions of current (such as V/R). Although seemingly obvious and trivial statements, we'll see that they are extremely useful guides for the design of stable references.

INTRODUCTION

In this chapter, we study the problem of delivering RF power efficiently to a load. As we'll discover very quickly, scaled-up versions of the small-signal amplifiers we've studied so far are fundamentally incapable of high efficiency, and other approaches must be considered. As usual, tradeoffs are involved, this time among linearity, power gain, output power, and efficiency.

In a continuing quest for increased channel capacity, more and more communications systems employ amplitude and phase modulation together. This trend brings with it an increased demand for much higher linearity (possibly in both amplitude and phase domains). The variety of power amplifier topologies reflects the inability of any single circuit to satisfy all requirements.

GENERAL CONSIDERATIONS

Contrary to what one's intuition might suggest, the maximum power transfer theorem is largely useless in the design of power amplifiers. One minor reason is that it isn't entirely clear how to define impedances in a large-signal, nonlinear system. A more important reason is that even if we were able to solve that little problem and subsequently arrange for a conjugate match, the efficiency would be only 50% because equal amounts of power are then dissipated in the source and load. In many cases, this value is unacceptably low. As an extreme (but realistic) example, consider the problem of delivering 50 kW into an antenna if the amplifier is only 50% efficient. The circuit dissipation would be 50 kW as well, presenting a rather challenging thermal management problem.

INTRODUCTION

One characteristic of RF circuits is the relatively large ratio of passive to active components. In stark contrast with digital VLSI circuits (or even with other analog circuits, such as op-amps), many of those passive components may be inductors or even transformers. This chapter hopes to convey some underlying intuition that is useful in the design of RLC networks. As we build up that intuition, we'll begin to understand the many good reasons for the preponderance of RLC networks in RF circuits. Among the most compelling of these are that they can be used to match or otherwise modify impedances (important for efficient power transfer, for example), cancel transistor parasitics to provide high gain at high frequencies, and filter out unwanted signals.

To understand how RLC networks may confer these and other benefits, let's revisit some simple second-order examples from undergraduate introductory network theory. By looking at how these networks behave from a couple of different viewpoints, we'll build up intuition that will prove useful in understanding networks of much higher order.

PARALLEL RLC TANK

Let's just jump right into the study of a parallel RLC circuit. As you probably know, this circuit exhibits resonant behavior; we'll see what this implies momentarily. This circuit is also often called a tank circuit (or simply tank).