Thermal Effects on Low-Power RF-to-dc Voltage Multiplier for Battery-Free Sensing and IoT

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Thermal Effects on Low-Power RF-to-dc Voltage
Multiplier for Battery-Free Sensing and IoT
Abstract—This work investigates and demonstrates the
thermal effects on low-power RF-to-dc voltage multipliers based
on Schottky diodes. Such a voltage multiplier is crucial to leverage
dc output voltage rectified from low RF input power to meet the
threshold voltage of battery-free sensors and Internet of Things
devices. An analytical model is developed, considering thermal-
sensitive diode SPICE parameters. The accuracy of this model has
been verified based on a result comparison with commercial ADS
Harmonic Balance simulator. The analytical model predicts the
optimum operating temperature for enhanced RF-to-dc
conversion efficiency. Further experimental results show that a 5-
stage voltage multiplier based on SMS7630 has an optimum
temperature of 7.5 ºC at −25 dBm. This work can offer a reference
or benchmark for optimizing RF-to-dc voltage multipliers at their
operating temperatures and avoiding potential service
interruptions due to temperature variations.
Keywords—Battery-free sensing, IoT, rectifiers, Schottky diodes,
thermal effects, voltage multiplier, wireless power harvesting
I. INTRODUCTION
The global battery-free sensing market is projected to grow
by 27.6% annually from 2021 to 2026, from a market size of
USD 32 million in 2021 to USD 109 million by 2026 [1]. The
primary driver of such growth of battery-free sensors is their
increasing applications in the Internet of Things (IoT)
technology, which can improve production efficiency and
reduce operational and maintenance costs, as well as
environmental footprints. A reliable and sustainable powering
solution is required for such sensors operating without batteries.
Far-field wireless power harvesting is a promising method that
has the potential to provide power to a large number of sensors
scattered in our living environment [2], [3].
A far-field wireless power harvesting system for battery-free
sensing mainly contains five parts: antenna, matching network,
RF-to-dc rectifier, energy storage, and power management unit
[4]. Since the far-field wireless power harvesting typically deals
with low RF power [5], the dc output is limited, often not enough
to drive sensors directly. The common method to leverage dc
output voltage is to use an RF-to-dc voltage multiplier. As for
any semiconductor device, there is an optimum operating
temperature for which RF-to-dc power conversion efficiency
can be maximized [6]. This work explores the thermal effects on
low-power RF-to-dc voltage multipliers. A closed-form model
is developed, considering thermal-sensitive SPICE parameters
of Schottky diodes. With the aid of this model, the optimum
temperature of voltage multipliers for enhanced conversion
efficiency can be observed. This work provides a vital reference
or technical benchmark for optimizing RF-to-dc voltage
multipliers based on their operating temperature.
II. ANALYTICAL MODEL OF RF-TO-DC VOLTAGE MULTIPLIER
A typical diagram of a zero-bias N-stage RF-to-dc voltage
multiplier is presented in Fig. 1(a), with 2N diodes and 2N
This work was supported by the FRQNT Postdoc Re
search Fellowship.
...
P
in
D1
C1
C2
C3
C4
D3 D4
D(2N-1) D(2N)
C(2N)
C(2N
-
1)
D2
P
dc
(a)
...
...
D1 D2 D3 D4 D(2N-1) D(2N)
@f
0
(b)
...
D1 D2 D3 D4 D(2N-1) D(2N)
...
@dc
(c)
L
p
R
s
R
j
C
j
C
p
(d)
Fig. 1. (a) Schematic of a zero-bias N-stage RF-to-dc voltage multiplier.
Equivalent circuit models of the voltage multiplier at (b) RF frequency and (c)
dc. (d) Shockley diode model.
Xiaoqiang Gu
1,2
, Jorge Virgilio de Almeida
2
, Simon Hemour
3
, Roni Khazaka
1
, Ke Wu
2
1Department of Electrical and Computer Engineering, McGill University, Montreal, Canada
2Poly-GRAMES Research Center, École polytechnique de Montréal, Montreal, Canada
3IMS Laboratory, CNRS UMR 5218, Bordeaux INP, University of Bordeaux, Talence, France

capacitors in total [7]. Since capacitance can be considered
short-circuited at RF frequency and open-circuited at dc, two
sets of equivalent circuits can be derived based on the schematic
in Fig. 1(a). As shown in Fig. 1(b), the equivalent circuit
containing 2N diodes in parallel represents the case at RF
frequency. In contrast, these 2N diodes are in series, which
presents the equivalent circuit at dc (see Fig. 1(c)). For detecting
low-power RF signals, Schottky diode SMS7630, widely used
in rectifier design, is used in this work [8], [9]. The Shockley
diode model, shown in Fig. 1(d), is an effective tool to
characterize Schottky diodes, including nonlinear junction
capacitance , nonlinear junction resistance , series
resistance , and packaging parasitics  and .
Based on the equivalent circuit model in Fig. 1(b), all diodes
have the same ac voltage of input signal at RF frequency.
However, the generated dc voltage will be equally distributed on
each diode at dc, as shown in the equivalent circuit in Fig. 1(c).
Therefore, if the RF input signal possesses a magnitude of 
with frequency of , the voltage across the diode junction 
can be written as:

  (1)
in which  and  are dc output current and load resistance,
respectively. Thus, dc output voltage  is calculated by 
. The I-V relationship of Schottky diodes is characterized by:
 !"
#"$%& (2)
where  is the current passing through nonlinear junction
resistance.  and ' are the saturation current and ideality factor
of diodes. ()*+, is the thermal voltage. ), *, , are
Boltzmann constant, operating temperature (in Kelvin), and
electron charge, respectively. Substituting  into (2), the dc
output current  can be expressed as:
-./012
3(4!56718
9:;1<=
#"$ %> (3)
where .?@ is the Bessel function of the first kind of A, and 0 is
the imaginary unit. By using the Lambert W function, the
explicit expression of  becomes:

B
C
C
C
D
EF
B
C
D
18
9:;1<
1GF HF/IJ"12
#"$4K18
9:;1<
1GF
L
M
N
18
9:;1<
1GF %
L
M
M
M
N
(4)
in which '(+ is zero-bias junction resistance. The RF
input power can be calculated by:
OJ3 PK7QRQJSTFUGFRVGW<WQJSTFUGFRVGWX=
 (5)
in which  is zero-bias junction capacitance.  is the
magnitude of the fundamental current going through junction
resistance:
Y0./012
3(4!56718
9:;1<=
#"$ Z[ (6)
Thus, the conversion efficiency of the N-stage RF-to-dc
voltage multiplier can be obtained by:
\V
]^# _%``a (7)
The commercial simulation tool, ADS Harmonic Balance
(HB) simulator, is adopted to verify the accuracy of this closed-
form model. SMS7630 diode is selected for comparison, with its
key SPICE parameters listed in Table I. The dc output voltage
results as calculated by the analytical model are compared to HB
simulation against the number of voltage multiplier stages in
Fig. 2. The operating temperature is 25 ºC, and load resistance
is 5.8 MΩ. The input voltages are set as 0.1 V and 0.3 V,
respectively. Matching network and loss effects are removed to
1 2 3 4 5 6 7 8 9 10
0.0
1.0
2.0
3.0
4.0
5.0
Number of stages
dc output voltage (V)
0.3 V
0.1 V
Fig. 2. Comparison of calculated results using the proposed analytical model
and simulated ones by the ADS Harmonic Balance simulator. Solid lines
represent calculated results, while scatter are simulated results. The operating
temperature is 25 ºC and load resistance is 5.8 MΩ. Matching network and
loss effects are de-embedded in this comparison.
TABLE I
KEY SPICE PARAMETERS
SMS7630
Saturation current at 25 ºC


(A) 5e−6
Series resistance


(Ω) 20
Ideality factor
'
1.05
Zero-bias junction capacitance



(pF) 0.14
Grading coefficient
b
0.4


forward-bias coefficient
c

0.5
Junction (built-in) potential


(V) 0.34

focus on diode performance. From this comparison in Fig. 2, it
can be observed that calculation results match simulated ones,
proving a satisfactory accuracy of our proposed analytical
model.
III. THERMAL-SENSITIVE SPICE PARAMETERS
The proposed analytical model can offer a quick and
accurate solution for analyzing the thermal response of diodes-
based RF-to-dc voltage multipliers. Among the key SPICE
parameters listed in Table I, , , and  are thermal-
sensitive, thus requiring careful consideration [10]. Let us
define the operating temperature as *d, then the saturation
current e*d at this temperature becomes:
e*d_/fg
f4h$^
#!iIj
jgklm
#nj (8)
where o0 and pq are saturation current temperature exponent
and energy gap, respectively. The intrinsic carrier concentration
'J*d must be obtained to calculate thermal-sensitive junction
potential e*d [10-12]:
'J*d%rst_%`i/fg
f4iru_
!vwrwwxm
9nj Iwrwy5zrF9_wF5{_jg9
jg;wwF| m
9njg} (9)
Then, e*d can be written as:
e*d_fg
f~•fg
€_•'/3^f
3^fg4 (10)
The thermal-sensitive zero-bias nonlinear junction
capacitance 
e*d is defined as:

e*d_7%~b_ %~s_%`I‚_*d*
Gƒfg
G&= (11)
The SMS7630 diode is taken as one example. Fig. 3 shows
the ,  (inversely proportional to ), , and  against an
operating temperature range from −40 ºC to +40 ºC. As can be
seen in Fig. 3(a),  tends to increase exponentially with the
decrease of operating temperature. Whereas the change of 
and  against operating temperature is almost linear (see Fig.
3(b)), with  increasing and  decreasing at a lower
temperature.
Considering these thermal-sensitive SPICE parameters, the
proposed analytical model can predict the efficiency of the RF-
to-dc voltage multiplier at various operating temperatures. Fig.
4 shows the efficiency change of the SMS7630 diode-based 5-
-40 -30 -20 -10 0 10 20 30 40
1E-3
0.01
0.1
1
10
Saturation current I
s
(µΑ)
Operating temperature (°C)
1
10
100
1000
10000
Zero-bias junction resistance R
j0
(kΩ)
(a)
-40 -30 -20 -10 0 10 20 30 40
0.30
0.35
0.40
0.45
0.50
0.55
Operating temperature (
°
C)
Junction potential V
j
(V)
0.10
0.11
0.12
0.13
0.14
0.15
Zero-bias junction capacitance C
j0
(pF)
(b)
Fig. 3. Thermal-sensitive SPICE parameters change versus operating
temperature in a range of −40 ºC to +40 ºC: (a) diode saturation current


and
zero
-
bias junction resistance



; (b) j
unction
(built
-
in)
potential


and
zero
-

-40 -30 -20 -10 0 10 20 30 40
0
5
10
15
20
25
30
35
-20 dBm
-25 dBm
Efficiency (%)
Operating temperature (
°
C)
-30 dBm
Fig. 4. Conversion efficiency of a 5-stage voltage multiplier based on
SMS7630 versus operating temperature from −40 ºC to +40 ºC, at input
power levels of −20 dBm, −25 dBm, and −30 dBm, respectively.

stage voltage multiplier from −40 ºC to +40 ºC. The operating
frequency is set at 600 MHz, which falls into the frequency band
of digital TV broadcasting services in Canada. Three input
power levels are selected, −20 dBm, −25 dBm, and −30 dBm,
and the load resistances are set as 110 kΩ, 80 kΩ, and 63 kΩ,
corresponding to the above three power levels, respectively.
These load resistances are the optimum value at room
temperature for each power level. Fig. 4 shows that this voltage
multiplier can achieve higher efficiency at a lower temperature
(around 10 ºC).
IV. EXPERIMENTAL VERIFICATION
A 5-stage RF-to-dc voltage multiplier based on SMS7630
diodes is used for experimental verification. The entire setup is
presented in Fig. 5(a). A vector network analyzer (VNA)
working in the continuous-wave mode acts as the RF power
source. VNA monitors the reflecting coefficient of the voltage
multiplier, which can be used to compensate for the reflection
loss to ensure the RF input power at all temperatures at the same
level (−25 dBm). Various operating temperatures are created by
a TestEquity chamber (model 105). A multimeter reads the
harvested dc voltage. The operating frequency is set at 600
MHz, and load resistance is 80 kΩ.
The experimental results are demonstrated in Fig. 5(b). With
the insertion loss of the matching network, substrate loss, and
loss due to lumped components and diodes, the measured
efficiency results are lower than simulated ones. However,
experimental results confirm that an optimum operating
temperature exists for this 5-stage voltage multiplier in the range
of 5 ºC to 10 ºC. After more measurements within this
temperature range, the optimum operating temperature for this
5-stage voltage multiplier is found to be about 7.5 ºC.
V. CONCLUSION
This work derives and evaluates an analytical model for
accurately characterizing the thermal effects of low-power RF-
to-dc voltage multipliers based on Schottky diodes. Optimum
operating temperatures of such voltage multipliers exist for
achieving enhanced conversion efficiency. Such operating
temperature is associated with diode, RF input power, operating
frequency, and load resistance. This work has the potential to
optimize the design of low-power RF-to-dc voltage multipliers
according to their operating temperatures.
REFERENCES
[1] "Global Battery-free Sensors Market with COVID-19 Impact Analysis,
by Sensor Type (Temperature Sensors, Humidity/Moisture Sensors,
Pressure Sensors), Frequency, Industry (Automotive, Logistics,
Healthcare, Food & Beverages), and Region - Forecast to 2026,"
Accessed: Aug. 2021. [Online]. Available:
https://www.marketsandmarkets.com/Market-Reports/battery-free-
sensor-market-193645557.html#tab_default_2.
[2] X. Gu, S. Hemour, and K. Wu, "Far-Field Wireless Power Harvesting:
Nonlinear Modeling, Rectenna Design, and Emerging Applications,"
Proc. IEEE, vol. 110, no. 1, pp. 56-73, Jan. 2022.
[3] H. S. Vu, N. Nguyen, N. Ha-Van, C. Seo, and M. T. Le, "Multiband
Ambient RF Energy Harvesting for Autonomous IoT Devices," IEEE
Microw. Wirel. Compon. Lett., vol. 30, no. 12, pp. 1189-1192, Dec. 2020.
[4] Z. Popović, E. A. Falkenstein, D. Costinett, and R. Zane, "Low-power far-
field wireless powering for wireless sensors," Proc. IEEE, vol. 101, no.
6, pp. 1397-1409, Jun. 2013.
[5] X. Gu, L. Grauwin, D. Dousset, S. Hemour, and K. Wu, "Dynamic
Ambient RF Energy Density Measurements of Montreal for Battery-Free
IoT Sensor Network Planning," IEEE Internet Things J., vol. 8, no. 17,
pp. 13209-13221, Sept. 2021.
[6] X. Gu, L. Guo, S. Hemour, and K. Wu, "Optimum Temperatures for
Enhanced Power Conversion Efficiency (PCE) of Zero-Bias Diode-Based
Rectifiers," IEEE Trans. Microw. Theory Techn., vol. 68, no. 9, pp. 4040-
4053, Sept. 2020.
[7] G. De Vita and G. Iannaccone, "Design criteria for the RF section of UHF
and microwave passive RFID transponders," IEEE Trans. Microw.
Theory Techn., vol. 53, no. 9, pp. 2978-2990, Sept. 2005.
[8] X. Gu, S. Hemour, L. Guo, and K. Wu, "Integrated Cooperative Ambient
Power Harvester Collecting Ubiquitous Radio Frequency and Kinetic
Energy," IEEE Trans. Microw. Theory Techn., vol. 66, no. 9, pp. 4178-
4190, Sept. 2018.
[9] E. Kwiatkowski, J. A. Estrada, A. López-Yela, and Z. Popović,
"Broadband RF Energy-Harvesting Arrays," Proc. IEEE, vol. 110, no. 1,
pp. 74-88, Jan. 2022.
[10] P. Antognetti, G. Massobrio, and G. Massobrio, Semiconductor Device
Modeling With SPICE. New York, NY, USA: McGraw-Hill, 1998.
[11] H. Russell, Jr., The SPICE Diode Model. San Jose, CA, USA: Motorola
Inc. Opal Engineering, 1991.
[12] X. Gu, W. Lin, S. Hemour, and K. Wu, "Readout Distance Enhancement
of Battery-Free Harmonic Transponder," IEEE Trans. Microw. Theory
Techn., vol. 69, no. 7, pp. 3413-3424, Jul. 2021.
(a)
-40 -20 0 20 40
0
1
2
3
4
5
6
7
8
Operating temperature (
°
C)
Efficiency (%)
(b)
Fig. 5. (a) Experimental setup; (b) Measured efficiency of the 5-stage RF-to-
dc voltage multiplier versus operating temperature from −40 ºC to +40 ºC at
−25 dBm.