IMPEDANCE OPTIMIZATION OF WIRELESS ELECTROMAGNETIC ENERGY HARVESTERS FOR MAXIMUM OUTPUT EFFICIENCY AT µW INPUT POWER Antwi Nimo*, Dario Grgić and Leonhard M. Reindl University of Freiburg – IMTEK, Department of Microsystems Engineering, Laboratory for Electrical Instrumentation, Georges-Köhler-Allee 106, 79110 Freiburg, Germany Email:
[email protected] ABSTRACT This work presents the optimization of radio frequency (RF) to direct current (DC) circuits using Schottky diodes for remote wireless energy harvesting applications. Since different applications require different wireless RF to DC circuits, RF harvesters are presented for different applications. Analytical parameters influencing the sensitivity and efficiency of the circuits are presented. Results showed in this report are analytical, simulated and measured. The presented circuits operate around the frequency 434 MHz. The result of an L-matched RF to DC circuit operates at a maximum efficiency of 27 % at -35 dBm input. The result of a voltage multiplier achieves an open circuit voltage of 6 V at 0 dBm input. The result of a broadband circuit with a frequency band of 300 MHz, achieves an average efficiency of 5 % at -30 dBm and open circuit voltage of 47 mV. A high quality factor (Q) circuit is also realized with a PI network matching for narrow band applications. Keywords: RF energy harvesting, wireless power transmission, RF to DC circuit, Schottky diode, impedance matching
1. INTRODUCTION For autonomous powering of sensor nodes in remote or inaccessible areas, wireless power transfer provides the only viable option to power remote sensors from an energy source. Due to the low power density of ambient RF, there is the need to optimize each aspect of a wireless RF energy harvester for possible realistic applications. Today remote sensors are powered mostly by batteries which have limited lifespan. Renewable powering has the potential to power autonomous sensors perpetually. Ambient electromagnetic (EM) power is among the most common sources of ambient energy due to the expansion of telecommunications technology. There are power transmitters/receivers scattered in any modern society, ranging from television transmission stations to cell phone transmitters/receivers and even wireless routers in our homes/offices or mobile phones. These transmitters produce ambient energy which can be used as a source for powering remote microwatt budget sensors through wireless energy harvesting. This work reports different matching techniques based on different application requirements using Schottky diode based RF to DC circuits for wireless remote EM energy harvesting around the industrial, scientific and medical (ISM) band 434 MHz. The presented RF to DC circuits achieves high efficiencies and sensitivities. Additionally, the limitations of each technique for different applications are discussed. 1.1 State of Art 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 reflectors1. Wireless power transmission was then investigated and demonstrated for possible wireless remote powering by Tesla. Electromagnetic power beaming has been proposed in the 1950’s for far field wireless power transfer using collimated EM waves1. Recent advances in ultralow power sensors means ambient Omni-directional EM power can be used as a source for powering remote sensors without the need to collimate the EM energy through the wireless space. Mickle2, McSpadden3 have presented earlier work on wireless energy harvesting systems using antennas, schottky diodes and rectennas where the usability of ambient RF energy into DC power was shown. Sample4 has presented wireless harvester which can harvest energy from TV and radio base stations where 60 uW was harvested at a range of about 4 km. Hagerty 5 presented rectenna arrays for broadband ambient EM harvesting and characterized the harvesters from 2 GHz to 18 GHz. Rectennas combine impedance matching of the
RF to DC process and the antenna into one compact process, so there is no separate impedance matching network between the antenna and the rectifier. But an array of rectennas increases the overall size of an EM harvester. Umeda6 and Lee7 have presented a more integrated wireless energy harvester based on CMOS rectifying circuits. CMOS based rectifying circuits provide full compatibility with standard CMOS technologies and have advantages in batch processes for mass production. The drawback of CMOS based diode connected transistors is the need to bias the gate of the transistors for the rectifying circuits to effectively function. This gate bias is provided externally which makes the system not completely passive. Without the injection of external charges or a biasing of the transistor gate, the circuit results in low efficiency, especially when the amplitude of the input voltage is low8. Shameli9 presented passive CMOS RF to DC circuit with high sensitivity of 1 V at -14.1 dBm but the circuit efficiency was at 5 %. Sudou10 has presented a system on a chip which could provide pulsed output power from receiving near field RF energy from a mobile phone. Zbitou11 presented an RF to DC circuit based on Schottky diodes and achieved 56 % efficiency at 20 dBm. Ungan12,13 presented antennas and high Q RF to DC circuits at 300 MHz and 24 MHz for RF wireless harvesting at ultra low input power (-30dBm). The RF to DC circuit used high Q resonators for impedance matching the source and the diode impedance and achieved high open circuit voltage sensitivity of 1 V/µW but relatively low efficiency. Herb14 and Vullers15 have provided a comprehensive state of art for micro energy harvesting and have explored the various techniques used for harvesting ambient renewable energy.
2. RF TO DC SYSTEM DESIGN 2.1 Diode rectifier A simple diode rectifier is shown in Figure 1. AC voltage incident on a forward biased diode input is converted to DC voltage at the output. The current-voltage behavior of a single junction diode is characterized by the Shockley diode equation (equation 1).
VD
I
+ -
VS
VC
Figure 1. Diode detector; Vs is a sinusoidal source voltage, Vc is the voltage across the capacitor
qVD nKT I I S e 1
(1)
I is the current through the diode, IS is the leakage current, q is the charge of an electron, VD is the voltage across the diode, T is the temperature in degrees Kelvin, K is Boltzman’s constant. The voltage equation around the loop can be derived from Figure 1 and is given in equation 2.
VD VS VC
(2)
Since the current through the diode is the same current through the capacitor, one can find the average current through the circuit by integrating equation 1 over a time period. By substituting VD VS VC into equation 1, VC can be expressed in terms of VS by averaging the diode current to zero. This is given in equation 3.16
VC
KT qVS ln 0 q KT
(3)
where 𝜗0 is a series expansion of the sinusoidal source voltage. Equation 3 can be further simplified for very small amplitude VS as equation 4.
2
VC
qVS 4 KT
(4)
Equations 4 shows that for small input signals, the circuit output voltage is proportional to the square of the input sinusoidal voltage, hence in it’s so called square law operation. Extensions of this model for voltage multipliers and other input signals are presented in17,18. Equation 4 shows that for ultra low input voltages (power ≤10 dBm) an impedance matching network between the source and the diode is necessary to improve the detected output voltage and efficiency. 2.2 Impedance matching When dealing with AC signals, resistive and reactive components affect differently the flow or change of current. This relative change to the flow of current from a source can produce a loss of power at an output if not properly matched. For a source signal to flow freely to its destination there may be the need to adjust the resistive and reactive impedances in its path to maximize the output power. The power transfer theorem states that highest power is transferred to the load when the source resistance is the same as the load resistance. For reactive elements, the flow of power to the load is highest when the source and load impedance are the complex conjugate of each other. 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, if that is not the case already. This will ensure that maximum power is transferred to the output. For the purpose of this work, a 50 Ω resistive reference source is chosen for load impedance matching. The antenna which captures the ambient RF signals provides this source impedance for the RF to DC circuit in a complete EM wireless remote harvester. The load is the Schottky diode used for building the RF to DC circuits. 2.3 Diode Impedance Schottky diode HSMS-285C from Avago19 is used to build the RF to DC circuits. The HSMS-285x series of diodes are zero biased diodes optimized for low signal applications. This is ideal for RF to DC circuits used for EM wireless energy harvesting. The HSMS-285C is a series pair schottky diode packaged into an SOT-323 package. The impedance of the HSMS-285C diode is first measured so it can be matched to the source resistive impedance (50 Ω). The impedance of the diode was measured at an input power of -30 dBm at 1 MΩ load with a 100 pF filter capacitor. The circuit layout and measuring board are shown in Figure 2.
Figure 2. Circuit layout (left) and PCB (right) for input impedance measurement of the HSMS-285C diode
The board is fabricated such that components are soldered directly one into another to prevent additional impedances introduced by copper route. The PCB back-side had the ground layer. The measured input impedance from 300 MHz to 700 MHz is as shown in Figure 3. At input power of -30 dBm, the input impedance of the HSMS-285C diode is 72 Ω -j502 Ω at 434 MHz. The capacitive impedance is due to the junction capacitance provided by junction diodes. Since the impedance of diodes changes based on input power level, frequency and load, the input impedance at -30 dBm at 1 MΩ load around 434 MHz is chosen as a reference for impedance matching to the 50 Ω source. When an RF to DC circuit is matched to these reference conditions of the load (diode) impedance, the matching network functions less effectively at other frequencies and input power levels, the imperfection of the matching circuit at operating points different from -30 dBm input and other frequencies other than 434 MHz is accepted without changes to the matching network.
200
Impedance (Ohm)
100
0.434 GHz 71.7 0.434 GHz -502
-400
Re(Z[1,1]) HSMS285C
Im(Z[1,1]) HSMS285C
-900 0.3
0.4
0.5 Frequency (GHz)
0.6
0.7
Figure 3. Measured impedance (Δ resistive, □ capacitive) of the HSMS-285C diode at -30 dBm input from a 50 Ω resistive source.
2.4 Voltage doubler; L-matching The Delon voltage doubler16 is used for most of the RF to DC circuits presented in this work. The Delon voltage doubler is shown in Figure 4. The output voltage (Vout) is doubled what is detected by a simple detector circuit shown in Figure 1. The difference of the Delon doubler to the Greinacher doubler20 is that the input ground is not shared with the output ground. The diode impedance is matched to the reference 50 Ω source with an L-matching network; Figure 5a. The diode impedance measured in Figure 3 is taken as load for the L-matching network. An L-matching network converts source series impedance to the equivalent load parallel impedance or vice-versa and tunes out (subtract) any stray reactance from load or source with the counter impedance. Series impedance is converted to its parallel equivalent impedance using equations 5, 6 and 7.
Figure 4. (a)Circuit diagram of the Delon voltage doubler, (b) positive half cycle current path, (c) negative half cycle current path.
QS
XS RS
(5)
QP
RP XP
(6)
RP (Q 2 1) RS
(7)
Where Xs is the series reactive impedance, Rs is the series resistance (source resistance), RP is parallel resistance (or load resistance; RL), Xp is the parallel reactive impedance and Q is the circuit loaded quality factor. Qs and Qp are the series and parallel component quality factor respectively. The loaded Q of an L-circuit matching network can then be predicted from equation 7. At 434 MHz, the impedance of the diode is 72 Ω –j502 Ω at 1 MΩ load (Figure 2). Using equation 5, 6 and 7, this series impedance can be converted to its equivalent parallel impedance. The equivalent parallel impedance of the diode is found as 3519.36 Ω resistance in parallel with 510 Ω capacitive impedance at -30 dBm. For the purpose of
this work, inductors are only used for series impedance matching and capacitors as shunts. This prevents power seeping through any shunt inductor used for impedance matching. Using shunt inductors to match complex shunt capacitive impedance such as the HSMS-285C diode can give ‘perfect’ matching circuit and good return loss at the input for these complex loads but will result in less efficiency at the output due to loss of power arising from the short circuit provided by the inductor to ground. From equation 7 the RF to DC circuit loaded Q is found as 8.3 at -30 dBm for the 50 Ω source and 3519.36 Ω load at 434 MHz. From this loaded Q, a series inductive impedance of 416 Ω (152 nH @ 434 MHz) using equation 5 and a shunt capacitive impedance of 424 Ω (0.86 pF @ 434 MHz) using equation 6 will match the 50 Ω source to the 3519.36 Ω resistive load at -30 dBm input. Since the diode inherently provides 510 Ω (0.7 pF) shunt capacitive impedance at -30 dBm input at a frequency of 434 MHz, a resultant shunt capacitive impedance of 1834 Ω (~0.2 pF @ 434 MHz) is needed to tune the complete HSMS-285C diode impedance at -30 dBm input at a frequency of 434 MHz. Figure 5b shows these calculated values. Figure 5b assumes perfect characteristic impedance between the various components in the matched circuit. When copper route is introduced between components and on material substrate, it must be accounted for in the total impedance as seen by the source or load. This PCB impedance compensation is carried out in Advance Design Systems from Agilent21. ADS has extensive models for microstrip substrates to account for its impedances. The optimized layout using ADS microstrip models and its compensated values in the passive tuning components is shown in Figure 5c.
Figure 5. (a) Delon Voltage doubler with L-circuit matching network, VL is the load voltage, Ps is the source power, Pin is the power into the matching network, Zin is the equivalent L-matching input impedance as seen from the source, Xp* is the resultant impedance from the shunt load impedance and the shunt tuning impedance (b) L-network matching values used for matching the HSMS-285C diode at 434 MHz at -30 dBm input. (c) PCB layout of the L-matching network with adjusted values due to impedances provided by copper route. (d) Fabricated PCB of the L-network matched voltage doubler.
From Figure 5a the power dissipated in the load (PL) is given by equation 8, the source power (PS) is given by equation 9 where Vs* is the root mean squared (RMS) source voltage. Half of the source power is transferred to the load at match conditions. Equating PL and PS /2 gives a condition of voltage gain for a matched network. Equation 10 shows that the voltage sensitivity of the matched circuit depends on the load and source resistance. The load resistive impedance is
dependent on the diode realized parameters, signal frequency, output load resistance (RL) and the input power level. The source impedance is determined by the impedance of the antenna. According to Shameli9, the voltage sensitivity at matched conditions can be expressed in terms of the load quality factor (Qs or Qp); equation 11. 2
PL
VL RL
(8) 2
PS
2
VS V or PS S * RS 2 RS
VL 1 VS 2
(9)
RL RS
(10)
VL 1 1 QP VS 2
(11)
For maximum efficiency, the ratio of the source resistance to the load resistance must tend to zero. The efficiency (η) of the circuit is given by equation 12.
PL R ; 1 when S 0 PS RL
(12)
Higher circuits efficiencies will be achieved if the load resistance is much bigger than the source resistance. 2.5 Voltage doubler; L-matching results The circuit reflection coefficient (S11) and input impedance at open circuit are shown in Figure 6. There is good return loss and resonance around the ISM band 434 MHz. The circuit input impedance at open circuit conditions is around ~38 Ω at resonance (~459 MHz) for -40 dBm and ~17 Ω (~460 MHz) at -10 dBm input. 150
0
100
-8 -12 -16
0.439 GHz -9.46 dB
-20 0.284
DB(|S[1,1]|) -10dBm
DB(|S[1,1]|) -30dBm
DB(|S[1,1]|) -20dBm
DB(|S[1,1]|) -40dBm
0.384 0.484 Frequency (GHz)
0.584
Impedance (Ohm)
S11 (dB)
-4 0
-100
-200
-300 0.284
0.384
Re(Z[1,1]) -10dBm
Re(Z[1,1]) -40dBm
Im(Z[1,1]) -10dBm
Im(Z[1,1]) -40dBm
0.484
0.584
Frequency (GHz)
Figure 6. Measured open circuit reflection coefficient of the L-network matching Delon circuit at different input power levels from a 50 Ω source (left), Measured Open circuit input impedance at -10 dBm and -40 dBm of the Lmatched circuit to a 50 Ω source (right).
0 dBm -10 dBm -20 dBm -30 dBm -35 dBm
Efficiency (%)
50 40 30 20 10 0 1.E+02
DC output voltage (V)
60
Open Circuit Voltage
4
17 kOhm Load
0.4
0.04 1.E+03
1.E+04
Load (Ω)
1.E+05
1.E+06
-35
-30
-25
-20
-15
-10
-5
0
Circuit Input Power (dBm)
Figure 7. Measured L-network circuit efficiency versus load at various input power levels at 434 MHz (left), Measured Open circuit voltage and at 17 kΩ load versus input power at 434 MHz (right).
The RF to DC circuit efficiency and sensitivity measurements were made with Keithley 2400 source meter and Keithley 6514 system electrometer with Agilent E4432B signal generator providing the RF signal into the circuit board. The closed circuit current drawn by the RF to DC circuit is determined by the Keithley 2400 source meter and then limits the current (creates virtual load resistances) to the circuit up to a lowest current of 0.1 µA. The 6514 system electrometer is used to measure the output voltage. The number of data point is set through Labview as well as the measurements. Additionally open circuit voltage or at specific loads and frequency sweep can be made through the Labview program. At -40 dBm input power level and below, the detected voltages and currents are difficult to measure accurately with the Keithley’s; hence measurements were made up to only -35 dBm input for all the circuits presented. The maximum measured efficiency at -35 dBm is 27 % (~20 kΩ load) and an open circuit voltage of 76 mV. At 0 dBm, the efficiency and open circuit voltage is 55 % and 4.2 V respectively. At the optimal load (~20 kΩ), the detected voltage is 39 mV and 2.9 V at -35 dBm and 0 dBm respectively. From a 50 Ω resistive source, -35 dBm and 0 dBm corresponds to a RMS input voltage of about 3 mV and 0.16 V respectively, this shows an open circuit voltage gain of 19 and 26 respectively. The measured efficiency at -35 dBm is higher than that of -30 dBm (22 %) due to the better matched circuit impedance at -35 dBm (~38 Ω) than at -30 dBm (~27 Ω) to the 50 Ω impedance source. The L-matching doubler has a loaded Q, sensitivity and efficiency determined by the load and source resistive impedances at matched conditions. An L-matched RF to DC circuit may be applied for an all purpose application where a bit of everything is needed. 2.6 Voltage doubler; PI matching A high Q circuit is preferred for applications where small harvester operating band is required. The high Q circuit is realized with a PI network in-between the source and the diode. 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 networks22. For the purpose of this work, a loaded Q of 60 is chosen for matching.
Figure 8. (a) Impedance diagram of the Delon voltage doubler with matched PI network, (b) Resultant matched PI network and diode resistive load.
The loaded Q of the PI-network is given by equation 13.22
Q
RH 1 R
(13)
where RH is the largest terminating resistance and R is a virtual resistance. Equation 13 is the same as equation 7 except the lowest resistive impedance (Rs or Rp) in equation 7 is substituted with the virtual resistance which is dependent on the newly desired circuit loaded Q. For a desired circuit loaded Q of 60, and the HMSC-285C diode resistive parallel impedance of 3519 Ω, R turns out to be ~1. The virtual resistance provides load for the first section of the L-network and source for the second section. From equation 13, 5 and 6 the values of the combined series inductors and the two shunt capacitance can be found. The shunt capacitance of the diode (Figure 8a; 0.7 pF) can then be subtracted from the calculated tuning shunt capacitance to find a resultant matched shunt capacitance of 5.6 pF (Figure 8b). The voltage sensitivity and the efficiency of a PI matched network are characterized by equations 10 and 12.
Figure 9. (a)PCB layout of the Delon voltage doubler with matched PI network, (b) Picture of the fabricated RF to DC circuit.
Figure 9a shows the adjusted values on the PCB based on the substrate copper route dimensions. Figure 9b is a picture of the fabricated PI-network matched voltage doubler PCB. 2.7 Voltage doubler; PI-matching results The circuit reflection coefficient (S11) and open circuit input impedance are shown in Figure 10. The circuit resonate around 434 MHz and the realized circuit loaded Q is around 60 for -20 dBm and -10 dBm. The circuit input impedance at open circuit is around 30 Ω at resonance (~431 MHz) for -40 dBm and 48 Ω (~432 MHz) at -10 dBm input. 10
60
40
Impedance (Ohm)
S11 (dB)
0
-10
-20 DB(|S[1,1]|) -10dBm
DB(|S[1,1]|) -30dBm
DB(|S[1,1]|) -20dBm
DB(|S[1,1]|) -40dBm
0.434
Frequency (GHz)
Im(Z[1,1]) -40dBm
Re(Z[1,1]) -40dBm
Im(Z[1,1]) -10dBm
20
0
-20
-30
-40 0.384
Re(Z[1,1]) -10dBm
0.484
-40 0.284
0.384 0.484 Frequency (GHz)
0.584
Figure 10. Measured open circuit reflection coefficient of the PI- matching network Delon circuit at different input power levels from a 50 Ω source (left), Measured Open circuit input impedance at -10 dBm and -40 dBm of the PI-matched circuit to a 50 Ω source (right).
The high Q circuit is very sensitive to component tolerances and the tuning may not be exact as calculated due to the big influence of the component tolerances on the circuit. The matching of the PI-network (Q=60) was done at a reference power of -30 dBm but from Figure 10 (left), a Q of 60 occurs at an input of -20 dBm and -10 dBm.
35 0 dBm
30
-30 dBm
25
-35 dBm
20 15 10
DC output Voltage (V)
-20 dBm
Efficiency [100%]
Open Circuit Voltage
17kOhm Load
-10 dBm
3.6
0.36
5 0 2.E+02
2.E+03
2.E+04
2.E+05
Load [Ω]
0.036 -35
-30
-25
-20
-15
-10
-5
0
Circuit Input Power (dBm)
Figure 11. Measured PI-network circuit efficiency versus load at various input power levels at 434 MHz (left), Measured Open circuit voltage and at 17 kΩ load versus input power at 434 MHz (right).
The maximum measured efficiency at -35 dBm is 21 % (~13 kΩ load) and an open circuit voltage of 62 mV. At 0 dBm, the efficiency and open circuit voltage is 30 % and 3.5 V, respectively. At the optimal load (~13 kΩ), the detected voltage is 29 mV and 2.1 V at -35 dBm and 0 dBm respectively. From a 50 Ω resistive source, -35 dBm and 0 dBm corresponds to a RMS voltage of about 3 mV and 0.16 V, respectively, this shows an open circuit voltage gain of 10 and 13 respectively. The efficiency is higher at -35 dBm input than at -30 dBm (13 %); hence the circuit is better matched at -35 dBm input. Outside the perfect matched point, the circuit performance degrades. The PI-matching network provides an RF to DC circuit with high Q operation. Outside its optimal operation band, the functionality of the circuit degrades rapidly.
2.8 Voltage Quadrupler A two stage cascaded Delon circuit forms a voltage quadrupler. For applications where high voltage sensitivity is required, multipliers can be a good choice if the circuit input voltage is sufficient to turn-on the several diodes forming the multiplier. Karthaus23 showed that the output voltage of a multiplier is given by equation 14.
VDD n(VS VD )
(14)
where VDD is the output voltage of the multiplier and n the number of stages. Equation 14 shows that the amplitude of the source voltage is critical for a voltage multiplier to multiply. For fixed small input power levels, each diode in the multiplier network consumes an amount of current and hence the magnitude of the input voltage (Vs) decreases, which can even be smaller than the diode voltage (VD). In such situations, the multiplier will not multiply and will perform worse than a single voltage doubler shown in section 2.4 due to the loss of power across each of the diode in the multiplier network. The efficiency of the circuit is influenced to a greater degree by the voltage drops across the diodes at low input power levels; this is true even if the reflection coefficient (S11) or the circuit input impedance may be better matched to the 50 Ω impedance source. The presented voltage quadrupler consists of series pair diodes connected in parallel to each other. The input impedance of the quadrupler is the parallel combination of the impedances from the series pairs. The measured input impedance of the series pair HSMS-285C diode at 434 MHz is 3519.36 Ω in parallel with a capacitive impedance of 510 Ω at -30 dBm. This impedance in parallel with the same impedance gives a resultant impedance of 1759.68 Ω resistive in parallel with 255 Ω (1.4 pF @ 434 MHz) capacitive impedance. Hence the input impedance of the two stage voltage quadrupler is 1759.68 Ω in parallel with a 255 Ω (1.4 pF @ 434 MHz) at 434 MHz
at -30 dBm input. This shows as diodes are cascaded in parallel as in multipliers, the input resistance decreases but their shunt capacitance increases.
Figure 12. (a) Circuit of voltage quadrupler, (b) L-network matching values used for matching the HSMS-285C diode at 434 MHz at -30 dBm input. (c) PCB layout of the L-matching network with adjusted values due to impedances provided by copper route. (d) Fabricated PCB of the L-matching voltage quadrupler.
The values of the L-matching network follow the same analysis as in section 2.4, however the intrinsic shunt capacitance of the cascaded diodes is greater than the calculated shunt capacitance in the L-network (Figure 12b), the resultant matching capacitance is short of 0.2 pF to match the capacitive impedance of the diodes. Due to this, no shunt capacitance was needed for matching the circuit at around 434 MHz at -30 dBm input. The total inductance provided by the copper route in front of the diodes and the chip inductor (Figure 12c and 12d) was just good enough to provide an acceptable match of the 50 Ω impedance source and the cascaded diodes impedance. By using shunt inductors, ‘perfect’ matching and good return loss at the input can be achieved as in 24 but at the expense of circuit efficiency and voltage sensitivity due the short circuit provided by the inductor and hence a loss of power at the output. Figure 12b shows that for loads with large shunt capacitances (low capacitive impedance), it can be unmatchable in an L-matching network if one restricts itself to using inductors only for series matching for certain values of source impedance. 2.9 Voltage qudrupler; results The circuit reflection coefficient (S11) and input impedance at open circuit are shown in Figure 13. There is good return loss and resonance around the 434 MHz. The circuit input impedance at open circuit conditions is around ~30 Ω at resonance (~476 MHz) for -40 dBm and ~13 Ω (~472 MHz) at -10 dBm input.
100
S11(dB)
-4
-8
-12
0.443 GHz -9.36 dB -16 0.284
0.384
DB(|S[1,1]|) -10dBm
DB(|S[1,1]|) -40dBm
DB(|S[1,1]|) -20dBm
DB(|S[1,1]|) -30dBm
0.484
Impedance (Ohm)
0
0
-100
-200 0.284
0.584
Re(Z[1,1]) -10dBm
Re(Z[1,1]) -40dBm
Im(Z[1,1]) -10dBm
Im(Z[1,1]) -40dBm
0.384
0.484
0.584
Frequency (GHz)
Frequency (GHz)
Figure 13. Measured open circuit reflection coefficient of the voltage quadrupler at different input power levels from a 50 Ω source (left), Measured Open circuit input impedance at -10 dBm and -40 dBm of the voltage quadrupler from a 50 Ω source (right).
60
0 dBm
Efficiency (%)
-20 dBm
40
-30 dBm
30 20 10 0 2.E+02
2.E+03
2.E+04
Load (Ω)
2.E+05
2.E+06
Open Circuit Voltage (V)
-10 dBm
50
Open Circuit Voltage
4.4
17 Kohm Load
0.44
0.044 -30
-25
-20
-15
-10
-5
0
Circuit Input Power (dBm)
Figure 14. Measured circuit efficiency versus load at various input power levels at 434 MHz (left), Measured Open circuit voltage and at 17 kΩ load versus input power at 434 MHz (right).
The maximum measured efficiency at -30 dBm is 9 % (~16 kΩ load) and an open circuit voltage of 107 mV. At 0 dBm, the efficiency and open circuit voltage are 50 % and 6 V, respectively. At the optimal load (~16 kΩ), the detected voltage is 39 mV and 2.9 V at -30 dBm and 0 dBm respectively. From a 50 Ω resistive source, -30 dBm and 0 dBm corresponds to a RMS input voltage of about 3 mV and 0.16 V, respectively. This shows an open circuit voltage gain of 13 and 40 respectively. The Delon multiplier provides an RF to DC circuit with good functionality at sufficient input power levels. The voltage gain of 40 at 0 dBm is higher than the L-matched single Delon circuit but for low power levels (≤ -10 dBm), the voltage quadrupler performs worse in both efficiency and sensitivity compared to the L-matched single Delon circuit. 2.10 Broadband circuit A broadband network is preferred when the RF to DC circuit is to be operated in a wide band of frequencies. The broadband circuit is realized by connecting L-networks together in a multi-network. The result is a low Q circuit around the frequency of interest. The loaded Q of the broadband circuit is given in equation 13. The lowest possible Q is found for a virtual resistance (R*) given in equation 15.22. Similar to the situation discussed in section 2.8. There is ~0.4 pF inherent diode capacitance which is untuned using a two stage L-matching network (Figure 15b). Hence the matching network is not perfect at a loaded Q of 2.7 due to the stray untuned shunt capacitance of the HSMS-285C diode. Nevertheless, there is acceptable return loss from 300 MHz to 600 MHz (Figure 16 left) providing an operating band of 300 MHz. The impedance of the circuit shows multiple resonances (Figure 16 right).
R*
RS RL
(15)
Figure 15. (a) Broadband circuit around 434 MHz with loaded Q of 2.7, (b) Resultant impedance matching network with unturned (stray) capacitance of 0.4 pF.
2.11 Broadband circuit 500
5
Re(Z[1,1]) -10dBm
Im(Z[1,1]) -40dBm
Re(Z[1,1]) -40dBm
Im(Z[1,1]) -10dBm
Impedance (Ohm)
0
S11 (dB)
-5 -10 -15 -20 -25 0.034
DB(|S[1,1]|) -10dBm
DB(|S[1,1]|) -30dBm
DB(|S[1,1]|) -20dBm
DB(|S[1,1]|) -40dBm
0.334
0.634
0
-500 0.234
0.834
0.334
Frequency (GHz)
0.434
0.534
Frequency (GHz)
10
100
1
10
Efficiency (100 %)
Open Circuit Voltage (V)
Figure 16. Measured open circuit reflection coefficient of the broadband circuit around 434 MHz at different input power levels from a 50 Ω source (left), Measured Open circuit input impedance at -10 dBm and -40 dBm of the broadband circuit from a 50 Ω source (right).
0.1
0.01
1
0.1 -30dBm input, 17kOhm load
-30dBm input
-10dBm input -10dBm input; 17kOhm Load
0.01
0.001 200
250
300
350
400
Frequency (MHz)
450
500
200
250
300
350
400
450
Frequency (MHz)
Figure 17. Measured open circuit voltage versus frequency sweep from 200 MHz to 500 MHz for -10 dBm and -30 dBm (left), Measured efficiency at 17 kΩ load versus frequency sweep for -10 dBm and -30 dBm (right).
500
The average open circuit voltage is 47 mV and 1.1 V at -30 dBm and -10 dBm, respectively. The broadband circuit achieves average efficiency of 5 % at -30 dBm input power and 30 % at -10 dBm when operating from 200 MHz to 500 MHz.
3. CONCLUSION The study of impedance optimization of Schottky diode based RF to DC circuits using different matching techniques are presented for wireless EM energy harvesting applications. The results showed that the efficiency and sensitivity of a matched RF to DC circuit depends on the source and load resistive impedances. The optimization of an RF harvester circuit will improve possible use of lower density renewable ambient EM energy for micro sensors which require microwatt power range for its operation. The results in this report can also be used as a base for chosen the appropriate RF to DC circuit for a specific application requirement. The analysis presented are not only limited to 434 MHz but can be extended to any required frequency.
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). Special thanks to Vassil Jankov, Hans Baumer and Omar Gorgis for PCB fabrication.
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