Ultra-low-power electronic systems often utilize batteries. The battery is frequently the heaviest and most critical portion of a portable system. The battery's size, weight, energy density, power density, form factor, cycling properties and lifetime can dictate constraints under which a portable electronic system must operate. Such constraints include the overall power dissipation of the system, the number of recharges that are possible in the system, the expected lifetime of the system, the overall size of the system, and the overall cost of the system. In this chapter, we shall provide a brief introduction to batteries with an emphasis on intuition and knowledge that is useful for providing insight into battery operation and ultra-low-power system design.

First, we shall begin with an exposition of the basic principles by which chemical energy is converted to electrical energy in a battery. Then, we shall discuss an equivalent circuit for a battery that intuitively describes several effects that are observed in practical batteries. We shall discuss the basics of lithium-ion and zinc-air batteries, two of the most common and most efficient batteries in existence in ultra-low-power electronic systems, particularly biomedical ones. We shall also briefly discuss the benefits of fuel cells and ultra capacitors, devices that are capable of being used in conjunction with or instead of batteries, and that are likely to be important in the future.

Ultra-low-power systems have the potential to operate in a battery-free fashion by harvesting energy from their environment. Such energy may take the form of solar energy in a solar-powered system, chemical energy from carbohydrates in an enzyme-based system, mechanical energy from vibrations in the system's platform, thermal energy in systems that exploit temperature differences between themselves and their environment, or radio-frequency electromagnetic energy in the environment. In Chapter 26, we shall discuss several forms of energy harvesting. In this chapter, we will focus on energy harvesting with radio-frequency antennas or rectennas as they are sometimes called.

Radio-frequency electromagnetic energy is increasingly becoming ubiquitous due to the growing presence of cellular phones, local area networks, and other wireless devices. Systems that operate by harvesting electromagnetic energy need an antenna for sensing electromagnetic waves and a rectifier for converting the sensed ac energy to a dc power supply. The created power supply can then be used to power an ultra-low-power system such as a radio-frequency identification (RF-ID) tag in a grocery store or a medical monitoring tag on the body of a person (see Chapter 20 on medical monitoring). In this chapter, we shall discuss important principles and building blocks for creating such RF-energy-harvesting systems including antennas and rectifier circuits. We shall discuss an example of a complete functioning experimental system to illustrate system-level tradeoffs. We begin by reviewing the fundamentals of antenna operation.

This book, Ultra Low Power Bioelectronics, is about ultra-low-power electronics, bioelectronics, and the synergy between these two fields. On the one hand it discusses how to architect robust ultra-low-power electronics with applications in implantable, noninvasive, wireless, sensing, and stimulating biomedical systems. On the other hand, it discusses how bio-inspired architectures from neurobiology and cell biology can revolutionize low-power, mixed-signal, and radio-frequency (RF) electronics design. The first ten chapters span feedback systems, transistor device physics, noise, and circuit-analysis techniques to provide a foundation upon which the book builds. Chapters that describe ultra-low-power building-block circuits that are useful in biomedical electronics expand on this foundational material, followed by chapters that describe the utilization of these circuits in implantable (invasive) and noninvasive medical systems. Some of these systems include cochlear implants for the deaf, brain implants for the blind and paralyzed, cardiac devices for noninvasive medical monitoring, and biomolecular sensing systems. Chapters that discuss fundamental principles for ultra-low-power digital, analog, and mixed-signal design unify and integrate common themes woven throughout the book. These principles for ultra-low-power design naturally progress to a discussion of systems that exemplify these principles most strongly, namely biological systems.

With this chapter, we begin our study of circuits by understanding a classic feedback topology used to sense currents and convert them into voltage, i.e., transimpedance amplifiers. Transimpedance amplifiers are widely used in several sensor and communication applications including microphone preamplifiers, amperometric molecular and chemical sensors, patch-clamp amplifiers in biological experiments, photoreceptors for optical communication links, barcode scanners, medical pulse oximeters for oxygen-saturation measurements, and current-to-voltage conversion within and between chips. After a brief introduction to transimpedance amplifiers, we shall focus on a specific application, i.e., the creation of a photoreceptor, a transimpedance amplifier for sensing photocurrents on a chip. The photoreceptor example will serve as a good vehicle for concretely illuminating several issues that are typical in sensors and transimpedance-amplifier design. It will also serve as a good application for illustrating how the fundamentals of device physics, feedback systems, and noise affect the operation of real circuits and systems.

The photoreceptor discussed here was inspired by the operation of photoreceptors in turtle cones and was first described in [1]. A photoreceptor similar to the one described in this chapter is used to create the low-power pulse oximeter described in Chapter 20 and in [2]. The photodiode basics described here are also useful in understanding how low-power imagers (see Chapter 19) and solar cells (see Chapter 26) work.

An analog-to-digital converter converts real-world continuous analog signals into symbolic discrete digital numbers. It is often abbreviated as an ADC, A-to-D, or A/D. ADCs are ubiquitous in all electronic systems. A digital-to-analog converter performs the inverse function and is correspondingly abbreviated as a DAC, D-to-A, or D/A. Figure 15.1 shows the input-output curve of an ADC. The input and output are equal to each other within a quantization error of ± Δ/2, a consequence of the fact that we need to round up or round down real numbers to the nearest integer to represent them digitally. The digital numbers are usually represented with binary digits or bits. If, because of the input statistics, any error between [-Δ/2, + Δ/2] is equally likely, then, from evaluation of the second moment of a flat probability distribution, the rms error of the quantized representation of a real number can be shown to be Δ2/12. If the ADC samples its input at a sampling frequency fS, the power spectrum of the quantization noise is well approximated as being white from 0 to fS/2 and therefore having a noise per unit bandwidth of Δ2/(12(fS/2)).

In this chapter, we will discuss low-power transconductance amplifiers and circuits built with them such as first-order filters. Transconductance amplifiers are one of the most widely used building-block analog circuits. They implement a controlled linear conductance, which along with a set of capacitors, suffice to create any linear system with a finite number of state variables. Nonlinear transconductance amplifiers and capacitors can create any similar nonlinear dynamical system if the nonlinearity can be easily implemented by the transconductance amplifier. For example, tanh, sigmoid, and sinh nonlinearities are easily implemented in the subthreshold domain and are useful in a wide variety of computations based on statistical-mechanical exponential primitives.

We will begin by focusing on how to use feedback-linearization techniques to construct a low-power transconductance amplifier capable of wide-linear-range operation in the subthreshold and above-threshold domains. These techniques will involve using the well of the transistor as an input, using a well-known technique called source degeneration, a novel technique that we term gate degeneration, and a technique called bump linearization. We shall analyze how extending the linear range of an amplifier affects its offset and noise. We shall find that extensions of linear range arrive with extensions of dynamic range in thermal-noise-limited filters constructed with transconductance amplifiers but not in similar filters constructed with 1/f-noise-limited amplifiers.

In this chapter, we discuss how to model effects that arise in transistors with short channel lengths. Such short-channel transistors have correspondingly thin gate oxides, shallow source/drain junctions, high doping, and small operational supply and threshold voltages. The models are accurate for transistor lengths that range from 1 μm to 0.01 μm (10 nm), where semi-classical approximations of transistor function are still valid. We shall allude to some quantum phenomena as well. We shall begin by first describing the EKV model in a long-channel transistor. The EKV model is an insightful charge-based model that captures subthreshold and above-threshold operation in a simple analytic fashion. It is named after its originators, Enz, Krummenacher, and Vittoz. Then, based on a short-channel model in [2], we shall modify the long-channel EKV model to describe a short-channel effect that is important in above-threshold operation, namely velocity saturation. As the lateral electric field in a transistor increases with increasing drain-to-source voltage, the drift velocity of electrons in short-channel transistors begins to saturate and limit at a maximum velocity vsat; the drift velocity is then no longer related to the lateral electric field via the mobility proportionality constant as it is in long-channel transistors.

Energy surrounds us, is within us, and is created by us. In this chapter, we shall discuss how systems can harvest energy in their environments and thus function without needing to constantly carry their own energy source. The potential benefits of an energy-harvesting strategy are that the lifetime of the low-power system is then not limited by the finite lifetime of its energy source, and that the weight and volume of the system can be reduced if the size of the energy-harvester is itself small. The challenges of an energy-harvesting strategy are that many energy sources are intermittent, can be hard to efficiently harvest, and provide relatively low power per unit area. Thus, energy-harvesting systems are usually practical only if the system that they power operates with relatively low power consumption.

We shall begin by discussing energy-harvesting strategies that have been explored for low-power biomedical and portable applications. First, we discuss the use of strategies that function by converting mechanical body motions into electricity. A circuit model developed for describing energy transfer in inductive links in Chapter 16 is extremely similar to a circuit model that accurately characterizes how such mechanical energy harvesters function. Thus, tradeoffs on maximizing energy efficiency or energy transfer are also similar.

In many systems, certain important transistors in an architecture that determine most of its performance are operated such that the current through them has a large-signal dc bias component around which there are small-signal ac deviations. The voltages of these transistors correspondingly also have a dc large-signal operating point and small-signal ac deviations. If the ac deviations are sufficiently small, the transistor may be characterized as a linear system in its ac small-signal variables with the parameters of the linear system being determined by the dc large-signal variables. In this chapter, we will focus on the small-signal properties of the transistor.

Given that the transistor is a highly nonlinear device, it may be surprising that we are interested in its linear small-signal behavior. However, the transistor's linear small-signal behavior is most important in determining its behavior in analog feedback loops that are intentionally designed to have a linear input-output relationship in spite of nonlinear devices in the architecture. For example, most operational amplifier (opamp) circuits are architected such that negative feedback inherent in the topology ensures that the input terminal voltages of the opamp, v+ and v−, will be very near each other and, therefore, that the small-signal properties of the transistors in the opamp determine its stability and convergence in most situations.

Implantable electronics refers to electronics that may be partially or fully implanted inside the body. Several implanted electronic systems today have revolutionized patients' lives. For example, more than 130,000 profoundly deaf people in the world today have a cochlear implant in their inner ear or cochlea that allows them to hear almost normally. Some cochlear-implant subjects have word-error recognition rates in clean speech that are better than those of normal hearing subjects, and they understand telephone speech easily. Cochlear implants electrically stimulate the auditory nerve, the nerve that conducts electrical impulses from the ear to the brain, with an ac current. Cochlear implant subjects are so profoundly deaf that even the feedback-limited ~1000× gain of a hearing aid is not large enough to help them hear. Therefore, an implant that directly stimulates their auditory nerve is necessary. Cochlear implants today are partially implanted systems: the electrodes and a wireless receiver are implanted inside the body while a microphone, processor, and wireless transmitter are placed outside the body.

Patients with Parkinson's disease have had their quality of life significantly improve because of a deep brain stimulator (DBS) that has been fully implanted inside their bodies. This stimulator provides ac electrical current stimulation to a highly specific region in their brain, which is most commonly the subthalamic nucleus (STN).

In this chapter, we present ten general principles for ultra-low-power analog and mixed-signal design. We shall begin by comparing the paradigms of analog computation and digital computation intuitively and then quantitatively. The quantitative analysis will be based on fundamental relationships that dictate the reduction of noise and offset with the use of power, area, and time resources in any computation. It shall reveal important tradeoffs in how the power and area resources needed for a computation scale with the precision of computation in analog versus digital systems. From these results, we shall discuss why, from power considerations, there is an optimum amount of analog preprocessing that must be performed before a signal is digitized. If digitization is performed early and at high speed and high precision, as is often the case, the power costs of analog-to-digital conversion and digital processing become large; if digitization is performed too late, the costs of maintaining precision in the analog preprocessing become large; at the optimum, there is a balance between the two forms of processing that minimizes power.

There are detailed similarities between power-saving principles in analog and digital paradigms because they are both concerned with how to represent, process, and transform information with low levels of energy. We shall itemize and discuss several of these similarities.

Noninvasive medical electronics refers to electronics for medical instruments that do not invade or penetrate the body. The sensors in these instruments can and often do contact the body. Examples of such sensing include:

• Electrocardiogram (EKG or ECG) measurements of heart function.

• Photoplethysmographic (PPG) measurements of blood-oxygen saturation, or pulse oximetry.

• Phonocardiogram (PCG) measurements of heart sounds.

• Electroencephalogram (EEG) measurements of brain function.

• Magnetoencephalogram (MEG) measurements of brain function.

• Electromyogram (EMG) measurements of muscle function.

• Electrooculogram (EOG) measurements of eye motion.

• Electrical impedance tomography (EIT): measurements to infer composition of the body's tissues. Impedance cardiography (ICG) is a further specialization within the field.

• Temperature measurements.

• Blood-pressure (BP) measurements.

• Pulmonary auscultation (lung-sound) measurements.

• Biomolecular detection of small molecules, DNA, proteins, cells, viruses, or microorganisms for point-of-care or lab-on-a-chip applications, which often exploit BioMEMS (Bio Micro Electro Mechanical Systems) and microfluidic technologies, mostly in a noninvasive fashion thus far.

When such sensing is done chronically, for example as heart tags on patients with a high risk for myocardial infarction (MI), i.e., a heart attack, it is often called wearable electronics. The various sensors on the body may form a body sensor network (BSN) or body area network (BAN) that communicate with each other and/or the patient's cell phone, or with an RF-ID, Bluetooth, Zigbee, MICS, UWB, or other wireless receiver in the home, hospital, or battlefield.

In this chapter, we shall review important principles for ultra-low-power digital circuit and system design. We shall focus on operation with extremely low power-supply voltages and on subthreshold operation, although we shall provide some analysis of moderate-inversion and strong-inversion operation with the EKV model as well. As Chapter 6 on deep submicron effects in transistors discussed, because threshold voltages scale significantly less strongly than power-supply voltages, subthreshold operation is an increasingly dominant fraction of the voltage operating range. Subthreshold operation has become and will continue to get increasingly fast such that ultra-low-power operation in this regime does not sacrifice bandwidth in many applications. In biomedical and bioelectronic applications, subthreshold operation is ideal since bandwidth requirements are typically modest while energy efficiency is of paramount importance. An insightful paper by Meindl, that was way ahead of its time, pioneered subthreshold digital design. An analysis by Burr and Peterson analyzed the optimal energy efficiency of ultra-low-power subthreshold circuits. A more recent publication by Vittoz, the pioneer of subthreshold analog design, has analyzed issues in subthreshold digital design using his EKV model. Through such pioneering and other work, subthreshold digital design has been revived and is an active field of research in several academic and industrial institutions.

We shall begin by discussing the operation of a subthreshold CMOS inverter. Operation in the subthreshold regime is highly subject to transistor mismatch.

Devices that are hooked to each other at various terminals create a circuit. Almost all nontrivial circuits comprise topologies where output terminal(s) are directly or indirectly coupled back to input terminal(s), thus forming a feedback circuit. When the output feeds back to reduce the effects of the input, the feedback is termed negative feedback, and when the output feeds back to increase the effects of the input, the feedback is termed positive feedback. Purely feed-forward circuits are usually simple to build and easy to analyze, even when nonlinear, such that most of the complexity and richness in circuits arises from the feedback embedded within them.

Negative-feedback circuits function by creating forces within the circuit that attempt to restore its signals to a desired equilibrium point if these signals deviate away from this point. Negative-feedback circuits often serve regulatory functions improving the precision of the output to that provided by a precise equilibrium-setting reference input and/or that of a precise sensor or feedback network. Such precision is achieved in spite of imprecision in an actuator or feed-forward network in the circuit and/or disturbances present at the output of the circuit.

Positive-feedback circuits function by creating forces within the circuit that attempt to move its signals further away from a point if these signals deviate from that point.