Practical design considerations for piezoelectric and thermal energy harvesting

It's hard not to get excited about what's going on today in the energy harvesting field. Consider: New devices now coming to market can transform as little as tens of microwatts of harvested energy into usable voltages. Some of these devices are tuned magnetic transducers that start up from as little as 10 milli-gs of vibration. Or they may take the form of a low-impedance source such as a thermal-electric generator that can output or 20 mV or more from a temperature differential of one degree Celsius.

Energy harvesting could be beneficial in a variety of areas. Harvesters could play a role in monitoring aircraft structural health, tracking and monitoring assets, controlling building temperature and lighting, plant automation, industrial process monitoring, auto toll tags, tire pressure monitoring systems, and in perimeter monitoring. In general, energy harvesting systems are candidates for any remote application that requires monitoring but is difficult to service.

Harvesting systems can also lengthen the usefulness of electronics normally operating from battery power. Battery manufacturers such as Tadiran now make cells with a 20-year life. This gives the battery the same operational expectancy as the electronics it powers. Adding energy harvesting to an existing battery-powered sensor could extend battery life or make it possible to use one with a smaller capacity for the same life expectancy.

Consider the architecture of a typical battery-powered wireless sensor node (WSN). A node typically includes sensors, an MCU, a transceiver, a power management device, and a battery. The battery must be replaced at some standard service interval. The cost of the replacement battery is insignificant compared to the expense of sending a service technician to the wireless sensor node. Practical applications often need many WSNs. Routine servicing of such systems could be a full-time job for a technician. Energy harvesting systems offer a way to make WSN systems self-sustaining and to eliminate routine service calls.

Piezoelectric transducers are mechanical devices that convert one form of energy into another. For energy harvesting, they convert vibrational energy to electrical energy. A piezo harvesting system typically consists of the transducer, a rectifier, an energy storage element comprising either a battery or a capacitor, a voltage regulator, and a wireless transceiver. Optionally, the system may also incorporate a charging circuit between the rectifier and the energy storage element. The function of the charging circuit could be to manipulate the output voltage of the piezo transducer such that it operates at its maximum power point.

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However, some systems with exceptional performance don't incorporate a charging circuit. There are trade-offs associated with using a charger that provides peak-power-point tracking. One trade-off pertains to the reality that nothing comes for free and many harvester designs that do incorporate a charger don't get the anticipated benefit. The reason is that a peak power tracking circuit can consume more power than is gained by having the piezo element operate at its maximum power point.

Energy harvesting vibration sources

In general, sources of harvestable vibration are varied in both frequency and amplitude. But many vibration sources get power from the line voltage, so common vibration frequencies in the United States are 60 and 120 Hz. In large machines, mechanical resonances dominate and the frequencies tend to be lower, say between 13 and 70 Hz.

The accompanying table lists various sources and their peak resonant frequency along with the associated acceleration and “g-level.” The term g-level is used to represent the normalized amount of acceleration with respect to earth's gravitational field. By definition, 1 g = 9.8 m/sec2 of acceleration.

Consider a piezo sensor modeled as a cantilevered beam with a tip mass at the end. If x(t) is the displacement of the beam, then

where A is the peak amplitude of the displacement, in meters (m) and ω is the resonant frequency, in rad/sec. Solving for the peak displacement, A, as a function of frequency, f in Hz and acceleration in g's, yields:

where A(g,f) is in µm. The accompanying table shows the results of evaluating Equation 4 at frequencies between 21 and 358 Hz for acceleration levels of between 25 milli-g and 4 g. The results demonstrate that it takes little actual movement to create an appreciable amount of acceleration. For the frequencies of interest, the displacement is typically measured in micrometers.

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The specification of a piezo transducer for a harvesting application demands precise measurement of the vibration source's resonant frequencies and the amplitude of the acceleration at those frequencies. Typical piezos such as Volture products from Mide Technology Corp. have a three-Hertz-wide 50% power bandwidth. In other words, if the piezo's excitation frequency is off by more than ±1.5 Hz from its resonance point, it will put out half the power available at peak resonance. For this reason, most vibration harvesting designs will need a custom piezo device, tuned and optimized for the expected frequencies and power management circuit. Most piezoelectric manufacturers have instrumentation for characterizing the vibration source. It's best to involve them early to better understand the possible options for optimizing the piezo.

WSN designers interested in using standard off-the-shelf piezo transducers have a number of questions to consider. Besides identifying the vibration source and its frequencies, designers must know the minimum, nominal and maximum acceleration under which the WSN must operate. As with any project, the operating voltage and energy requirements are needed up front. Factors affecting power drain include the frequency of WSN transmissions (sets the average power needed from the transducer) and the turn-on threshold for the power management device. (This sets the minimum open circuit voltage of the piezo at the source vibration frequency and minimum acceleration.)

There are also physical practicalities such as the amount of area that can be dedicated to mounting the piezo element, the height available for the piezo and its enclosure, and the type of mounting the application needs. As with any installation environmental conditions (moisture, temperature, etc.) can be important as well.

WSN energy needs

Most low-power microcontrollers and sensors can run directly from a 3.3-V rail. Applications needing additional rails can make use of extremely low-power buck regulators such as the LTC3388 which can run from as little as one microamp. For simplicity, consider only systems with a 3.3-V power rail. We can calculate the amount of energy they require from the current-vs-time profile during each recording and transmission period. Suppose the current profile for a single transmission is this:

This 227 µJ of energy is required for every transmission after the network is established. Depending upon the network protocol, the initial network configuration can consume two or three times this amount of energy because it takes multiple transmissions to establish the available nodes in the system. The other specification to consider is the transmission interval. For this example suppose the transmission interval is once per minute. The average power needed from the transducer is then 3.8 µW (227.7 µJ/60 sec).

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The next step is to evaluate possible piezo transducers. You'll need a graph from the piezo manufacturer showing the open-circuit voltage verse peak g level for a given tip mass and resonant frequency. This open-circuit voltage data combined with the figure for the power management unit's start-up voltage reveals whether the piezo will power-up the wireless sensor node. As an example, consider the Mide V21BL piezoelectric transducer and the LTC3588-1 Piezoelectric Energy Harvesting Power Supply. The accompanying figure shows laboratory data for open-circuit voltage versus peak g-level with a tip mass of 0.22 gm and a resonant frequency of 120 Hz.

A pulsed-load test circuit can be constructed with the LTC3588-1 where all the energy stored in the input capacitor, CStorage, between voltages VIN_UVLO_RISING and VIN_UVLO_FALLING, transfers to the output and is dissipated in the LED. In a WSN, this stored energy would be used as described above to power the microcontroller, sensor and transmitter. The LTC3588-1 has two input undervoltage lockout (UVLO)-rising and three UVLO-falling settings, depending on the output voltage set point. (UVLO lets charge accumulate on an input capacitor until it can efficiently transfer to the output. UVLO rising refers to the case where the input voltage Vin is rising. Conversely, UVLO falling refers to cases of a falling Vin.)

For the 3.3-V output, the UVLO-rising threshold is 5.05 V and the UVLO falling threshold is 3.6 V. When an input of 0.73 g's peak at a frequency of 120 Hz was applied to the piezo it took 18.5 sec for the 36 µF input cap to charge from the UVLO falling threshold to the UVLO rising threshold. Hence, the energy, E, stored in the input capacitor and the average power output, P, from the piezo can be calculated as:

Coincidently, the energy stored in the input capacitor (226 µJ) of this test circuit is approximately equal to the energy needed for the wireless sensor node example that uses 227.7 µJ. The average power from the piezoelectric transducer at 120 Hz with 0.73 g's is 12.2 µW. The application needs only 3.8 µW based on a transmission interval of 60 sec. This analysis excluded the effects of the sleep current which, if not minimized, will significantly lengthen the recharge time and reduce the transmit rate. If the sleep current is kept extremely low, this piezo-powered node could transmit about three times more frequently than the 60 sec spec. In other words, it could operate once every 20 sec.

One assumption for sizing the output capacitor is that the application can run from 3.3 down to 3.0 V. So the application energy must be stored in this narrow voltage range. Also, the energy needed from the output capacitor must accommodate the process of initial network configuration, which requires three times the energy of a single transmission event. The minimum output capacitor, Cout_min, is then calculated as:

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For the input capacitor selection there are a couple options. If the application requires that the output capacitor charge at each UVLO rising event, the input capacitor must store enough energy within the input UVLO hysteresis range to charge the output cap and supply the load. Alternatively, it may be OK to charge the output capacitor from multiple UVLO rising events, in which case much smaller values of input capacitor will suffice The equation for determining the minimum input capacitance value that will charge the output capacitor in one UVLO event is then:

The LTC3588-1 has a quiescent current of 450 nA when its VIN is below the UVLO rising threshold and the output is not in regulation. So the maximum amount of harvested energy can go toward charging the input capacitor. The first output transmission will take longer than the subsequent transmissions because the input capacitor is starting from ground rather than from the UVLO_falling threshold. The start-up time, TSTART_UP, for the first pulse is given by:

If this isn't too much time, consider adding Li-ion or thin-film batteries. Thin-film batteries are available from suppliers such as Infinite Power Solutions, Autec Power Systems, and GS Nano Tech Co. When integrating batteries, the LTC4071 shunt charger/battery disconnect circuit can serve to protect the batteries from damage caused by a deep discharge, which is normally the function of the pack-protect circuitry.

Thermal energy harvesting

First-generation TEGs (thermoelectric generators) have a low source impedance (generally 1 to 5 Ω) and usually generate 20 to 50 mV/°C temperature differential. They use the Seebeck effect where a voltage, the thermoelectric EMF, is created in the presence of a temperature difference between two different metals or semiconductors. First-generation devices used bimetallic junctions and were bulky. More recent devices use bismuth telluride (Bi2Te3) and semiconductor p-n junctions and can have thicknesses in the millimeter range.

The thermal conductivity of a TEG is low because it is primarily a silicon component. To get a significant output voltage, TEGs must exhibit a high V/Δ°C ratio (Seebeck coefficient). A common approach is to place many thermo-elements in series, boosting the effective output resistance of the generator. Thus power is only efficiently transferred to loads with matched resistance; otherwise power is lost across the TEG's source resistance. A generator with high output impedance is effectively a temperature sensor and not a generator.

First-generation TEG voltage vs. temperature (T) behavior is essentially a straight line with a slope of about 250 µV • ΔT • N where N = the number of couples (PN junctions). It is hard to find this relationship in vendor literature. So the above expression is an approximation from empirical testing.

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Because TEG outputs are so low, it takes special ICs to boost their signals to a usable range. One chip in this category is the recently introduced LTC3109. It is an ultralow-voltage step-up converter and power manager specifically designed to greatly simplify the task of harvesting and managing surplus energy from TEGs and other extremely low bipolar-input voltage sources. Its step-up topology operates from input voltages as low as 30 mV. This is significant because it lets the LTC3109 harvest energy from a TEG with as little as 1°C temperature differential - something a discrete implementation struggles to meet because such circuits typically have a high quiescent current.

The accompanying circuit uses a small step-up transformer to boost the input voltage source to a LTC3109, which then manages power for a wireless sensing and data acquisition application. The LTC3109 can harvest small temperature differences and generate system power instead of using traditional battery power.

The LTC3109 utilizes two depletion mode N-channel MOSFETs to form a resonant step-up oscillator using an external step-up transformer and a small coupling capacitor. This allows it to boost input voltages as low as ±30 mV, high enough to provide multiple regulated output voltages for powering other circuits. The frequency of oscillation is determined by the inductance of the transformer's secondary winding and input capacitance of the LTC3109. The resultant resonant frequency is typically in the range of 10 kHz to 100 kHz.

For input voltages as low as ±30 mV, a primary-to-secondary turns ratio of about 1:100 is best. Higher input voltages can use a lower turns ratio to provide greater output power. These transformers are standard, off-the-shelf components, and are readily available from magnetic suppliers.

The LTC3109 takes a “systems level” approach to solving a complex problem. It can start up from a low voltage source and manage the energy between multiple outputs. The ac voltage produced on the secondary winding of the transformer is boosted and rectified using an external charge pump capacitor (from the secondary winding to pin C1A or C1B) and rectifiers internal to the LTC3109. This rectifier circuit feeds current into the VAUX pin, providing charge to the external VAUX capacitor and then to the other outputs.

The internal 2.2-Volt LDO (low drop-out regulator) can support a low-power processor or other low-power ICs. The LDO is powered by the higher value of either VAUX or VOUT. This enables it to become active as soon as VAUX has charged to 2.3 V, while the VOUT storage capacitor is still charging. In the event of a step load on the VLDO output, current can come from the main VOUT capacitor if VAUX drops below VOUT. The VLDO output can supply up to 5 mA.

The main output voltage on VOUT is charged from the VAUX supply and is user-programmable to one of four regulated voltages using the voltage select pins VS1 and VS2. The four fixed output voltages are: 2.35 V for supercapacitors, 3.3 V for standard capacitors and RF or sensor circuitry, 4.1 V for lithium-ion battery termination, or 5 V for higher energy storage and a main system rail to power a wireless transmitter or sensors - thereby eliminating the need for multi-mega-Ohm external resistors to adjust output voltages. As a result, the LTC3109 does not require special board coatings to minimize leakage, as are often needed in discrete designs that require large-valued resistors.

A second output, VOUT2, can be turned on and off by the host microprocessor using the VOUT2_EN pin. When enabled, VOUT2 connects to Vout through a P-channel MOSFET switch. This output can be used to power external circuits such as sensors or amplifiers that do not have low-power sleep or shutdown capability.

The VSTORE capacitor may have a large value (thousands of microfarads or even farads), to provide holdup during times of lost input power. Once power-up has completed, the main, backup and switched outputs are all available. If the input power fails, operation can still continue, operating from the VSTORE capacitor. The VSTORE output can be used to charge a large storage capacitor or rechargeable battery after VOUT has reached regulation. Once VOUT has reached regulation, the VSTORE output will be allowed to charge up to the VAUX voltage, which is clamped at 5.3 V. The storage element on VSTORE can be used to power the system if the input source is lost. It can also be used to supplement the current demanded by VOUT, VOUT2 and the LDO outputs if the input source lacks sufficient energy.

A power-good comparator monitors the VOUT voltage. Once VOUT has charged to within 7.5% of its regulated voltage, the PGOOD output will go high. If VOUT drops more than 9% from its regulated voltage, PGOOD will go low. The PGOOD output is designed to drive a microcontroller or other chip I/O but not a higher current load such as an LED.

Though these chips make it possible to harvest piezoelectric and TEG energy, there is still some missing information. For one thing, a lot of TEG and piezo data is still empirical. Vendors of such transducers will need to provide data on their products which were unnecessary in the past when these devices only served as sensors or coolers, not generators.

From piezo manufacturers, the system designers need to know the open-circuit voltage versus acceleration for various tip masses and the associated source impedance of the piezo under the same vibration conditions. These graphs plus the UVLO-rising threshold of the power management circuit go into determining the minimum vibration level at which the WSN can operate.

From the TEG manufacturers, system designers need to know the open-circuit voltage-verse-temperature-differential and the associated source resistance. In addition, the TEG manufacturers need to provide thermal impedance of their products and models that will allow the users to calculate their actual temperature differential in a system with heat sinks on both sides of the TEG, with the heat sinks in different ambient temperatures and both with and without air flow.

All in all, energy harvesting applications are potentially everywhere. The first real benefit this new technology will likely offer is in extending the life of batteries so they last over the usable life of products. In some applications the batteries can be eliminated completely, which is a great benefit to the environment and the end user.

Vibration Source Acceleration [m/sec2] g-Level Frequency [Hz] Car engine compartment 12 1.22 200 Car instrument panel 3 0.31 13 Base of 3-axis machine tool 10 1.02 70 Kitchen blender 6.4 0.65 121 Clothes dryer 3.5 0.36 121 Door frame just as door closes 3 0.31 125 Small microwave oven 2.25 0.23 121 HVAC vents in office building 0.2 - 1.5 0.02 - 0.15 60 Wooden deck with foot traffic 1.3 0.13 385 Bread maker 1.03 0.11 121 External windows (sz. 2' × 3')next to busy street 0.7 0.7 100 Notebook computer while CD is being read 0.6 0.06 75 Washing machine 0.5 0.05 109 Second story floor of a wood frame office building 0.2 0.02 100 Refrigerator 0.1 0.01 240

Peak acceleration and resonant frequency of various vibration sources (Source: “RFID: Sensors and Energy Harvesting” – LIUC Universita Carlo Cattaneo – June 5, 2009)

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Peak Displacement (A) - [um]g Acceleration w.r.t to GravityFrequency - [Hz}21 50 60 80 100 120 140 220 358 0.025 14.07 2.48 1.72 0.97 0.62 0.43 .032 0.13 0.55 0.1 56.29 9.93 6.90 3.88 2.48 1.72 1.27 0.51 0.19 0.2 112.58 19.86 13.79 7.76 4.96 3.45 2.53 1.03 0.39 0.3 168.87 29.79 20.69 11.64 7.45 5.17 3.80 1.54 0.58 0.4 225.16 39.72 27.58 15.51 9.93 6.90 5.07 2.05 0.77 0.5 281.45 49.65 34.48 19.39 12.41 8.62 6.33 2.56 0.97 0.6 337.74 59.58 41.37 23.27 14.89 10.34 7.60 3.08 1.16 0.7 394.03 69.51 48.27 27.15 17.38 12.07 8.87 3.59 1.36 0.8 450.32 79.44 5.16 31.03 19.86 13.79 10.13 4.10 1.55 0.9 506.61 89.37 62.06 34.91 22.34 15.51 11.40 4.62 1.74 1 562.90 99.29 68.95 38.79 24.82 17.24 12.67 5.13 1.94 1.5 844.34 148.94 103.43 58.18 37.24 25.86 19.00 7.69 2.91 2 1125.79 198.59 137.91 55.57 49.65 34.48 25.33 10.26 3.87 2.5 1407.24 248.24 172.39 96.97 62.06 43.10 31.66 12.82 4.84 3 1688.69 297.88 206.86 116.36 74.47 51.72 38.00 15.39 5.81 3.5 1970.13 347.53 241.34 135.75 86.88 60.34 44.33 17.95 6.8 4 2251.58 397.18 275.82 155.15 99.29 68.95 50.66 20.52 7.75