2.3 Voltage doubler matching considerations

Rectifiers C, D, E, and F were designed on an FR-4 substrate, and are used to discuss the effect of the matching circuit on the stability of the |S11| resonance that defines the matching, and on the 10 dB bandwidth of the |S11|. As can be seen from Figures 5 and 6, the matching depends on the input power level. For different power levels, the exact position of the resonance that defines the matching (|S11| < 10 dB) shifts, and for certain values, the rectifier is mismatched, and as a result, the RF-to-DC efficiency degrades. Rectifiers C and D, which are compared in Figure 5, use different diode types, (Broadcom and Skyworks, respectively), and

Voltage-Doubler RF-to-DC Rectifiers for Ambient RF Energy Harvesting and Wireless Power… DOI: http://dx.doi.org/10.5772/intechopen.89271

similar matching networks that consist of shorted and radial matching stubs. The |S11| resonance remains rather stable as the input power varies, but it is narrowband (25 MHz). The different diode models have minimum effect on the matching, but

Figure 4. Voltage doubler (A) and single stage rectifier (B) comparison; (a) Rectifier A |S11|, (b) Rectifier B |S11|, (c) |S11| at 10 dBm comparison, and (d) RF-to-DC efficiency.

Figure 5.

Rectifier (C) and rectifier (D) comparison; (a) Rectifier C |S11|, (b) Rectifier D |S11|, (c) |S11| at 10 dBm comparison, and (d) RF-to-DC efficiency.

loss, the available power at the receiver is rather low. However, the received power level is random and cannot be predicted, and the efficiency plots for Rectifiers A and B cross at the 15 dB input power mark (Figure 4d), therefore a direct comparison of the efficiency performance is not straight forward. The improved average efficiency performance over the entire power range is the main reason why the voltage doubler was preferred over the single stage rectifier and was further studied in detail. The free-space loss is inversely proportional to λ<sup>2</sup> and this is the reason why the UHF frequency (relatively low frequency) was preferred for the

Rect. Schematic Description (matching network) Diode

shorted stub, two-stage tapered line, radial stub followed by

shorted stub, two-stage tapered line, radial stub followed by

stub and a radial stub at the beginning and at the end of a

shorted stub, a radial stub followed by a distributed inductor

shorted stub, a radial stub followed by a distributed inductor

shorted stub, two-stage tapered line, a radial stub followed

radial stub, a shorted stub, and a series inductor

SMS7630

SMS7630

HSMS2850

SMS7630

HSMS2850

SMS7630

HSMS2850

HSMS2850

SMS7630

SMS7630

HSMS2850

A Consists of low-loss distributed elements, which include

B Consists of low-loss distributed elements, which include

C Consists of distributed elements, which include a shorted

D Consists of distributed elements, which include a shorted stub and a radial stub

E Consists of a hybrid matching network, which includes a

F Consists of a hybrid matching network, which includes a radial stub and two series inductors

G Consists of low-loss distributed elements, which include a

H Consists of low-loss distributed elements, which include a

I Consists of low-loss distributed elements, which include a

by a distributed inductor

J Consists of a hybrid matching network, which includes a radial stub and two series inductors

K Consists of a hybrid matching network, which includes a radial stub and two series inductors

U-shaped microstrip line

distributed inductor

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distributed inductor

Rectifiers C, D, E, and F were designed on an FR-4 substrate, and are used to discuss the effect of the matching circuit on the stability of the |S11| resonance that defines the matching, and on the 10 dB bandwidth of the |S11|. As can be seen from Figures 5 and 6, the matching depends on the input power level. For different power levels, the exact position of the resonance that defines the matching (|S11| < 10 dB) shifts, and for certain values, the rectifier is mismatched, and as a result, the RF-to-DC efficiency degrades. Rectifiers C and D, which are compared in Figure 5, use different diode types, (Broadcom and Skyworks, respectively), and

presented study.

200

Table 1.

Implemented rectifiers labeled A to K.

2.3 Voltage doubler matching considerations

Spice model of the Skyworks SMS7630 diode was characterized at 1.8 GHz, and the

Voltage-Doubler RF-to-DC Rectifiers for Ambient RF Energy Harvesting and Wireless Power…

Considering the direct comparison between the efficiency of rectifier C (Broadcom HSMS2580) and D (Skyworks SMS7630) presented in Figure 5d, the general observation is that the rectifier with the Skyworks diodes has better efficiency for input power less than 3 dBm, and the diode with the HSMS2580 diodes has better efficiency for input power higher than 3 dBm. The same behavior is verified by inspecting Figure 6d, where the efficiencies of rectifiers E and F are presented. This can be explained by noting that the SMS7630 diode requires a forward bias voltage between 60 and 120 mV, and it has a breakdown voltage of 2 V, while the HSMS2850 diode has a forward bias voltage between 150 and 250 mV, and it has a breakdown voltage of 3.8 V. For the implementation of highefficiency UHF rectifiers with lower input power levels, the Skyworks SMS7630 diodes are preferred, since improved RF-to-DC efficiency can be achieved as a result of the model's lower saturation current and lower junction capacitance. By comparing the efficiencies for rectifiers C, D, E, and F, another important observation can be made. The use of series lumped inductors for the matching circuit seems to degrade the RF-to-DC efficiency, something verified by comparing the maximum efficiency of C (46%) with E (42%) and the efficiency of D (50%) with F (42%). For a simulated voltage doubler circuit, a real inductor was modeled as an ideal inductor in series with an ohmic resistor to model the inductor's losses. A small variation in the ohmic resistance has a direct significant impact on the simulated efficiency, as can be verified in Figure 7. Based on this observation, Rectifier H was fabricated using one printed distributed inductor (meander shaped thin line in the inset of Figure 8b) instead of lumped inductors in the matching circuit. The comparison between Rectifier H and Rectifier K is presented in Figure 8. Although the matching bandwidth for the rectifier with the distributed inductor decreased, the lack of ohmic losses for the packaged lumped inductor caused a small improvement

Effect of the ohmic losses of the lumped inductor modeled as series resistor, on the simulated efficiency.

S-parameter measurements of the implemented rectifier indicated a shift in the |S11| resonance. The resonance shift could be remedied with the matching network, and especially by modifying the inductance values of the inductors that were used for the matching. For the Broadcom HSMS2580 diode, an ADS library model was available and the measurements indicated that the S-parameter simulations using the ADS library model were more accurate. Similar rectifier prototypes with similar matching networks using either type of Schottky diodes (C and D or E and F) were

same model was used for the UHF rectifier simulations.

DOI: http://dx.doi.org/10.5772/intechopen.89271

implemented.

Figure 7.

203

Figure 6.

Rectifier E and rectifier F comparison; (a) Rectifier E |S11|, (b) Rectifier F |S11|, (c) |S11| at 10 dBm comparison, and (d) efficiency.

they affect the efficiency as will be discussed subsequently. For Rectifiers E and F, presented in Figure 6, that use a combination of radial stubs with series inductors, the |S11|shift is much more evident. For this hybrid matching circuit, what overcomes the mismatch problem in the UHF frequency is the considerably wider bandwidth (greater than 65 MHz) for both rectifiers. Apparently, the combination of radial stubs with lumped inductors and the resulting hybrid matching network enhances the bandwidth and makes the matching more tolerant to frequency shifts.

#### 2.4 RF-to-DC efficiency

For any RF-to-DC rectifier, the figure of merit is the RF-to-DC efficiency, which has been shown to depend non-linearly on both the input power and the termination load, as can be verified from Figure 3b. In an attempt to identify the design parameters that affect the efficiency, several rectifier prototypes were fabricated and tested. Parameters such as the diode type, the use of distributed or lumped inductors for the matching network and their associated losses and quality factor, or the substrate losses of the preferred fabrication board were investigated experimentally.

The Skyworks SMS7630 [19] and Broadcom HSMS2580 [20] diodes were chosen for the high-efficiency voltage doubler topologies that were investigated at low input power, because they have been the most commonly used diodes. In the recent years, the Broadcom HSMS2852 type has been a popular diode for many RF-to-DC rectifiers used for WPT systems. For low input power levels, the higher series resistance (compared to, e.g., the Broadcom HSMS-286x family) does not seem to degrade the measured efficiency. In addition to their specifications, an important role for the selection of the diodes had to do with the availability (or not) of the diode model for the Keysight - Advanced Design System (ADS) simulator. The

#### Voltage-Doubler RF-to-DC Rectifiers for Ambient RF Energy Harvesting and Wireless Power… DOI: http://dx.doi.org/10.5772/intechopen.89271

Spice model of the Skyworks SMS7630 diode was characterized at 1.8 GHz, and the same model was used for the UHF rectifier simulations.

S-parameter measurements of the implemented rectifier indicated a shift in the |S11| resonance. The resonance shift could be remedied with the matching network, and especially by modifying the inductance values of the inductors that were used for the matching. For the Broadcom HSMS2580 diode, an ADS library model was available and the measurements indicated that the S-parameter simulations using the ADS library model were more accurate. Similar rectifier prototypes with similar matching networks using either type of Schottky diodes (C and D or E and F) were implemented.

Considering the direct comparison between the efficiency of rectifier C (Broadcom HSMS2580) and D (Skyworks SMS7630) presented in Figure 5d, the general observation is that the rectifier with the Skyworks diodes has better efficiency for input power less than 3 dBm, and the diode with the HSMS2580 diodes has better efficiency for input power higher than 3 dBm. The same behavior is verified by inspecting Figure 6d, where the efficiencies of rectifiers E and F are presented. This can be explained by noting that the SMS7630 diode requires a forward bias voltage between 60 and 120 mV, and it has a breakdown voltage of 2 V, while the HSMS2850 diode has a forward bias voltage between 150 and 250 mV, and it has a breakdown voltage of 3.8 V. For the implementation of highefficiency UHF rectifiers with lower input power levels, the Skyworks SMS7630 diodes are preferred, since improved RF-to-DC efficiency can be achieved as a result of the model's lower saturation current and lower junction capacitance.

By comparing the efficiencies for rectifiers C, D, E, and F, another important observation can be made. The use of series lumped inductors for the matching circuit seems to degrade the RF-to-DC efficiency, something verified by comparing the maximum efficiency of C (46%) with E (42%) and the efficiency of D (50%) with F (42%).

For a simulated voltage doubler circuit, a real inductor was modeled as an ideal inductor in series with an ohmic resistor to model the inductor's losses. A small variation in the ohmic resistance has a direct significant impact on the simulated efficiency, as can be verified in Figure 7. Based on this observation, Rectifier H was fabricated using one printed distributed inductor (meander shaped thin line in the inset of Figure 8b) instead of lumped inductors in the matching circuit. The comparison between Rectifier H and Rectifier K is presented in Figure 8. Although the matching bandwidth for the rectifier with the distributed inductor decreased, the lack of ohmic losses for the packaged lumped inductor caused a small improvement

Figure 7. Effect of the ohmic losses of the lumped inductor modeled as series resistor, on the simulated efficiency.

they affect the efficiency as will be discussed subsequently. For Rectifiers E and F, presented in Figure 6, that use a combination of radial stubs with series inductors, the |S11|shift is much more evident. For this hybrid matching circuit, what overcomes the mismatch problem in the UHF frequency is the considerably wider bandwidth (greater than 65 MHz) for both rectifiers. Apparently, the combination of radial stubs with lumped inductors and the resulting hybrid matching network enhances the bandwidth and makes the matching more tolerant to frequency shifts.

Rectifier E and rectifier F comparison; (a) Rectifier E |S11|, (b) Rectifier F |S11|, (c) |S11| at 10 dBm

For any RF-to-DC rectifier, the figure of merit is the RF-to-DC efficiency, which has been shown to depend non-linearly on both the input power and the termination load, as can be verified from Figure 3b. In an attempt to identify the design parameters that affect the efficiency, several rectifier prototypes were fabricated and tested. Parameters such as the diode type, the use of distributed or lumped inductors for the matching network and their associated losses and quality factor, or the substrate losses of the preferred fabrication board were investigated

The Skyworks SMS7630 [19] and Broadcom HSMS2580 [20] diodes were chosen

for the high-efficiency voltage doubler topologies that were investigated at low input power, because they have been the most commonly used diodes. In the recent years, the Broadcom HSMS2852 type has been a popular diode for many RF-to-DC rectifiers used for WPT systems. For low input power levels, the higher series resistance (compared to, e.g., the Broadcom HSMS-286x family) does not seem to degrade the measured efficiency. In addition to their specifications, an important role for the selection of the diodes had to do with the availability (or not) of the diode model for the Keysight - Advanced Design System (ADS) simulator. The

2.4 RF-to-DC efficiency

comparison, and (d) efficiency.

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Figure 6.

experimentally.

202

in the efficiency, which can be verified in Figure 8d. This is also verified in the comparison between Rectifier A and Rectifier J presented in Figure 9, that were both fabricated on Rogers 5880 material. The efficiency of Rectifier A is consistently better than the efficiency of Rectifier J (Figure 9d), while the use of tapered lines for Rectifier A improved the bandwidth as well. Comparing the maximum efficiency of K (46%) from Figure 8d and the efficiency of J (56%) from Figure 9d, which have similar designs with the same diode models, it is obvious that the

Voltage-Doubler RF-to-DC Rectifiers for Ambient RF Energy Harvesting and Wireless Power…

When distributed inductors are used instead of lumped inductors, the substrate losses become even more critical for the implemented efficiency. Low loss substrates limit the quality factor of the implemented inductors and consequently degrade the efficiency. Figure 10a shows the simulated rectifier efficiency when the loss tangent (tanδ) of the substrate was varied. For the lower end of the input power, around 24 dB, the low loss of the Rogers 5880 (tanδ = 0.009) results in 30% efficiency, while for the same design, tanδ = 0.035 reduces the efficiency to approximately 15%. For low input power, even small variations in the copper's

Effect of the substrate loss on the simulated efficiency (a) with variations in the loss tangent (tanδ) and

Rectifier (G) and rectifier (H) comparison; (a) Rectifier E |S11|, (b) rectifier F |S11|, (c) |S11| at 10 dBm

substrate losses are important in the resulting efficiency.

DOI: http://dx.doi.org/10.5772/intechopen.89271

Figure 10.

Figure 11.

205

comparison, and (d) efficiency.

(b) variations in the copper's conductivity.

Figure 8.

Rectifier K and rectifier H comparison; (a) Rectifier E |S11|, (b) Rectifier F |S11|, (c) |S11| at 10 dBm comparison, and (d) efficiency.

Figure 9.

Rectifier (A) and rectifier (J) comparison; (a) Rectifier A |S11|, (b) Rectifier J |S11|, (c) |S11| at 10 dBm comparison, and (d) efficiency.

### Voltage-Doubler RF-to-DC Rectifiers for Ambient RF Energy Harvesting and Wireless Power… DOI: http://dx.doi.org/10.5772/intechopen.89271

better than the efficiency of Rectifier J (Figure 9d), while the use of tapered lines for Rectifier A improved the bandwidth as well. Comparing the maximum efficiency of K (46%) from Figure 8d and the efficiency of J (56%) from Figure 9d, which have similar designs with the same diode models, it is obvious that the substrate losses are important in the resulting efficiency.

When distributed inductors are used instead of lumped inductors, the substrate losses become even more critical for the implemented efficiency. Low loss substrates limit the quality factor of the implemented inductors and consequently degrade the efficiency. Figure 10a shows the simulated rectifier efficiency when the loss tangent (tanδ) of the substrate was varied. For the lower end of the input power, around 24 dB, the low loss of the Rogers 5880 (tanδ = 0.009) results in 30% efficiency, while for the same design, tanδ = 0.035 reduces the efficiency to approximately 15%. For low input power, even small variations in the copper's

in the efficiency, which can be verified in Figure 8d. This is also verified in the comparison between Rectifier A and Rectifier J presented in Figure 9, that were both fabricated on Rogers 5880 material. The efficiency of Rectifier A is consistently

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Rectifier K and rectifier H comparison; (a) Rectifier E |S11|, (b) Rectifier F |S11|, (c) |S11| at 10 dBm

Rectifier (A) and rectifier (J) comparison; (a) Rectifier A |S11|, (b) Rectifier J |S11|, (c) |S11| at 10 dBm

Figure 8.

Figure 9.

204

comparison, and (d) efficiency.

comparison, and (d) efficiency.

Effect of the substrate loss on the simulated efficiency (a) with variations in the loss tangent (tanδ) and (b) variations in the copper's conductivity.

Figure 11.

Rectifier (G) and rectifier (H) comparison; (a) Rectifier E |S11|, (b) rectifier F |S11|, (c) |S11| at 10 dBm comparison, and (d) efficiency.

conductivity affect the efficiency, as can be verified in Figure 10b. The importance of a low-loss substrate is evident in the measured efficiencies for the implemented rectifiers presented in Figure 11, where the lossy FR-4 (tanδ = 0.016) was used for Rectifier H, and the more expensive low loss (tanδ = 0.0009) Rogers 5880 was used for Rectifier G. Figure 11d verifies that the efficiency of rectifier G fabricated on the low-loss material is consistently higher than the efficiency of the similar design Rectifier H.

distributed printed inductors and further improve the bandwidth of rectifiers with distributed inductors, the use of multi-stage tapered microstrip lines was considered. Rectifier I was implemented on FR-4 and used a two-stage tapered microstrip line. The performance of Rectifier I is compared with the performance of Rectifier H, which uses conventional microstrip lines, in Figure 13. The bandwidth of Rectifier I is 40 MHz and the bandwidth of I is 36 MHz. The 10% bandwidth enhancement (Figure 13c) in addition to the improved efficiency, as can be seen in Figure 13d, implies that if there are not strict size constraints, the best efficiency rectifier should have the following characteristics: (a) should use Skyworks 7630 diodes, (b) should use tapered microstrip lines with distributed inductors for the matching circuit, and (c) should be fabricated on low-loss material. From the implemented rectifiers A to K, Rectifier A has the aforementioned characteristics.

Voltage-Doubler RF-to-DC Rectifiers for Ambient RF Energy Harvesting and Wireless Power…

The detailed design parameters of the implemented Rectifier A are presented in

Figure 14a and are summarized in the figure caption. The matching network consists of a shorted linear stub, a two-stage tapered microstrip line for bandwidth enhancement, and a printed inductor. The maximum measured efficiency is almost 60% at 3 dB. For input power higher than 3 dB, the voltage saturates close to 2 V and as a result the RF-to-DC efficiency degrades, since only the denominator RF power increases while the DC power remains saturated. The simulated results presented in Figure 14b indicate the non-linear dependence of the efficiency with the termination load. Although the peak efficiency per power level is shifted, the rectifier parameters were optimized for a termination load equal to 13.5 kΩ. The

Rectifier A (a) schematic with design details, (b) simulated and measured efficiency vs. input power, (c) efficiency versus termination load, and (d) efficiency as a function of input power and the load resistance. All dimensions are in mm: L= 43, lt1 =7, lt2 =9.5, lt3 =6.85, lt4 =5.67, lt5 =7, lt6 =4.14, lrs =2, ls1 =2.2, ls2 =8.75,

W= 20, wt1 = 2.4, wt2 = 1.6, wt3 = 5, wt4 = 4.35, wt5 = 0.315, θrs =60°, and θ<sup>s</sup> =90°.

2.6 Proposed UHF rectifier – Rectifier A

DOI: http://dx.doi.org/10.5772/intechopen.89271

Figure 14.

207
