Implanted medical devices are rapidly becoming ubiquitous. They are used in a wide variety of medical conditions such as pacemakers for cardiac arrhythmia, cochlear implants for deafness, deep-brain stimulators for Parkinson's disease, spinal-cord stimulators for the control of pain, and preliminary retinal implants for blindness. They are being actively researched in brain-machine interfaces for paralysis, epilepsy, stroke, and blindness. In the future, there will undoubtedly be electronically controlled drug-releasing implants for a wide variety of hormonal, autoimmune, and carcinogenic disorders. All such devices need to be small and operate with low power to make chronic and portable medical implants possible. They are most often powered by inductive radio-frequency (RF) links to avoid the need for implanted batteries, which can potentially lose all their charge or necessitate re-surgery if they need to be replaced. Even when such devices have implanted batteries or ultra-capacitors, an increasing trend in upcoming fully implanted systems, wireless recharging of the battery or ultra-capacitor through RF links is periodically necessary.

Figure 16.1 shows the basic structure of an inductive power link system for an example implant. An RF power amplifier drives a primary RF coil which sends power inductively across the skin of the patient to a secondary RF coil.

Noise ultimately limits the performance of all systems. For example, the maximum gain of an amplifier is limited to VDD/vn where VDD is the power-supply voltage and vn is the noise floor at the input of the amplifier. Gains higher than this limiting value will simply amplify noise to saturating power-supply values and leave no output dynamic range available for discerning input signals.

Since power is the product of voltage and current, low-power systems have low voltages and/or low current signal levels. Hence, they are more prone to the effects of small signals such as noise. A deep understanding of noise is essential in order to design architectures that are immune to it, in order to efficiently allocate power, area, and averaging-time resources to reduce it, and in order to exploit it. We will begin our study of noise in physical devices from a first-principles view of some of the fundamental concepts and mathematics behind it.

The mathematics of noise

We pretend that macroscopic current is the flow of a smooth continuous fluid. However, the current is actually made up of tiny microscopic discrete charged particles that flow in a semi-orderly fashion. The random disorderly portion of the charged-particle motion manifests itself in the macroscopic current as noise. Figure 7.1 reveals how macroscopic current is actually made up of tiny fluctuations around its mean value which constitute current noise.

To deeply understand any electronic circuit, whether it is low power or not, it is essential to have a good mastery of the devices from which that circuit is made. In this chapter, we will begin our study of device physics with the metal oxide semiconductor (MOS) transistor, the most important active device in electronics today. The MOS transistor is a field effect transistor (FET) and MOSFETs are abbreviated as nFETs if their current is due to electron flow and as pFETs if their current is due to hole flow. In this chapter, we shall focus on fundamental principles and on exact mathematical descriptions that are applicable to transistors built in technologies with relatively long dimensions. In later chapters, we shall study practical approximations needed to simplify these exact mathematical descriptions (Chapter 4), study small-signal dynamic models of the MOS transistor (Chapter 5), and discuss effects observed in deep submicron transistors with relatively short dimensions (Chapter 6).

Figure 3.1 shows a zoomed-in view of an n-channel FET or nFET built in a standard bulk complementary metal oxide semiconductor (CMOS) process. There are four terminals referred to as the gate (G), source (S), drain (D), and bulk (B), respectively. The control terminal, the metal-like polysilicon gate, is insulated from the silicon bulk via a silicon dioxide insulator; the source and drain terminals are created with n+ regions in the p-type silicon bulk.

In this chapter, we shall discuss a feedback technique for analyzing linear circuits, invented by Hendrik W. Bode in his landmark book, Network Analysis and Feedback Amplifier Design published in 1945. The technique, known as return-ratio analysis, allows one to compute the return ratio of an active dependent generator or passive impedance in a linear circuit as a function of its dependent gain or of its passive impedance, respectively. The return ratio is a quantity analogous to the loop transmission in a feedback loop: just as we can use the loop transmission in a feedback loop to analyze how the dynamics of the loop changes as we vary its dc gain, we can use the return ratio of an element to analyze how transfer functions in the circuit change as we vary the dependent gain or passive impedance of the element. The return ratio also gives us a measure of the robustness of the circuit to changes in the gain or impedance of the element in the same manner that the loop transmission gives us a measure of the robustness of a feedback loop to changes in its feedforward gain. The return ratio explicitly realizes that circuits are composed of bidirectional elements and loading such that the creation of unidirectional block diagrams with feedforward gain a(s) and feedback gain f(s) to analyze them is not unique and sometimes cumbersome.

Information is represented by the states of physical devices. It costs energy to transform or maintain the states of these physical devices. Thus, energy and information are deeply linked. It is this deep link that allows us to articulate information-based principles for ultra-low-power design that apply to biology or to electronics, to analog or to digital systems, to electrical or to non-electrical systems, at small scales or at large scales. The graphical languages of circuits and feedback serve as powerful unifying tools to understand or to design low-power systems that range from molecular networks in cells to biomedical implants in the brain to energy-efficient cars.

A vision that this book has attempted to paint in the context of the fields of ultra-low-power electronics and bioelectronics is shown in the figure below. Engineering can aid biology through analysis, instrumentation, design, and repair (medicine). Biology can aid engineering through bio-inspired design. The positive-feedback loop created by this two-way interaction can amplify and speed progress in both disciplines and shed insight into both. It is my hope that this book will bring appreciation to the beauty, art, and practicality of such synergy and that it will inspire the building of more connections in one or both directions in the future.

Devices that dissipate energy, such as resistors and transistors, always generate noise. This noise can be modeled by the inclusion of current-noise generators in the small-signal models of these devices. When several such devices interact together in a circuit, the noise from each of these generators contributes to the total current or total voltage noise of a particular signal in a circuit. In this chapter, we will understand how to compute the total noise in a circuit signal due to noise contributions from several devices in it. We shall begin by discussing simple examples of an RC circuit and of a subthreshold photoreceptor circuit. We shall see that the noise of both of these circuits behaves in a similar way. We shall discuss the equipartition theorem, an important theorem from statistical mechanics, which sheds insight into the similar noise behavior of circuits in all physical systems. We shall then outline a general procedure for computing noise in circuits and apply it to the example of a simple transconductance amplifier and its use in a lowpass filter circuit. We will then be armed with the tools needed to understand and predict the noise of complicated circuits, and to design ultra-low-noise circuits.

We shall conclude by presenting an example of an ultra-low-noise micro-electro-mechanical system (MEMS), a capacitance-sensing system capable of sensing a 0.125 parts-per-million (ppm) change in a small MEMS capacitance (23-bit precision in sensing).

In this chapter, we shall discuss circuits that use current inputs and current outputs to create static and dynamic linear and nonlinear systems. Current-mode circuits can operate at low power-supply voltages and over a wide range of currents with exponential subthreshold or bipolar transistors. For reasons that will become clear at the end of the chapter, current-mode signal processing implemented with exponential devices is also often termed log-domain signal processing.

We shall begin by discussing static translinear circuits, which were invented by Barrie Gilbert in the bipolar-circuit domain and that are easily generalized to the subthreshold-MOS domain. Then, we shall discuss circuits for constructing linear current-mode dynamical systems analogous to Gm − C filters in the voltage domain, which were invented and developed by Seevinck, Tsividis, Frey, Toumazou, Andreou, Vittoz, Minch and others. We shall present gain-control techniques for achieving a nearly constant signal-to-noise ratio over a wide dynamic range of inputs, developed by Tsividis for use in linear current-mode input-output systems. Such adaptive techniques separate signal-to-noise ratio (SNR) and dynamic-range variables enabling low-power operation over a wide dynamic range of inputs.

Biomedical implants such as cochlear implants, retinal implants, brain implants, cardiac pacemakers, implanted defibrillators, and electronic pills require information to be wirelessly communicated from outside the body to inside the body and vice versa. Wired links from an external electronic unit to an implanted unit inside the body are prone to infection in the long term and are thus unlikely to meet approval by regulatory agencies such as the Food and Drug Administration (FDA). Thus, wireless communication is essential in such implants. in Chapter 16, we discussed how to wirelessly transmit power to such implants via an RF inductive near-field link. Near-field communication is important when the distance of communication, often 1 mm to 10 mm across the skin of the patient, is considerably less than the RF carrier wavelength. In contrast, in far-field communication systems used in most traditional radios, the communication distance is significantly in excess of the carrier wavelength. The relationship between near-field and far-field communication is discussed in quantitative depth in Chapter 17 on antennas and RF energy harvesting.

In this chapter, we shall first focus on how to communicate data via ultra-low-power near-field RF telemetry in such implants.

The cells in the human body provide examples of phenomenally energy-efficient sensing, actuation, and processing. An average ∼10 μm-size human cell hydrolyzes several energy-carrying adenosine-tri-phosphate (ATP) molecules within it to perform nearly ~107 ATP-dependent biochemical operations per second. Since, under the conditions in the body, the hydrolysis of each ATP molecule provides about 20 kT (8 ×10−20 J) of metabolic energy, the net power consumption of a single human cell is an astoundingly low 0.8 pW! The ~100 trillion cells of the human body thus have an average resting power consumption of ~80 W, consistent with numbers derived from the Appendix of Chapter 23.

The cell processes its mechanical and chemical input signals with highly noisy and imprecise parts. Nevertheless, it performs complex, highly sensitive, and collectively precise hybrid analog-digital signal processing on its inputs such that reliable outputs are produced. Such signal processing enables the cell to sense and amplify minute changes in the concentrations of specific molecules amidst a background of confoundingly similar molecules, to harvest and metabolize energy contained in molecules in its environment, to detoxify and/or transport poisonous molecules out of it, to sense if it has been infected by a virus, to communicate with other cells in its neighborhood, to move, to maintain its structure, to regulate its growth in response to signals in its surround, to speed up chemical reactions via sophisticated enzymes, and to replicate itself when it is appropriate to do so.

Just to be absolutely clear – even though this book is about digital wireless communication (DWC) signals, the wireless signal itself is analog. All wireless signals, and actually all signals whether wireless or not, are single, real, continuous-time analog waveforms.

The characteristic which makes us consider them as digital signals is that the information in the signal is only available at particular times, which are separate from one another and distinct. As far as the information is concerned, what the signal does in between these time instances is of no concern. But – and this is an extremely important BUT – the usefulness of the signal in actual transmission is extremely sensitive to the detail of the signal behavior at all times, particularly the time intervals between the information points. Indeed, much of this book is concerned with the fine details of what the DWC signal of choice is doing at all times.

So let us begin by examining what makes us consider that these signals are digital. No matter if signal phase, frequency, amplitude, or some combination is used for modulation, all digital wireless communication signals are a sequence of states. This simply means that the information in the digital wireless communication signal can only be represented by a (usually short) finite list of particular and very specific signal characteristics. Outside of this very restricted set of signal characteristics, the information content of the signal is undefined.

Spread spectrum is not really a modulation type, but is rather a communication system technique. Many different types of modulation can be, and have been, used in the implementation of spread spectrum systems. Of the various spread spectrum techniques that have been proposed and implemented over the years, there are two that survive to dominate the present implementations. These two are direct sequence spread spectrum (DSSS) and frequency hopping spread spectrum (FHSS).

One interpretation of any spread spectrum method is that the spreading process “breaks apart” the information signal into little pieces, using some type of code. A corresponding de-spreading process, using the same code, “knows” where these pieces are and reassembles them back together. In this reassembly process, any other signal (such as interference) will not match this reassembly process and therefore is effectively broken up into pieces of its own. Direct sequence and frequency hopping have different physical mechanisms for spreading and de-spreading, and have different properties in how they reject narrowband interference.

There are parallels among DSSS and FHSS systems which have led some authors to propose that these approaches are duals of each other. However there are some very distinct differences which show that these two approaches cannot be considered as duals of each other. Rather, each must be examined and evaluated on its individual merits. The proper choice of direct sequence or frequency hopping as a spread spectrum technique depends on the actual environment in which the system will be deployed.