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This work presents the optimization of antenna captured low power radio frequency (RF) to direct current (DC) power converters using Schottky diodes for powering remote wireless sensors. Linearized models using scattering parameters show that an antenna and a matched diode rectifier can be described as a form of coupled resonator with different individual resonator properties. The analytical models show that the maximum voltage gain of the coupled resonators is mainly related to the antenna, diode and load (

For autonomous powering of sensor nodes in remote or inaccessible areas, wireless power transfer provides the only viable option to power them from an energy source. Due to the low power density of ambient RF at far-field from transmitters, there is a need to optimize each aspect of a wireless RF energy harvester for possible realistic applications. Today remote autonomous sensors are mostly powered by batteries, which have limited lifespan. Renewable powering has the potential to power autonomous sensors perpetually. Due to the expansion of telecommunications technology ambient electromagnetic (EM) power is among the most common sources of ambient energy. There are power transmitters/receivers scattered in practically any society, ranging from television transmission stations to cell phone transmitters and even wireless routers in our homes/offices or mobile phones. These transmitters in our environment and others which are on special dedicated frequencies produce ambient RF power (on the order of microwatts) which can be used as a source for powering remote microwatt budget sensors through wireless energy harvesting. This work presents different matching techniques based on different application requirements using Schottky diode-based RF to DC power converting circuits for wireless remote EM energy harvesting around 434 MHz and 13.6 MHz. Generalized analytical models and limitations of the matched RF to DC power converters are discussed. A wireless RF energy harvester consisting of an antenna and a matched diode rectifier is then realized and its performance tested. Passive wireless energy harvesting also finds applications in near field communications (NFC) [

Hertz was the first to demonstrate the propagation of EM waves in free space and to demonstrate other properties of EM waves such as reflection using parabolic reflectors [

A junction diode equivalent circuit and simple Schottky diode rectifier are shown in _{DS}_{DS}_{DP}_{DP}

The diode capacitive impedance is mainly due to the junction capacitances provided by the metal, its passivation and the semiconductor forming the diode. AC power incident on a forward biased diode input is converted to DC power at the output. The current-voltage behavior of a single metal/semiconductor diode is described by the Richardson equation [_{S}_{D}

Since the same current flows through the diode and the capacitor, one can find the average current through the circuit by integrating _{C}_{S}_{0} is the series expansion of the sinusoidal source voltage. _{S}

The maximum power transfer theorem states that the highest power is transferred to the load when the source resistance is the same as the load resistance. For systems with both resistive and reactive impedances from source and load, the source and the load impedance should be adjusted in a way that they are the complex conjugate of each other through impedance matching. For the purposes of this work, a 50 Ω resistive source is chosen as reference for load impedance matching. The antenna which captures the ambient RF signals is tuned to provide this source resistance at resonance for the rectifying circuit in a complete EM wireless remote harvester. The load is the resistance of the Schottky diodes and the actual connected resistance (

Schottky diodes HSMS-285C and HSMS-286C from Avago [

The board is fabricated such that components are soldered directly one into another to prevent additional impedances introduced by copper route. The PCB backside had the ground layer. An example of measured input impedance for HSMS-285C and HSMS-286C is shown in

The diodes quality factor is given by _{DS}R_{DS}^{−1}, where _{DS}

The Delon voltage doubler and Greinacher doubler are both used to realize the RF to DC power converters presented in this work. The Delon voltage doubler and Greinacher doubler are shown in _{out}

An L-match network converts a source series impedance to its equivalent load parallel impedance or _{P}_{S}

_{S}_{P}_{S}_{P}_{P}_{S}

Using Equations (

The classical matching technique using Equations (

_{K}_{L}_{LL}_{DS}_{DS}_{S}_{A}_{A}_{A}_{L}_{L}_{L} is given by _{L} is the series resistance of the diodes and load:

The source power; P_{S} is given by _{S}* is the root mean squared (RMS) antenna captured source voltage. Half of the source power is transferred to the resistance of the diodes (and connected load) at match conditions as described by the maximum power transfer theorem:

Equating _{L}_{S}

From

_{S}_{1}_{2}

Using Cramers rule, _{2}

The voltage across _{L}_{L}_{2}R_{L}

The voltage gain of the coupled resonator can be expressed as in

At resonance, there is no resultant reactance in the RLC resonators or the capacitive and inductive impedances become equal; hence

Equations in _{gain} is the voltage gain. _{gain}

This gives the results as in

_{K(max)}_{Kmax}_{K(max)}_{gain}

For wireless harvesters consisting of an antenna and a diode rectifying circuit, the diode resistive impedance at any condition is dependent on the diode realized parameters, signal frequency, connected load and the input power level. The source impedance is determined by the impedance of the antenna. For maximum efficiency, the ratio of the source resistance to the load resistance must tend to zero at matched conditions. The efficiency

The presented circuit was L-matched between the 50 Ω resistance of the antenna source and the resistance of the HSMS-285C diodes (and load) at 434 MHz for −30 dBm input as shown in _{DP}

The circuit reflection coefficient (S_{11}) and input impedance at open circuit are shown in

The measured L-matched circuit efficiency and voltage sensitivity is shown in

The open circuit voltage gain is 25 at −30 dBm and 40 at −10 dBm. The maximum measured efficiency at −35 dBm is 27%. This is higher than that of −30 dBm due to the better matched circuit impedance at −35 dBm (35 Ω) than at −30 dBm (27 Ω) input. The L-matched RF to DC power converter has a loaded

A highly selective or small frequency bandwidth RF power converter is realized with a PI-network in-between the source impedance from the antenna and the diode rectifier. A PI-network is a ‘back to back’ L-network that are both configured to match the load and source impedance to an invisible resistance located at the junction between the two L-networks [_{P}_{P}_{S}_{S}_{P}_{S}_{P}_{S}_{P}_{S}_{P}_{S}_{P}

An example of a PI-matched RF to DC converter using the HSMS-285C diodes operating at 434 MHz for −30 dBm input is presented first and then the generalized model is discussed. The circuit is matched for _{P}

The first parallel RLC resonator is modeled as impedance from the antenna and some passive matching components. The second parallel RLC resonator is modeled as impedance from the linearized diodes, its connected load and some passive matching components. _{S}_{A}_{1}

Load voltage (_{L}_{S}

From _{L}

The maximum of

Since _{1}_{1}_{L}_{S}/I

Under these conditions and an optimal coupling coefficient _{1max}_{1max}

The analysis of Section 2.5.2 and parallel coupled RLC resonators show that any antenna and matched rectifying diode can be described as an equivalent circuit of a coupled resonator at a defined operating point. This general model can be applied to optimize other harvesters with complex output impedance such as piezo-harvesters or vibration harvesters for maximum transfer of power or voltage to its connected load. The model can also be applied to near field magnetically coupled antennas/coils for optimization.

A broadband network is preferred when an RF to DC power converter is to be operated for a wide range of frequencies. A broadband converter is realized by connecting successive L-networks together in a multi-network between the antenna source and the rectifying diodes. The result is broadband or multiband RF power converter around certain frequencies. This can be deduced from the general model of a coupled resonators that by choosing certain passive components between a source and the load, it is possible to have more frequencies (

The quality factor of the L-network with the series resistance is given by

From _{S}_{P}

_{S}_{P}

For complex loads such as rectifying diodes or transistors, the largest achievable bandwidth prescribed by

The antenna source resistance was broadband matched to the HSMS-285C diodes (and load) resistance at −30 dBm input around 434 MHz. For a desired _{P}_{S}_{P}_{P}

Therefore the broadband circuit is matched for _{P}_{11} at various input power levels and input impedance at open circuit conditions. From

The broadband circuit achieves average efficiency of 5% at 17 kΩ load for −30 dBm and 30% at 17 kΩ load for −10 dBm input power from 200 MHz to 500 MHz. _{S}* and Q_{P}* of ∼2.7, the circuit response is broadband around 434 MHz.

The current state of the art low power remote sensors would require a DC voltage supply of about 1 V and DC current of about 30 μA for operation. Therefore, the issue is not only how efficient a wireless EM harvester is in converting RF to DC power, but also what the output DC voltage and current of the EM harvester are at the RF input power level [

The presented result was L-matched using 50 Ω resistance of the antenna source and the resistance of the HSMS-286C diodes (and load). The HSMS-286C diodes do provide high resistive impedance at low frequencies; notwithstanding the flicker noise which causes its resistive (and reactive) impedance to fluctuate. The HSMS-286C has low forward junction potential (∼350 mV at 1 mA) per diode and series impedance of ∼1.5–j8.1 kΩ or parallel impedance of ∼−

The high voltage sensitive EM harvester operating at 13.6 MHz is as shown in

The measured S_{11} and input impedance at open circuit are shown in

The efficiency and voltage sensitivity of the high voltage sensitive wireless EM harvester are shown in

The maximum measured efficiency at −30 dBm is 20% for ∼200 kΩ load and an open circuit voltage of 0.5 V. At −10 dBm, the maximum efficiency and open circuit voltage are 54% and 5.4 V respectively. At the optimal load of ∼200 kΩ, the detected voltage is 0.2 V and 2.9 V at −30 dBm and −10 dBm respectively. The open circuit voltage gain is 100 at −30 dBm and 108 at −10 dBm.

Even though the RF to DC converter presented in Section 2.5.3 is the same as the L-match circuit realized with the HMSM-286C diodes at 13.6 MHz, the voltage gain is increased by a factor of 4 due to the large difference between the diodes (and load) resistance and source resistance so that at matched conditions high voltage gain occurs. The loaded

A wireless EM harvester, consisting of a rectifying antenna (

The antenna (planar) part of the rectenna is based on our earlier work [

HFSS [_{11} and impedance. _{11} results. From

At far field between wireless EM transmitting and receiving antenna, the coupling mechanism between the transmitting and receiving antenna is neither capacitive nor inductive as is the case for the RF to DC converters. The coupling is radiative which can be described by the Friis equation of transmission on the assumption that the transmitting and receiving antenna are in free space [_{envt}

The efficiency of the rectenna's antenna is ∼20% at resonance. A ‘perfectly’ matched RF to DC power converter operating in its square law region has efficiencies in the region of 20% as depicted in Section 2. The transmitting antenna was the same as the antenna incorporated in the rectenna. By transmitting the EM power with a small antenna (5 cm × 5.2 cm) at 437 MHz with efficiency of ∼20% and at a gain of −6 dBi, the power delivered by the rectenna is generally low at far-field from the transmitter as can be seen in ^{−2} fit as shown in _{envt}

Optimization of Schottky diode-based RF to DC power converters using different matching techniques for wireless EM energy harvesting applications is presented. Using scattering parameters for small signal modeling, it is shown that wireless EM harvesters can be generally described as coupled resonators with efficiencies and maximum voltage sensitivity depending mostly on the source and load resistances under matched conditions. The analytical models allow systematic control in the design of passive wireless EM harvesters. Based on these analyses, a rectenna is built and tested for lower limit functionality from harvesting ambient EM waves. The analysis presented in this work may also be applied to optimize derivatives of wireless EM harvesters like RFID tags, NFC, wireless chargers

This work is part of the graduate program GRK 1322 Micro Energy Harvesting at IMTEK, University of Freiburg, funded by the German Research Foundation (DFG). Special thanks to Daniela Ohnemus for the PCB preparations and Uwe Burzlaff for antenna range measurements.

The measuring setup is as shown in Figure A1.

The RF to DC circuit efficiency and voltage sensitivity measurements were made with a Keithley 2400 source meter and Keithley 6514 system electrometer with an Agilent E4432B signal generator providing 50 Ω RF signal into the circuit board.

The closed circuit current drawn by the RF to DC power converter (

(

(

Measured input impedance (Δ resistive, □ capacitive) of HSMS-285C (

Circuit diagram of voltage doubler, (

(

(

Measured open circuit S_{11} of the L-matched Delon circuit at different input power levels from a 50 Ω source (

Measured L-matched circuit efficiency

Impedance diagram of PI-matched RF power converter; (

Inductive coupled parallel RLC small signal model of a generalized PI-matched antenna and diode rectifier.

Impedance diagram of broadband RF power converter; (

Measured open circuit S_{11} of the broadband circuit around 434 MHz at different input power levels from a 50 Ω source (

Measured open circuit voltage

(

Measured open circuit S_{11} of the L-matched HSMS-286C diodes at 13.6 MHz for different input power levels from a 50 Ω source (

Measured circuit efficiency

Rectenna realized on a Duroid 5880, 1.57 mm substrate. (

Antenna HFSS simulated, antenna measured, and measured L-matched diode rectifier S_{11} on a Duroid 5880 PCB for −30 dBm input (

Rectenna receiving range performance by sending 17 dBm (50 mW) at a gain of −6 dBi at 437 MHz. Output DC voltage

RF to DC Power converter characterization setup.

RF to DC power converter characterization circuit.