1.1.1 Market Demand

Consumers continue to enjoy and, in consequence, demand smaller and more functionally dense products. Unfortunately, tiny devices necessarily constrain sources to small spaces, limiting the amount of energy they store and how much power they supply to impractically low levels. Consider, to cite an illustrative example, that 100 μW, which is drastically below what wireless telemetry requires today to transmit over a distance of 100 m, completely discharges a 5 × 3.8 × 0.037-cm³ 1 mA·Hr thin-film lithium ion battery (Li ion) in 10 h. Adding functionality, as in the case of cellular phones and the applications they now support, only exacerbates the issue because the extra power overhead drains a source that is already easily exhaustible even faster. Although today’s efforts aim at reducing the energy that each additional function requires, the cumulative load that wireless transmission and several low-power functions present to a miniature source is nonetheless substantial, reducing the operational life of the system considerably, to the point at which consumers lose interest.

Perhaps a more significant application space emerges in the wake of integration in the form of in situ but nonintrusive devices, such as biomedical implants. While the motivation for and benefits of monitoring biological activity with in vivo contraptions without frequently replacing or recharging batteries are for the most part obvious, the commercial and societal advantages of retrofitting low-overhead, noninvasive intelligence into expensive and difficult-to-replace technologies like the power grid are arguably more economically, sociologically, and ecologically profound. Feeding performance metrics and the use of energy in a factory into a central processor, for instance, to determine the optimal use of power cannot only save energy on a grander scale when applied across a wide region, but also reduce the emission of environmentally harmful by-products and the need for politically charged petroleum. From a commercial standpoint, the potential ubiquity for such miniature sensors across factories, hospitals, airports, farms, homes, subway stations, shopping malls, and other such centers rivals and quite likely exceeds that of cellular phones at maybe 10 to 100 sensors for every 10 × 10 m² of surface area.

1.1.2 Energy and Power Requirements

Modern microelectronic systems necessarily embed both analog and digital functions—analog because they must not only manage and process continuous real-life signals (e.g., seismic activity, sound waves, motion, temperature, pressure, and others) but also draw energy and condition power from nonideal sources. State of-the-art applications, however, also include digital blocks because binary processes enjoy considerably higher noise margins, which is another way of saying they exhibit higher signal-to-noise ratios (SNRs). The fact is that a small voltage variation, say, from 20 to 400 mV, across a 0–1.8 V digital signal has little to no impact on the output word and its bit-error rate (BER), whereas the same variation in a rail-to-rail analog signal swing essentially eradicates more than 1% to 22% of the data. All this is to say the system draws quiescent and switching power from the source, as Figure 1.1 shows [1].

Because the going trend is to incorporate more functionality into a product, a fixed supply voltage is no longer optimal, especially when seeking to extend operational life. While digital-signal processors (DSPs), for example, may draw milliwatts at 1 V, voltage-controlled oscillators (VCOs) and analog–digital converters (ADCs) can demand considerably less power at maybe 1.8 V and power amplifiers (PAs) significantly more power at 3 V. The end result is a system that, to operate optimally, includes multiple supply voltages capable of feeding diverse power levels.

In the end, irrespective of the supply voltages needed, featuring multiple tasks ultimately burdens a source with additional loads. The problem with a miniature source is that energy is scarce and power levels are low. One way of reducing power in the system is to duty-cycle or time-division multiplex tasks across time so that no more than one set of interdependent functions operates at any given point. Similarly, powering blocks only when absolutely necessary, as in on-demand, reduces energy that the system would otherwise waste. As a result, systems today dynamically change operating modes on the fly, as Figure 1.1 illustrates, where all average and peak power, pulse width, and switching frequency change according to the tasks performed.

Extending the operational life of smart microsensors remains a challenge, even after power-moding and duty-cycling functions. The point is that marketable micro-systems must draw little to no power. Luckily, portable and sensor applications naturally call for low duty-cycle operation because devices need not function continuously. The cellular phone, for instance, is for the most part alert—that is, ready to receive calls—and while transmission demands milliwatts, awareness only requires microwatts, which is why radio-frequency (RF) power amplifiers are mostly in the light-to-moderate power region of operation, as Figure 1.2 demonstrates [2]. Said differently, while talking continuously on the phone for 3 to 5 hours exhausts a fully charged battery, idling might do so in 5 to 7 days.

While energy and power unavoidably relate, meeting the energy requirements of a microsystem does not necessarily imply the source can also supply the power needed. This means that reducing losses to save energy, for example, by shutting off unused circuit blocks, is as important as duty-cycling tasks over time to decrease power. The source and the circuits that manage the source must therefore account for and respond to various mixed-signal modes whose average and peak power levels, pulse widths, rise and fall times, and switching frequency change over time.

1.1.3 Technology Trends

Trends in technology dictate how and to what extent emerging applications succeed. Not surprisingly, the public’s affinity to small microelectronic gadgets is motivating scientists and engineers to find innovative ways of confining products into tiny spaces. Accordingly, incorporating as much as possible into the silicon die has been and continues to be increasingly popular. Research and industry are not only building more semiconductor devices on a common substrate, but also postprocessing copper layers, microelectromechanical systems (MEMS), and MEMS-like inductors on top.

The problem with system-on-chip (SoC) integration is higher cost because arbitrarily adding processing steps of increasing complexity to the fabrication process diminishes the commercial appeal of the product. As a result, engineers are also copackaging technologies, for example, like high-frequency gallium–arsenide (GaAs) dies with low-cost complementary metal–oxide semiconductor (CMOS) dies. Power integrated circuit (IC) designers are similarly integrating relatively mature and, therefore, lower cost discrete 1–10 μH power inductors in the 2 × 2 × 1 mm² range with their controlling CMOS and bipolar circuits. SoC and system-in-package (SiP) integration, however, are often insufficient, so engineers are also exploring system-on-package (SoP) strategies, for example, by attaching antennae and thin-film Li ions to the external surface of the material encapsulating the silicon die.

Higher SoC integration means machinery with finer photolithographic resolutions, for example, of 45 nm semiconductor devices with thinner barriers and smaller junctions of increasing doping concentration. The resulting electric fields are more intense and their corresponding breakdown voltages are consequently lower, on the order of 1–1.8 V, constraining circuits to operate with lower supply voltages. While reducing the voltages across charging and discharging parasitic capacitors and steady-state loads mitigates power losses, a low supply also decreases usable dynamic range, which translates to a lower SNR and, more generally, reduced noise margin.

Unfortunately, while additional on-chip functions inject and cross couple more noise, SoC, SiP, and SoP designs suffer from diminished filtering capabilities, challenging engineers to design with even lower dynamic ranges. The problem is that, unlike in discrete printed circuit-board (PCB) implementations, on-chip solutions cannot possibly hope to attenuate noise by sprinkling several nanofarad and even microfarad capacitors across sensitive supplies, input pins, and output pins without increasing the silicon real estate to cost-prohibitive levels. Just to cite an example, consider that capacitance-per-unit areas of 15–20 fF/μm² are typical in state-of-the-art technologies and one 1 nF would occupy roughly 225 × 225 to 260 × 260 μm² of the die, which today probably represents one-quarter to one-eighth of the total area of a relatively complex system. Regrettably, increasing areas beyond, say, 2 × 2 mm² decreases the commercial appeal of the chip because the silicon wafer’s die density drops, which is indicative of how many chips and how much profits each 8-or 12-in. wafer produces. Inductors, incidentally, are even more costly because air-gap inductors not only occupy considerable space, which limits inductances to maybe 40–100 nH, but also exhibit relatively poor quality factors, which is another way of saying they include considerable parasitic series resistances.

The lower filter densities and breakdown voltages that SoC, SiP, and SoP strategies impose on the design shift the burden of attenuating noise to the power-supply and signal-processing circuits of the system. Functional blocks, like phase-locked loops (PLLs), ADCs, VCOs, and DSPs, must survive more noise in the substrate and supplies and the linear and switched regulators that supply them must also generate less and more effectively suppressed switching noise. In other words, higher bandwidth and higher power-supply rejection (PSR) in supply and interface circuits are necessary to counter the effects of noise in time, before they propagate through the system. To add insult to injury, supply voltage variations must also be lower, on the range of 10–50 mV, to extend dynamic range maximally under low breakdown voltages; this is especially difficult without a large on-board capacitor in the presence of fast rising and falling load dumps—and all this with only cost-effective CMOS and maybe bipolar–CMOS (BiCMOS) technologies.

1.2.1 Light Energy

Solar light is perhaps the most appealing source because, when exposed to the sun, photovoltaic (PV) cells can generate 10–15 mW/ cm² [4], which is well above those of its counterparts. In effect, incoming photons break loosely tied electrons, as Figure 1.4 shows, and the built-in potential across the p–n junction shown in Figure 1.4(a) pulls these free electrons to the n-type region to establish current flow. The voltage that results across the cell, however, forward biases the parasitic diode that Figure 1.4(b) models to sink and lose some of the generated current.

The problem with solar energy is that output power falls drastically when direct sunlight is unavailable, down to 10–20 μW/ cm². These power levels are so low that the act of harnessing, which is the work performed by circuits to transfer energy into a battery, may dissipate most, if not all of the power available, negating the harvesting objective of the system. Notwithstanding, a few researchers find solace in how often microsystems idle because producing any power whatsoever for extended periods still translates to appreciable energy in the long run.

Industry and research today concentrate most of their efforts on either larger scale systems, where larger surface areas compensate for the lower power densities that artificial lighting generates, or smaller photovoltaic cells that receive direct sunlight, where even 2 × 2 mm² can generate substantial power for a microsystem. Relying on solar energy, however, limits wide-scale adoption because applications may not always place harvesting nodes in places that receive direct sunlight, so overcast days and evenings interrupt the harvesting process. Many applications, in fact, are not only indoors, like wireless microsensors in factories, hospitals, and homes, but also mobile, where the host may or may not receive sunlight, as with automobiles, bicycles, airplanes, and people. All of this is to say that harnessing artificial lighting is important, but also challenging under microscale constraints.

1.2.2 Kinetic Energy

By definition, mobile products, which represent an increasingly expansive market space, move. And from a commercial standpoint, harnessing kinetic energy from motion is attractive because vibrations are consistent and abundant—be it an engine at 1,000 to 10,000 revolutions per minute or a person at one to two strides per second. Kinetic transducers can also generate up to 200 μW/ cm², providing the onboard harvesting microelectronics more power to operate than artificial lighting can. Although power is nowhere near what photovoltaic cells produce when exposed to direct sunlight, harnessing power from dependable 1–300 Hz vibrations over extended periods can accumulate appreciable energy.

Electromagnetic transducer. One way of drawing power from motion is electromagnetically [5], by allowing vibrations to move a mass attached to a conducting coil about a stationary magnet, as Figure 1.5 illustrates. The electromagnetic field that the magnet generates works against the kinetic force in the moving mass to dampen and decelerate it, thereby transferring the energy in the mass into the coil in the form of a voltage. The role of the spring is to avoid losing remnant energy by temporarily storing and releasing whatever kinetic energy remains so that the mass may once again move back toward the magnet. Unfortunately, harnessing energy this way is difficult in small spaces because power and voltages are substantially low at approximately 1 μW/ cm³ and tens of millivolts. Additionally, conforming and integrating a magnet and a coil into a microsystem also present considerable challenges.

Electrostatic transducer. Perhaps a more effective means of harnessing ambient kinetic energy is by pumping charge electrostatically into a storage device because the power generated is on the order of 50–100 μW/ cm² and variable capacitors are more easily integrated with MEMS technologies. The idea is for vibrations to vary the vertical or lateral separation distance between two parallel plates of a variable capacitor C_VAR, like the ones that Figure 1.6(a) and 1.6(b) illustrate, so that, when a battery or another capacitor fixes the voltage across C_VAR to precharge voltage V_PC, a reduction in capacitance pumps charges q_C out of C_VAR:

and generates output dq_C/ dt current [6]. Alternatively, a reduction in capacitance raises C_VAR’s v_C when C_VAR is disconnected (i.e., with a fixed q_C) to augment C_VAR’s energy E_C:

This latter scenario produces a net energy gain because, while C_VAR decreases linearly in E_C, ${\text{v}}_{\text{C}}^2$ rises quadratically. Allowing v_C to increase to, say, 100–300 V, however, which is not atypical, exceeds the breakdown limits of most standard CMOS and BiCMOS process technologies. As a result, at least for the time being, constraining v_C to voltages that near the breakdown limits of the process seems more practical than fixing q_C.

The electrical equivalent of these moving parallel plates is the variable-capacitor model that Figure 1.6(c) shows. Unfortunately, the physical device also includes parasitic static capacitors C_P, C₊, and C_–. Contact material also introduces a series of parasitic resistance R_S that dissipates ohmic power. Of these, C_P, C₊, and C_– are often more problematic because they drain some of the energy that C_VAR harnesses from motion.

Piezoelectric transducer. Although piezoelectric transducers are perhaps more difficult to integrate, they can generate higher power, up to maybe 200 μW/ cm². Here, when fastened to a stationary base, as Figure 1.7(a) illustrates, a shimmed piezoelectric cantilever generates electrical energy in the form of alternating charge when mechanical energy in motion induces the material to bend and oscillate about its fixed point [7]. The advantages of this approach are that piezoelectric research is relatively mature in its evolution and transducers generate higher power than their electrostatic and electromagnetic counterparts. The disadvantage, of course, is integrating the device into a small space, which is why attaching it to the outer surface of a chip is probably one of the best ways of realizing a small SoP platform.

Operationally, motion rearranges and polarizes the molecular structure of a piezoelectric material to generate charge. The resulting electrical current, which i_PZ in Figure 1.7(b) models, charges and discharges the capacitor C_PZ that appears across the terminals of the transducer. The magnitude and direction of i_PZ change with the acceleration and orientation of the moving mass. Unfortunately, contacts and leakage paths introduce series and parallel resistances R_S and R_P, but not to the extent that they negate the harvesting benefits of the structure. Ultimately, the energy that C_PZ receives is the power the transducer draws from motion, which returns to the mechanical domain when uncollected.

1.2.3 Thermal Energy

Temperature represents another source of energy. Thermocouples that rely on the Seebeck effect, for example, derive thermal energy from a temperature difference. Here, as in Figure 1.8(a), heat flux carries dominant charge carriers: electrons in n-type and holes in p-type materials, from high-to low-temperature regions, much like diffusion carries particles from high-to low-concentration regions. Here, however, departing electrons in the n-material leave behind ionized molecules in the hot side that attract the electrons that the p-region generates when holes drift toward the cold end. As these electrons flow from p-to n-type regions to deionize molecules, they harness thermal energy and jump to higher energy states. This way, electrons accumulating at the cold end of the n-type rod establish a negative potential with respect to the holes that accrue at the cold side of the p-type counterpart, generating thermally induced voltages across each pile. Since each n–p pile combination generates a small voltage v_TH, engineers often cascade several of these in series to produce a combined voltage v_TEG, which is higher. The silicon rods and interconnecting metals, of course, introduce parasitic series resistances that R_S in Figure 1.8(b) models.

Unfortunately, high temperature alone is not sufficient to generate power. Said differently, a thermocouple generates a voltage only when a temperature differential exists. Designers, as a result, usually attach one of the terminals to a heat-absorbing material. This requirement, however, impedes integration in several ways. In the first place, a heat sink occupies considerable space. In the second, finding a cool source against which to attach the transducer is not always possible. And, thirdly, output power is proportional to the temperature difference across the device and, because microsystems are tiny, temperature differentials are correspondingly low, below maybe 10°C. The voltage and power levels they produce are consequently low at about 15 μW/ cm³ [5], which nears the levels produced by photovoltaic cells when illuminated with artificial lighting and electromagnetic transducers in response to vibrations. Note that power is also proportional to the Seebeck coefficient of the thermoelectric materials used.

1.2.4 Magnetic Energy

There is also energy in a magnetic field, such as around an AC power line. Drawing power from such a source inductively, however, is challenging in three respects. To start, as in the case of harnessing kinetic energy electromagnetically, the power levels and voltages generated are substantially low at microwatts and millivolts. Unfortunately, the act of transferring energy already dissipates microwatts and, therefore, drains most of the little power that is available. Plus, conditioning power in the form of millivolts is, from an integrated circuit’s perspective, problematic. As a result, some researchers opt to accumulate and convert magnetic energy into the mechanical domain first, so that a kinetic transducer can then generate power in a more benign form. Each conversion, however, suffers from power losses that further reduce what little energy was available in the first place.

The second issue with an electromagnetic source is that power falls drastically with distance: quadratically in the far field and even faster in the near field. Therefore, to produce practical power levels, the transducer should remain close to a rich source. Inductively coupling energy across a near-field separation of, say, 8 mm to charge the battery of a portable device like a cellular phone wirelessly is possible this way. However, increasing the separation beyond this point, which many remote wireless-sensor applications demand, lowers system efficiency to such an extent that extracting power is no longer practicable. The third challenge with harvesting magnetic energy is, of course, integration, because tiny inductors harness a small fraction of the magnetic energy available.

1.2.5 Conclusions

As mentioned earlier, there is no ideal source because, while harvesters, atomic batteries, and fuel cells store appreciable energy, they supply little power. Conversely, inductors and capacitors source high power, but stow little energy. And Li ions and super capacitors are moderate in both respects, sacrificing energy for power and power for energy. Additionally, while filter passives supply power almost instantaneously, Li ions and supercapacitors require time to respond—and fuel cells even more time—whereas atomic batteries and harvesters remain virtually unresponsive to load changes. As a result, systems today normally supply what is close to instantaneous power, which refers to the rising and falling edges of the load shown in Figure 1.1, with capacitors and semisustained bursts with a Li ion.

Relegating the tasks of storing energy and supplying power bursts to a Li ion or supercapacitor, however, represents a compromise in energy that is difficult to accept under microscale constraints where both energy-and power-density requirements are severe. Replacing the Li ion with a fuel cell similarly trades power for energy, loading capacitors and inductors with more power and, as a result, increasing output voltage variations in response either to load dumps or space requirements. Further decoupling energy from power is therefore important in microsystems, which is the motivation for classifying technologies into energy sources, energy/ power caches, and power supplies.

Harvesters, atomic batteries, and fuel cells fall under the category of energy sources. Of these, atomic batteries are less popular because they are unsafe, and costly and tiny fuel cells because they produce chemical by-products. Li ions and supercapacitors basically cache energy and power for moderate loads, but while Li ions are perhaps more mature and popular, ultracapacitors survive more charge–discharge cycles, which is why the latter are garnering interest, albeit with higher leakage. Lastly, capacitors and inductors both supply power, but only capacitors supply instantaneous current, so systems use capacitors to store charge and supply quick load dumps and inductors to supply the collective steady-state needs of the load and momentary demands of capacitors.

Of the ambient sources discussed here, solar energy generates the most power, followed by kinetic energy when harnessed by piezoelectric or electrostatic transducers. Thermal and magnetic energy are less appealing under microscale integration because their power and voltage levels are low. Similarly, artificial lighting also generates low power levels, as does drawing kinetic energy with an electromagnetic device. As a result, some engineers favor solar photovoltaic and vibration-sensitive piezoelectric and electrostatic transducers over their competing counterparts.

1.3.1 Linear Switch

Perhaps the most accurate means of conditioning power is linearly because the circuit is always alert, ready to respond to any and all variations in load and source. In other words, in addition to not generating switching noise, a linear conditioner reacts to oppose the effects of disturbances injected and coupled into its output. Admittedly, the circuit suppresses noise only up to its bandwidth [9], beyond which the system is unable to respond. Nevertheless, a linear circuit is relatively simple, so it reaps the high-bandwidth benefits that smaller devices and fewer transistors offer.

Architecturally, as Figure 1.9 shows, a controller modulates the conductance of a series switch linearly to conduct whatever current the system demands. In the case shown, p-channel metal–oxide semiconductor (MOS) field-effect transistor (FET) M_SW is only a sample, though a popular embodiment of the switch. Low-dropout (LDO) linear regulators, for example, use this topology and sample output voltage v_O to ensure that v_O remains near a user-defined target. To illustrate another application, sensing input current i_IN and regulating M_SW’s conductance or equivalent series resistance R_SW to draw as much i_IN as the source allows satisfy the objectives of a harvester.

Irrespective of its conditioning aim, what is ultimately important to conclude is that the circuit does not generate switching noise; current i_IN only flows to the output (i.e., in one direction), so input v_IN must exceed output v_O, and the circuit dissipates conduction power across M_SW as P_SW:

and quiescent power through the controller as P_C for a total power loss P_LOSS of

where v_IN – v_O is the voltage across M_SW and I_Q that the current v_IN supplies to the controller. Although all three points are important, the last one deserves attention because microsystems cannot afford to lose power indiscriminately. Efficiency here, in fact, cannot ever reach output-to-input voltage ratio v_O / v_IN because the voltage across M_SW is v_IN – v_O and I_Q is a finite and load-independent physical requirement for the circuit to operate properly:

Consider, for example, that when a 3.6 V Li ion supplies a 1.8 V load, η_L is no better than 50%, and that is only when I_Q is negligibly smaller than i_IN, which is largely not the case in microsystems, particularly when they idle.

1.3.2 Switched Capacitors

Introducing one or more intermediate steps into the energy-transfer process further decouples the needs of the input from those of the output, adding flexibility to the conditioning function. A transitional stage, therefore, receives, stores, and releases energy when prompted, as a capacitor would when configured accordingly. Charge pumps, as many circuit design engineers refer to them, switch the connectivity of “flying” capacitors in alternating phases across a switching period T_SW to first receive energy from a source, be it the actual input or a previous stage, and then release it to a load, which could be just another stage. Charging several flying capacitors in parallel, for instance, from input v_IN, as C_F1 through C_FN illustrate in Figure 1.10, and discharging them in series to a load effectively “steps up” or “boosts” the input v_IN to a higher voltage v_O, which is an otherwise impossible feat for a linear conditioner to achieve. Similarly, just to show how flexible the architecture can be, charging capacitors from v_IN in series and connecting them in parallel to v_O in the alternate phase “steps down” or “bucks” v_IN to a lower voltage.

This flexibility, however, results at the expense of noise because decoupling v_IN from v_O implies that v_IN and v_O are, at times, disconnected, so i_IN momentarily raises v_IN and the load similarly discharges whatever output capacitance C_O is present at v_O. Allowing v_IN and v_O to rise and fall this way before periodically loading and recharging them with the flying capacitors creates a systematic noise ripple in the input and output. To this, the switches whose task is to reconfigure the connectivity of the network, inject additional noise because the signals that drive them at switching frequency f_SW rise and fall quickly across maybe 10 ns or less—coupling displacement noise energy into sensitive nodes through parasitic gate-source and -drain capacitors C_GS and C_DG that complementary MOS (CMOS) switches embody.

Because the voltages across conducting switches are dynamic and decrease with time, switched-capacitor circuits do not dissipate the quasistatic and limiting v_IN -v_O voltage-drop conduction power that linear conditioners do across M_SW. Still, the switches lose momentary switching losses when conducting current with decreasing, but nonetheless, finite voltages across them. The initial voltage across the switch that connects v_IN to the flying capacitors in phase 1 of Figure 1.10, for example, is the voltage the load drooped in phase 2, which is often not a trivial amount. Similarly, the fully charged flying capacitors and the drooped C_O also present a voltage difference to their connecting switch at the beginning of phase 2. To help quantify these losses, consider that while v_IN in Figure 1.11(a) loses energy E_IN to charge equivalent flying capacitor C_F from v_C(INI) to v_IN:

C_F‘s energy E_C rises from E_C(INI) to E_C(FIN) for a positive gain of ΔE_C:

which is nonetheless a fraction of E_IN, so the switch loses the difference [10] as E_SW:

Similarly, because connecting capacitors in parallel like in Figure 1.11(b) amounts to charging them in series from a source whose voltage is the initial voltage across the switch v_C(INI) -v_O(INI) or Δv_SW, the switch consumes

of the energy that was initially stored in C_EQ as 0.5 ${\mathrm{C}}_{\mathrm{E}\mathrm{Q}}{\mathrm{v}}_{\mathrm{C}\mathrm{(}\mathrm{I}\mathrm{N}\mathrm{I}{\mathrm{)}}^2}$, where C_EQ is the series combination of C_F and C_O. In other words, charge pumps generally and necessarily lose switching energy 0.5 ${\mathrm{C}}_{\mathrm{E}\mathrm{Q}}\Delta {\mathrm{v}}_{\mathrm{S}{\mathrm{W}}^2}$ in the interconnecting switches.

Although this fundamental loss in the switch is by no means negligible, it decreases with reductions in steady-state i_IN(AVG) because all the capacitors droop less (so Δv_SW is smaller) with lower currents, which is good for microsystems because they supply and demand little power. In practice, however, v_IN still supplies the energy switching noise and leakage currents drawn from the capacitors, the quiescent power that energizes the controller, and the power parasitic gate and base capacitors require charging and discharging every time they switch. So to summarize, a charge pump generates switching noise, can buck or boost its input, and dissipates 0.5 ${\mathrm{C}}_{\mathrm{E}\mathrm{Q}}\Delta {\mathrm{v}}_{\mathrm{S}{\mathrm{W}}^2}$ across interconnecting switches, which rises quadratically with i_IN(AVG). Relative to its linear counterpart, the output is noisy and less accurate, but also flexible. The circuit also impresses voltages across the switches that decrease not only with load but also with time. Additionally, charge pumps dissipate power to charge and discharge parasitic capacitors that would normally not switch periodically in a linear conditioner.

1.3.3 Switched Inductor

Just as charge pumps employ capacitors to transfer energy, magnetic-based switching converters use inductors to cache and release input energy temporarily to one or several loads [11]. They achieve this by energizing and draining inductors in alternating cycles. In more specific terms, an input source v_IN energizes a transfer inductor L_X by inducing L_X to draw current from v_IN—that is, by connecting the other terminal of L_X to a lower voltage like ground in phase 1 of Figure 1.12(a). During this time, L_X’s current i_L rises linearly, as the graph in Figure 1.12(b) shows, because L_X’s voltage v_L or L_Xdi_L/ dt is positive and, for the most part, constant at, in this case, v_IN – 0, or more generally, at energizing voltage v_E. Reversing the polarity of v_L to, say, –v_O, as shown in phase 2 of Figure 1.12(a), causes L_X to release the energy it received during phase 1. Because the circuit either regulates the voltage across a load or charges a battery with a well-defined, low-ripple, slow-changing voltage, v_O is, for all practical purposes, a constant and, in this case, also L_X’s de-energizing voltage v_DE. As a result, i_L generally rises at v_E/ L_X when v_IN energizes L_X across phase 1 and falls at v_DE/ L_X when L_X delivers energy to v_O in phase 2 [12].

A switched-inductor conditioner embodies a few idiosyncrasies worth mentioning. First, L_X conducts a steady-state current i_L(AVG) about which the ripple in Figure 1.12(b) rides. Conducting current continuously like this places the circuit in what experts call continuous-conduction mode (CCM). Inducing L_X to stop conducting current momentarily, which is equivalent to i_L reaching zero and remaining there for a finite fraction of the period, amounts to operating in discontinuous-conduction mode (DCM). What sets i_L(AVG) is either the power needs of a load or the sourcing capabilities of its source.

Another trait or, rather, feature is that a switched-inductor circuit can buck or boost v_IN because L_X can release energy to any output voltage as long as energizing and de-energizing voltages v_E and v_DE remain positive and negative, respectively. In fact, permanently attaching L_X’s input terminal to v_IN is a derivative embodiment of the general form shown in Figure 1.12(a) that, to release L_X’s energy, requires v_O to exceed v_IN. Likewise, connecting L_X’s output terminal to v_O directly demands that v_IN stay above v_O for L_X to energize. These two special cases implement the well-known boost [13] and buck [14] configurations reported in the literature. One last peculiarity to note is that inductors, unlike capacitors, receive or deliver energy, but do not store it statically over time; this is not a problem in conditioners because the overriding aim is to draw and deliver power—not store it, as rechargeable batteries and large capacitors would.

Within the context of operational life and efficiency, the only elements in a power stage that incur first-order conduction losses are the switches because a capacitor does not conduct steady-state current and the steady-state voltage across an inductor is zero. Interestingly, while capacitors hold the initial voltage across a switch by sourcing whatever instantaneous currents are necessary, an inductor maintains its current steadily by instantly swinging its voltage until it finds a suitable source or sink for its current. In other words, after a connecting switch opens, i_L raises or lowers L_X’s open terminal voltage instantaneously until a source or sink clamps it. As a result, the small series resistance R_SW in the interconnecting switches and power path drop a voltage v_SW or i_LR_SW that consumes power P_SW or iL(RMS)2R_SW. Since R_SW is small, v_SW and P_SW are both low. This quasi-lossless property is the driving force behind the commercialization and general adoption of switched-inductor conditioners.

In practice, these conduction losses are small, but nevertheless finite, so they reduce efficiency, as do second-order losses similar to those found in linear and charge-pump circuits. The controller, for example, requires sufficient quiescent current to manage the system and deliver a command signal in time before the onset of the next switching cycle. The circuit also dissipates switching power to charge and discharge the parasitic capacitors that the switches present to the controller. When lightly loaded, in fact, second-order quiescent and gate-drive losses become as important as and, in some cases, more important than first-order switch losses because the voltage dropped and power lost across the switches fade with decreasing load levels [15].

Note, however, that good and reasonably sized power inductors are bulky and difficult to integrate [16]. The unfortunate truth is that on-chip inductances typically fall below 100 nH and introduce considerable parasitic equivalent-series resistances (ESRs) that further dissipate conduction power and degrade efficiency. Discrete inductors, on the other hand, are considerably better and, to a certain extent, also relatively small—for example, a 2 × 2 × 1 mm³ 1 μH inductor that saturates at 1.8 A and introduces 0.2 × of series resistance. Accordingly, switched-inductor conditioners in microsystems should employ and co-package no more than one power inductor, which is why single-inductor multiple-output (SIMO) strategies are garnering interest in research circles [11]. Using smaller inductances is certainly possible, though at the expense of higher conduction losses because inductor ripple current Δi_L increases or gate-drive losses because switching frequency f_SW rises to bound Δi_L.

Because these magnetic-based circuits switch, they inject switching noise, like charge pumps do. If L_X connects directly to v_IN or v_O, however, as in boost or buck converters, L_X’s average current i_L(AVG) matches the source or load to keep the capacitance at v_IN or v_O from charging or discharging considerably. Even so, v_IN and v_O do not source or sink ripple currents, so Δi_L charges and discharges C_IN or C_O to create a corresponding ripple in v_IN or v_O. Unfortunately, decoupling the input or output from L_X with a switch, as in buck or boost converters, allows the source or load to charge or discharge C_IN or C_O when the switch opens, increasing the ripple in v_IN or v_O. In all, these magnetic conditioners generate switching noise, can buck or boost their inputs, dissipate iL(RMS)2R_SW across their interconnecting switches that rises quadratically with i_IN(AVG), and, when applied to microsystems, should employ no more than one co-packaged inductor.

1.3.4 Conclusions

In comparing performance, the functionality of the conditioners precedes all other parameters, and in the case of microsystems, losses arguably follow because they limit how long a system operates. So, on the first count, switching circuits can boost their inputs while linear circuits cannot—except that a boosting function is not always necessary. Consider, for example, that while boosting a 0.4 V photovoltaic cell to charge a 2.7–4.2 V Li ion requires a switching circuit, bucking a 2.7–4.2 V Li ion to supply a 1.8 V load does not.

From the perspective of power, as summarized in Table 1.1, the switch in a linear circuit drops v_IN – v_O continuously, whereas the terminal voltages across the switches in a charge pump and a switched inductor decrease with load and across time. In other words, switched circuits can dissipate less power than their linear counterparts. Switched capacitors, however, typically require more switches to implement than switched inductors, so capacitor networks dissipate more gate-drive losses P_GD.

Switch losses in all three cases, however, diminish with load, so when microsystems idle, efficiency is more sensitive to second-order losses, which is where linear circuits might gain an edge because they do not dissipate gate-drive power P_GD. The problem is that miniature devices demand little to no power when idling and moderate to substantial power when transmitting data wirelessly, so a linear circuit is more appealing when idling and less appealing otherwise, and vice versa for a switched inductor. In the end, functionality may become the deciding factor, which is why operating in DCM and reducing switching frequency f_SW in magnetic-based converters is so important when the load is light, as is lowering quiescent power P_Q in all three schemes. Notice, by the way, that parasitic series resistances in the inductor, capacitors, and board also dissipate ohmic losses.

Noise in the output may not be a problem for charging a Li ion but is certainly an issue when supplying a functional load like a data converter or sensor-interface circuit whose sensitivity to noise in the supply is often severe. Noise at the input is similarly problematic when drawing power from a PV cell because raising the voltage increases the current lost to the parasitic diode present and letting it drop lowers how much current the cell generates. Linear switches outshine their switching counterparts in this regard because they never disconnect from v_IN or v_O. Ripple current Δi_L in switched-inductor circuits, of course, adds noise. Charge pumps are probably the worst because flying capacitors momentarily and necessarily disconnect from v_IN and v_O. Switched-inductor circuits that decouple the outputs from the inductor also suffer from similar effects, in addition to the Δ_iL-induced noise already mentioned. Ultimately, reducing noise amounts to raising f_SW (to shorten how long v_IN and v_O float) and circuit bandwidth (to keep up with f_SW), and, in the case of inductor circuits L_X (and f_SW), to reducing Δi_L. Increasing f_SW, however, by and large degrades efficiency, and raising L_X demands more space, which is the conundrum engineers eventually face when designing these types of circuits: when and how to trade accuracy, efficiency, and integration.

1.4.1 Battery-Assisted Photovoltaic Charger–Supply Example

The switched inductor in Figure 1.13 draws power from both a 0.25–0.4 V PV cell v_PV and a 1.8 V power source v_PS or battery to supply a 1 V load [19]. Relying on only one small off-chip power inductor L_X is important because off-chip inductors are bulky and their on-chip counterparts are poor, but altogether excluding the inductor drastically reduces power-conversion efficiency. Input and output capacitors C_IN and C_O are also critical because they help keep L_X, the PV cell, and load currents i_L, i_PV, and i_O from slewing v_PV away from its maximum-power point and output v_O away from its target V_REF.

When lightly sourced, L_X draws and delivers energy to v_O—first from v_PV and then from v_PS. For this, switches S_PV and S_E energize L_X from v_PV, and S_PV and S_O subsequently drain L_X into v_O. After that, S_PS and S_O similarly energize L_X, and S_DE and S_O de-energize L_X into v_O. Otherwise, when heavily sourced, L_X supplies P_O to the load from v_PV and charges v_PS with what remains of P_PV. As before, S_PV and S_E energize L_X, and S_PV and S_O drain L_X into v_O, but unlike before, S_O opens after v_O receives sufficient energy to satisfy P_O, and i_L therefore charges switching node v_SW.O until diode D_PS forward-biases and charges v_PS with i_L.

The PV cell generates the most power when v_PV nears its optimal value of V_PV(OPT), which means that this system should adjust v_PV to V_PV(OPT). Since the switching network induces a ripple voltage in v_PV that shifts the PV cell from its maximum-power point, v_PV’s ripple Δv_PV should be small. The circuit should also be able to modify and track v_PV to new targets to accommodate changes in light intensity and conditions.

Harvesting performance hinges on reducing power losses. Considering this, tiny PV cells generate microwatts, ensuring that L_X conducts continuously without reversing the direction of current amounts to keeping its rippling current Δi_L within a small window, which happens when L_X switches quickly. Charging and discharging the gates of power switches more often, however, requires more power, which is why L_X should not conduct continuously and should switch slowly.

To ensure that L_X derives sufficient PV power P_PV in one energizing (t_E) and de-energizing (t_DE) sequence, i_L rises and peaks to i_L(PK) (about 6 mA in Figure 1.14). Transferring a larger energy packet E_PV in 1.6 μs draws sufficient P_PV from v_PV to keep v_PV from rising excessively over V_PV(OPT) across the remaining 11.4 μs of the 13 μs period T_SW. Had E_PV been smaller and T_SW shorter, Δv_PV would have been less than 20 mV; however, the power lost in switching more often negates the benefits of a smaller ripple.

Selecting the channel width–length ratios of the switches that balance conduction and gate-drive losses in the system and choosing the i_L(PK)–T_SW combination that reduces the percentage of PV power P_PV lost to P_LOSS enable the PV cell to supply the load fully or partially and, when possible, recharge the battery. When lightly loaded, the system regulates v_O and steers excess P_PV to the battery to charge v_PS in staircase fashion, as Figure 1.15 shows. When lightly sourced, the system draws both PV and battery power to supply and regulate the load.

1.4.2 Piezoelectric Charger Example

Drawing power from an intermittent source to supply the needs of an unpredictable and uncorrelated load is challenging. As a result, harvesting and regulation are often separate and distinct functions in a microsystem. While a regulator, for example, supplies a load from a battery, a harvester can charge the battery. So, in the more specific case of tiny piezoelectric conditioners, chargers convert and condition rippling sources to replenish capacitors, rechargeable batteries, or a combination of both capacitors and batteries.

Typical battery-supplied implementations use a bridge-based rectifier to convert an alternating signal into a steady-state voltage that subsequently feeds another converter whose aim is to condition and steer power into a battery. Unfortunately, each conditioning function dissipates power, and, collectively, they diminish the gains of a microscale harvester. To minimize this loss, the piezoelectric charger in Figure 1.16 combines rectification and conditioning into one stage [20]. The underlying aim is to derive power from positive piezoelectric voltages with harvesting inductor L_H and reverse L_H’s current flow to draw energy from negative voltages.

First, through v_PZT’s positive half cycle in Figure 1.17, switches S_I and S_N remain open to decouple the power stage from the transducer until v_PZT reaches its positive peak. S_I and S_N then engage (at 15.73 ms) to discharge C_PZT into L_H, until i_L peaks. Since LC resonance drives this energy transfer, the system estimates L_H’s energizing time by waiting for one-quarter of L_H–C_PZT’s resonance period at 0.5 π√(L_HC_PZT). Note that sensing i_L’s peak directly is more accurate, but also considerably more lossy. After this, S_N opens and i_L charges the parasitic capacitance at switching node v_SW⁺ quickly until noninverting diode-switch D_N forward biases and depletes L_H into V_BAT. During the negative half cycle, S_I and S_N again open to disconnect the circuit from the transducer until v_PZT reaches its negative peak. Afterward, S_I and S_N discharge C_PZT into L_H (at 20.69 ms) for one-quarter of L_H–C_PZT’s resonance period. S_I then opens and D_I conducts i_L into V_BAT. This way, the system deposits energy into V_BAT every half cycle in staircase fashion, as Figure 1.18 illustrates under vibrations of various strengths.

1.4.3 Electrostatic Charger Example

Harnessing energy from a variable capacitor C_VAR is possible because the work that vibrations exert to separate the conducting plates decreases the device’s capacitance. As a result, because charge q_C is the product of C_VAR and its voltage v_C or C_VARv_C, reducing C_VAR raises v_C, and the quadratic gain that v_C² represents in energy 0.5 C_VARv_C² overwhelms C_VAR’s linear drop. Unfortunately, v_C often rises to 100–300 V, well beyond the breakdown limits of low-cost CMOS process technologies.

Alternatively, clamping C_VAR to a large reservoir capacitor C_RES precharged to V_CLAMP constrains v_C and causes q_C to fall in response to reductions in C_VAR, which means that C_VAR drives charge into C_RES. The cycle-by-cycle progression shown in Figure 1.19 does just this: first, precharges C_VAR to V_CLAMP and then connects C_VAR to C_RES so that reductions in C_VAR pump charge into C_RES. Afterward, the system disconnects C_VAR, recovers remnant energy in C_VAR, and collects harvested charge into C_RES. After vibrations finish resetting C_VAR to C_MAX, the system starts another harvesting cycle by again precharging C_VAR to V_CLAMP [21].

Unfortunately, breakdown voltages in modern CMOS process technologies are low at 1.8–5 V. This means that the energy C_VAR holds at C_MIN with V_CLAMP can be so low that conduction and gate-drive losses in the recovery process can dissipate most, if not all of C_VAR’s energy. In these cases, skipping the recovery phase and clamping C_VAR directly to V_BAT (instead of C_RES) during the harvesting phase are prudent design choices because they reduce the sequence to precharge, harvest (to V_BAT), and reset and eliminate lossy energy-transfer transactions between C_RES and V_BAT. The switching network of Figure 1.20 does just this: Precharge C_VAR at C_MAX from V_BAT with switches S_E and S_D and inductor L_X, connect C_VAR to V_BAT and harvest C_VAR’s charge directly to V_BAT through S_H when C_VAR falls to C_MIN, and disconnect all switches to allow vibrations to reset C_VAR to C_MAX.

In this simplified progression, there are only two energy transfers: when pre-charging C_VAR and harvesting into V_BAT. For the first, while using a switch to connect and precharge C_VAR at C_MAX to V_BAT is simple, it is also the lossiest option because the switch consumes 0.5C_MAXV_BAT². This is the reason that S_E starts the precharge phase by energizing inductor L_X from V_BAT and S_D subsequently drains L_X into C_VAR [22]. Notice that C_VAR also charges when L_X energizes, so L_X caches only part of the energy that C_VAR ultimately receives when L_X finishes de-energizing into C_VAR.

Since C_VAR precharges to V_BAT (at 0 and every 33 ms after that in Figure 1.21), connecting C_VAR to V_BAT after precharge with S_H draws no current and, therefore, no power from either C_VAR or V_BAT. Afterward, through the first 16.5 ms of every cycle in Figure 1.21, C_VAR falls to C_MIN to drive harvesting current i_HARV into V_BAT via S_H. Because i_HARV is low, S_H dissipates little power across this phase. When C_VAR reaches C_MIN (at 16.5 and every 33 ms after that in Figure 1.21), all switches disconnect and, through the ensuing 16.5 ms, vibrations separate C_VAR’s plates until C_VAR rises to C_MAX, at which point another cycle begins.

As with every harvesting system, the ultimate goal is to generate sufficient power to output a net energy gain. The challenge is that miniature transducers generate little power and conditioning circuits can easily dissipate much of that power. In the electrostatic case presented, V_BAT invests $0.5{\mathrm{C}}_{\mathrm{M}\mathrm{A}\mathrm{X}}{\mathrm{V}}_{\mathrm{B}\mathrm{A}{\mathrm{T}}^2}$ as E_INV to charge C_VAR to V_BAT at C_MAX and harvests energy from C_VAR as C_VAR falls to C_MIN. As a result, V_BAT loses energy when the cycle begins (at 0 and every 33 ms after that in Figure 1.21) and harvests energy every half cycle after that to produce the staircase response in Figure 1.21. In other words, C_VAR generates more energy E_OUT than the system invests in E_INV and dissipates in E_LOSS:

where E_OUT is the charge energy that V_BAT receives as ΔQ_CV_BAT or (ΔC_VARV_BAT)V_BAT when C_VAR falls to C_MIN and ΔC_VAR is the difference between C_MAX and C_MIN. An important observation to note here is that output power from E_HARV is ultimately higher with larger C_MAX–C_MIN spreads and lower power-conditioning losses.

1.4.4 Conclusions

Hybrid supplies in microsystems generally suffer from full-scale integration and poor low-power efficiency. Tiny spaces, to start, constrain energy to such an extent that efficiency concerns overwhelm all other performance metrics, which means switched-inductor conditioners become almost indispensable. Power inductors, unfortunately, are bulky and difficult to integrate; this means that miniaturized chargers and supplies cannot afford to use more than one. And even if they are more efficient than linear and switched-capacitor implementations under moderate to heavy loads, magnetic-based supplies still dissipate conduction, gate-drive, and quiescent power. In fact, a fundamental challenge that designers face in ultra low-power chargers and supplies is keeping gate-drive and quiescent losses low—that is, managing complex systems with little to no power.

Harvesters bear the additional burden of synchronizing circuits to often unpredictable and uncorrelated ambient events and conditions. Not only that, starting and operating a system with no initial energy is especially problematic. Many implementations, therefore, rely on a battery storing sufficient initial charge to bias and start the system, much like cars depend on charged batteries to ignite their engines. In other words, ultrasmall solutions often complement a harvesting source with another technology, like a battery with some charge, to ensure that the system starts properly.