Investigating the Effects of Parasitic Components on Wireless RF Energy Harvesting

Antwi Nimo, Joan Albesa and Leonhard M. Reindl University of Freiburg – IMTEK, Department of Microsystems Engineering,

Laboratory for Electrical Instrumentation, Freiburg, Germany.

antwi.nimo, joan.albesa or reindl@imtek.de

Abstract—This work presents the effect of parasitic components on the performance of wireless RF energy harvesters. Since ambient RF power density is low, only optimal wireless RF energy harvesters will be able to power remote microwatt sensors. By knowing the effect of each parasitic component on the performance of wireless RF harvesters, components may be realized or selected that increases the overall efficacy of the harvester. The analytical and experimental investigation of the component parastics on the harvester output performance is compared at various operating frequencies; both at HF and UHF.

Index Terms— RF energy harvesting, RF energy transport, Schottky diode parasitics, reactive element parasitics.

I. INTRODUCTION The power from wireless radio frequency (RF) energy

harvesting has the potential to solely power microwatt sensors. In the future, RF energy harvesting may replace batteries or cables in supplying power to autonomous sensors. However the transition from powering sensors with batteries to RF energy harvesting must bring convenience and enhance economics for both industry and the end user. This is due to the fact that there are limitations on the amount of ambient RF power that can be sent through a wireless space, hence there is always less power density to harvest from. This is coupled to the fact that battery technology is advanced and well established in industry. Therefore RF harvesters must function based on worse case scenarios of ambient RF power sources. This pose engineering challenges in the design of wireless RF harvesters as there are limitations on the performance of composing components that make up the harvester. Today, most commercial off-the-shelf components are not necessarily optimized for RF energy harvesting, harvesters are realized based on existing components or on standardized CMOS processes that may not be optimized for RF energy harvesting. Fig. 1 shows a block diagram of a passive wireless RF energy harvester. Wireless RF harvesters generally consist of an RF-driving impedance (antenna) and the rectifier circuit. The antenna captures the ambient wireless RF power for rectification into direct current (DC) by using the rectifier. The rectifier circuit may be a single rectifier (diode or diode-connected transistors) or a cascade of rectifiers. In-between the antenna and the rectifier is an impedance matching or transformation network; to transform

the antenna impedance to that of the rectifier. The matching network consists of passive components providing inductive or capacitive reactance. The load consists of DC storage elements (capacitors, super-capacitors or rechargeable batteries) as required and the DC load (sensor) to be powered by the harvester.

In [1], the frontend of RF energy harvesters were modeled as coupled resonators. The components were modeled without directly separating the parasitic effects, hence insight into the quantitative effect of the parasitic components on the performance of the wireless RF harvester were not apparent. General effect of parasitic components on wireless RF harvesters were presented in [2]. This work presents quantifiable effect of component parameters on the performance of wireless RF harvesters, with emphasis on the rectifier and the reactive elements used for impedance matching/transformation. By knowing quantitatively the effect of each component parameter on the performance of the harvester, components may be engineered to optimize the performance of RF energy harvesting. The rest of the paper is organized as follows. In section II, Schottky diode RF rectifier and the effect of the saturation current (IS) or junction resistance (Rj), bulk resistance (RS) and the junction capacitance (Cj) on the impedance of the rectifier is examined. In section III, components that provide inductive reactance for impedance matching/ transformation in RF energy harvesters are examined. In section IV, the effect of the parasitic parameters on the net resistance/ reactance of the components are presented. Experimental results of the various parasitic effects on RF power transmission are presented section IV.

Fig. 1. Block diagram of a wireless RF energy harvester.

loadimpedancematching

rectifierantenna

Circuit operating at both HF, VHF and UHF were demonstrated in section IV. Section V presents the conclusions.

II. RF SCHOTTKY DIODE A Schottky diode has fast switching speed and relatively

low junction capacitance. This makes it suitable for RF energy harvesting. The RF model of a Schottky diode in forward bias is shown in Fig. 2 [3]. Rj and Cj are the junction resistance and capacitance respectively. RS, LS and CP are the bulk resistance, packaging inductance and capacitance respectively.

The admittance of the Schottky diode is given by equation (1). Ydiode is the diode admittance; where G is the conductance and B is the susceptance.

1j

jdiode S S P

jj

Rj C

Y G jB R j L j C1R j C

ωω ω

ω

−⎛ ⎞⎜ ⎟⎜ ⎟= + = + + +⎜ ⎟+⎜ ⎟⎝ ⎠

(1)

For a Schottky diode, Rj may be found from Richardson’s equation [4]. α is the thermal voltage, IS is the diode reverse saturation current and IDC in (2) is the DC current that goes through the diode. IDC is a controlled parameter dependent on the input RF power level and the load connected to the diode.

jS DC

RI I

α=

+ (2)

For the sake of investigating the effect of IS (or Rj), RS and Cj on the diode impedance, IDC is fixed so that it produces the same effect on each parasitic parameter. The effect of the parasitic components on the diode parallel resistance (RD=G-1) and parallel reactance (-XD=B-1) for the HSMS-286x Schottky diode from Avago Technology is presented. The diode parasitic parameters which were used in calculating the diode impedance are shown in Table 1.

Table 1: HSMS-286x Schottky diode parameters Is (nA) IDC (nA) Cj (pF) RS (Ω) LS (nH) Cp (pF)

50 2 0.18 6 2 0.08

Fig. 3 shows the calculated effect of IS, RS and Cj on the diode parallel resistive impedance. As the IS is increased from 50 nA

to 0.5 µA, the parallel resistive impedance of the diode reduces. For the junction capacitance Cj, an increased from 0.18 pF to 1 pF also resulted in a decrease in the resistive impedance of the diode. By increasing RS from 6 Ω to 25 Ω, the parallel resistive impedance reduces as well. Fig. 3 shows that a Schottky diode with low IS, RS and Cj will have high parallel resistive impedance.

Since the resistive impedance of a diode is quasi non-power dissipative, high resistive diode rectifier do not necessarily mean high power dissipate in the diode. It was shown in [1][5] that high resistive diode rectifier is needed for high RF voltage transformation at the input of the diode at matched conditions. Diodes are sensitive to voltage, hence highly efficient and voltage sensitive wireless RF harvesters may be realized with diode rectifiers having high resistive impedance; i.e. low IS, RS, Cj and also low CP. The trade-off of high resistive diode rectifier is its high frequency selectivity at matched conditions. For RF harvesting which requires broadband operations, low resistive diode rectifier may be preferred. In that case a diode with high IS, and Cj may be preferred. However broadband matched RF harvesters may have low efficiency (output DC power/input RF power) and low voltage sensitivity as a trade-

Fig. 2.RF model of a Schottky diode.

Rj

Cj

RSLS

CPbare diode

Fig. 3. The effect of the changes in saturation current (IS), bulk resistance (RS) and diode junction capacitance (Cj) on the diode

parallel resistance (RD).

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.0 0.5 1.0 1.5 2.0

Para

llel i

mpe

danc

e (M

Ω)

Frequency (GHz)

Rᴅ @ Is=50 nA,Cj=0.18 pF and Rs=6 Ω

Rᴅ @ Is=0.5 µA

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.0 0.5 1.0 1.5 2.0

Para

llel i

mpe

danc

e (M

Ω)

Frequency (GHz)

Rᴅ @ Is=50 nA,Cj=0.18 pF and Rs=6 ΩRᴅ @ Rs=25 ΩRᴅ @ Cj=1 pF

off; as was shown in [6]. The effect of IS, RS and Cj on the parallel reactive impedance of the Schottky diode is shown in Fig. 4. The results show that IS and RS has no effect on the parallel reactive impedance.

There is no change in the parallel reactive impedance by increasing IS from 50 nA to 0.5 µA or RS from 6 Ω to 25 Ω. However Fig. 4 shows that the higher the Cj, the lower the parallel reactive impedance and vice-versa. The reactive impedance of a diode is responsible for directing RF power away from the diode rectifying junction. Hence the reactive impedance of the diode must be matched through impedance matching / transformation. It can be seen from Fig. 3 that IS, RS and Cj has significant effect on the resistive impedance of a diode; which is responsible for directing the RF power to the rectifying junction for rectification. By knowing the impedance of a single diode, the input impedance of a diode doubler or multiplier arrangement can be directly estimated.

III. REACTIVE MATCHING COMPONENTS The reactive elements that are used for impedance

matching/ transformation may be realized with CMOS process [7][8] or by using packaged off-the-shelf components. Inductive elements will be discussed in this work since they exhibit most parasitic behavior at high frequencies. The inductive reactance may be provided by a coil resonator [9][10] or by a quartz crystal [5][11]. The equivalent circuit model of a coil resonator and a quartz crystal is shown in Fig. 5.

Rac, Lac and Cac are the series resistance, series inductance and shunt parasitic capacitance of the coil resonator respectively. Raq, Laq, and Caq are the series resistance, series inductance and series capacitance of the quartz crystal respectively. Coq is the shunt parasitic capacitance of the crystal. The net reactance and resistance of the resonators can be found from the equivalent circuit parameters. A coil or crystal can inherently provide high inductive reactance at low frequencies. Since at progressively low frequencies, the shunt capacitance becomes increasingly open circuited and the net reactance of the resonator is progressively inductive. At UHF frequencies or above, the shunt capacitance dominates current conduction and the net inductive reactance is reduced; only in the order of nanohenries is attainable with current state of the art. For coil resonators, its resonant frequency is determined by Lac, Cac and Rac. Up to the resonance frequency, the coil reactance is inductive. At the resonance frequency, there is no net inductive reactance (nor capacitive reactance) and at frequencies above the resonance frequency, the reactive impedance is capacitive. Fig. 6 shows the measured impedance of the 1812CS-273XJLB (27µH) and 1812CS-183XJLB (1.8µH) coil resonators from Coilcraft. The self-resonance frequency of the 1812CS-273XJLB coil is ~41 MHz while that of 1812CS-183XJLB coil is ~300 MHz.

As for the quartz crystal, it has two resonant frequencies (series and parallel). At both resonant frequencies, the crystal does not

Fig. 4. The effect of the changes in saturation current (IS) and diode junction capacitance (Cj) on the diode parallel reactance

(XD).

-0.13

-0.11

-0.09

-0.07

-0.05

-0.03

-0.01

0.01 0.05 0.50

Para

llel r

eact

ance

(MΩ

)

Frequency (GHz)

Xᴅ @ Cj=1 pF

Xᴅ @ Cj=0.18 pF, Rs=25 Ω and Is=50 nA or 0.5 µA

Fig. 5. (a)Equivalent circuit model of inductive coil resonator,

(b) Equivalent circuit model of a quartz crystal resonator.

(a) (b)

RacLac

Cac

RaqLaqCaq

Coq

Fig. 6. Measured impedance of two coil resonators.

-30-20-10

01020304050

1 21 41

Impe

dnac

e (kΩ

)

Frequency (MHz)

1812CS-273XJLB coil

ResistiveImaginary

0

5

10

15

20

25

80 130 180 230

Impe

danc

e (kΩ

)

Frequency (MHz)

1812CS-183XJLB coil

ResistiveImaginary

provide any net reactive impedance. In-between the series and parallel resonance, the quartz crystal provides inductive reactance. The quantum of inductive reactance that a quartz crystal may produce is characterized by the so-called capacitance ratio (Coq/Caq) [12]. The capacitance ratio defines the width of the quartz crystal inductive region. The lower the capacitance ratio, the higher the inductance and its associated quality factor (Q) and vice-versa. The measured impedance of commercially available Abracon ABLS-LR (series resonance of 13.5 MHz) and AxTal (series resonance of 88.475 MHz) Quartz is shown in Fig. 7. It can be seen that the inductive reactance provided by the crystal at HF (~13.56 MHz) is much higher than at VHF (~88.47 MHz).

IV. RF POWER TRANSMISSION A comparison of RF harvesters realized with inductive

coils resonators and quartz crystals will be presented for frequencies up to VHF. At UHF frequencies, the effect of high resistive diode rectifier and low resistive diode rectifier on the output performance of the RF harvester will be presented. From the impedance of the RF source (antenna) and the diode rectifier (as in Fig. 3 and Fig. 4). Standard matching techniques [1] may be used to find the required inductive and capacitive reactance that transform the RF source impedance and the diode impedance at a frequency. The circuits realized at ~13.56 MHz for inductive coil and for quartz crystal is show in Fig. 8. A modified Dickson voltage quadrupler is used for

rectification. Fig. 9 shows the realized RF harvesters for coil (1812CS-183XJLB) and the AxTal quartz crystal at ~88.4 MHz. At ~88.4 MHz, a voltage doubler is used for rectification. The employed diodes at ~13.56 MHz and ~88.4 MHz were HSMS-286x series from Avago Technologies. The circuits were realized on 1.5 mm thick FR4 substrates.

The results of the circuit performances comparing the coil and the quartz resonators at ~13.56 MHz are shown in Fig. 10 and Fig. 11. The results show that the RF harvester realized with the ABLS-LR 13.5 MHz crystal is more sensitive and efficient (more than twice) as that realized with the ELJFA150JF coil at 13.56 MHz. This is due the fact that the inductive reactance provided by the ABLS-LR 13.5 MHz crystal has less resistive losses (1.25 kΩ @ 13.56 MHz, Q=200) as compared to the 1812CS-273XJLB coil (1.3 kΩ @ 13.56 MHz, Q=15). By having less resistive loss across the reactive matching

Fig. 7. Measured impedance of the 13.5 MHz and 88.47 MHz

quartz crystals.

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

13.560 13.565 13.570 13.575

Impe

danc

e (M

Ω)

Frequency (MHz)

ABLS-LR 13.5 MHz Quartz

Resistive

Imaginary

-3

-1

1

3

5

88.474 88.479 88.484

Impe

danc

e (kΩ

)

Frequency (MHz)

AxTal 88.4 MHz Quartz

ResistiveImaginary

Fig. 8. RF harvesters realized at ~13.56 MHz. C = 100 pF, RL= Load. (a) Coil, CC = 3.3 pF. (b) Quartz, CC = 2 pF.

coil (1812CS-273XJLB)

quartzABLS-LR 13.5 MHz

2cm

(a)

(b)

C C

RL

C C

coil

CC

C C

RL

C C

CC

2cm

RF

pow

erR

F po

wer

Fig. 9. RF harvesters realized at ~88.4 MHz, RL= Load. (a)

Realized with coil. (b) Realized with quartz.

coil (1812CS-183XJLB)

diode doubler HSMS-286C

RL

RF

pow

er

HSMS-286C

RF

pow

er

quartzAxTaL 88.47 MHz

diode doubler

2cm

2cm

(a)

(b)

coil

47pF

0.3pF

100pF

100pF

0.2pF

RL

elements, RF power is efficiency transferred and transformed (into voltage) to the high resistive HSMS-286x diode rectifier. This result show that the loss-tangent of the impedance matching/transformation components is as critical as the rectifier properties in wireless RF energy harvesters.

As for the wireless RF harvester realized at ~88.4 MHz, the inductive coil resonator (1812CS-183XJLB) showed better voltage sensitivity and efficiency (factor 5 up to -10 dBm input RF power) as compared to the ~88.47 MHz crystal (see Fig. 12 and Fig. 13). This is due to the fact that at ~88.4 MHz, the inductive reactance of the 1812CS-183XJLB coil resonator (1.1 kΩ @ 88.479 MHz, Q = 92) provided less resistive losses than that provided by the AxTal quartz crystal (742 Ω @ 88.479 MHz, Q = 3). It is interesting to note that the parallel resistive impedance of the HSMS-286x diode is high (~ MΩ) at ~13.56 MHz (see Fig. 3), hence it does not load the impedance transformation network. At progressively high operating frequencies, the diode increasingly loads the impedance transformation network and voltage amplification at the input of the diode is limited.

The effect of a diode resistive impedance on the performance of wireless RF harvesters is presented at ~868 MHz. High resistive Schottky diode (HSMS-286x) and a low resistive Schottky diode (HSMS-285x; IS=3 µA, RS=25 Ω and Cj=0.18 pF) are compared for voltage sensitivity and efficiency. The circuits were realized using a diode voltage doubler as a rectifier with coil resonators (and chip capacitors) as impedance matching /transformation elements. The circuit were realized on a 1.5 mm FR4 substrate. The result of the measured voltage sensitivity is shown in Fig. 14. It can be seen that the RF harvester realized with the HSMS-286x diodes are more sensitive than that realized with the HSMS-285x diodes. Open circuit voltage sensitivity of factor 2 was measured for HSMS-286x Schottky diodes as compared to the HSMS-285x. This is due to the fact that the HSMS-286x diode provides higher parallel resistive impedance as compared to HSMS-285x diode at 868 MHz. It is worth noting that the HSMS-286x (or even HSMS-285x) diodes show low voltage sensitivity at ~868 MHz as compared to ~88.47 MHz or ~13.56 MHz. This is due to the low diode resistive impedance at UHF frequencies (see Fig. 3), hence voltage amplification at the input of the diodes is limited at matched condition or resonance.

Fig. 10. Measured output voltage of the RF harvester realized

with coil at ~13.56 MHz.

0.01

0.1

1

10

-45 -40 -35 -30 -25 -20 -15 -10

Out

put v

olta

ge (V

)

Input RF Power (dBm)

1812CS-273XJLB coil

Open circuit5 MΩ2 MΩ1 MΩ0.5 MΩ

Fig. 11. Measured output voltage of the RF harvester realized

with quartz crystal at ~13.56 MHz.

0.01

0.1

1

10

-45 -40 -35 -30 -25 -20 -15 -10

Out

put v

olta

ge (V

)

Input RF Power (dBm)

ABLS-LR 13.5 MHz Quartz

Open circuit5 MΩ2 MΩ1 MΩ0.5 MΩ

Fig. 12. Measured output voltage of the RF harvester realized

with coil at ~88.4 MHz.

0.01

0.1

1

10

-30 -20 -10 0

Out

put v

olta

ge (V

)

Input RF power (dBm)

1812CS-183XJLB coil

Open circuit2 MΩ1 MΩ0.5 MΩ100 kΩ

Fig. 13. Measured output voltage of the RF harvester realized

with quartz crystal at ~88.4 MHz.

0.001

0.01

0.1

1

10

-30 -20 -10 0

Out

put v

olta

ge (V

)

Input RF power (dBm)

AxTaL 88.4 MHz Quartz

Open circuit2MΩ1MΩ0.5MΩ100kΩ

When the RF voltage amplification at the input of the diode is limited; the rectifier efficiency is skewed toward diodes with high saturation current (IS). Fig. 15 shows that the RF harvester realized with the HSMS-285x diodes is almost twice as efficient as that of the HSM-286x at ~868 MHz. The measured -3 dB power bandwidth of the HSMS-285x RF harvester was twice as that of the HSMS-286x RF harvester.

V. CONCLUSION By knowing the effect of all major parasitic components on

the performance of a wireless RF harvester, optimal wireless RF harvesters can be realized which are capable of harvesting low ambient RF power levels. In this work, a harvester with -31 dBm sensitivity for dc output voltage of 1 V across a DC load of 5 MΩ is realized. Open circuit sensitivity of 1 V at -37 dBm input RF power is achieved. We show that the loss-tangent of the reactive matching elements has major influence on the performance of the harvesters. However for reactive matching elements with similar Q, harvesters operating at low-frequencies present higher sensitivity and efficiency compared to the systems at high-frequencies. This is due to the low resistive impedance of diodes rectifiers at high frequencies.

These results prove how the major parasitic components affect the performance of a wireless RF energy harvester.

VI. ACKNOWLEDGMENT 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).

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[3] H. A. Watson, Microwave semiconductor devices and their circuit applications. New York; Maidenhead: McGraw-Hill, 1969.

[4] C.-T. Sah, Fundamentals of solid-state electronics. Singapore; River Edge, NJ: World Scientific, 1991.

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[10] Peter CSURGAI et.al, “Quality factor modeling of surface mounted chip inductors in high frequency,” J. Adv. Res. Phys. Vol 2 No 1 2011, 2011.

[11] T. Ungan, X. Le Polozec, W. Walker, and L. Reindl, “RF energy harvesting design using high Q resonators,” in Wireless Sensing, Local Positioning, and RFID, 2009. IMWS 2009. IEEE MTT-S International Microwave Workshop on, 2009, pp. 1–4.

[12] STATEK Corporation, “The Quartz Crystal Model and its Frequencies.” STATEK Corporation, 2006.

Fig. 14. Measured voltage sensitivity of high resistive diode

(HSMS-286C) compared to low resistive diode (HSMS-285C) at ~868 MHz.

0.01

0.1

1

10

-40 -30 -20 -10 0

Ope

n ci

rcui

t vol

tage

(V)

Input RF Power (dBm)

HSMS-286C diodeHSMS-285C diode

Fig. 15. Efficiency of the HSMS (285x and 286x) diode at

various input RF power at ~868 MHz.

05

10152025303540

5.E+00 5.E+02 5.E+04

Eff

icie

ncy

(%)

Resistive Load (Ω)

285C @ -10dBm285C @ -15dBm286C @ -10dBm286C @ -15dBm