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1       Introduction

In recent years, technology has taken a turn towards low power and wireless systems. Along with that, medical advancements have been made to keep up with the trend of mobility. Significant efforts have been made to create biomedical sensors and implantable electronic devices. (Roy et al., 2021) Implantable Medical Devices (IMDs) are used for clinically assisting patients through a 2-step process: sensing particular in-body biomedical parameters, and reacting appropriately, usually through a sort of electrical stimulus. IMDs cover an extremely broad range of applications, and each operates at a different power range.

New state-of-the-art research is exploring wireless power transfer techniques in order to charge the batteries of an IMD and operate the IMD without the need for invasive surgeries and operations. (Mulders et al., 2022) Alternative solutions are needed to power and charge IMDs, and they must fit certain criteria, such as eliminating repetitive surgeries, offering a painless and comfortable alternative, not interfering in the patient’s day to day life, and preventing long-lasting harmful effects or diseases.

The purpose of this paper is to shed light on the difficulties of efficiently operating a wireless power transfer system operating at high frequency, particularly how the rectifier unit can reduce the efficiency and cause major losses. Section 2 explores wireless power transfer systems, while Section 3 elaborates on existing rectifier designs. Section 4 sets the parameters for our system and inspects the rectifier requirements while Section 5 provides detailed explanation on rectifier circuits designed and selected carefully for the purpose of this paper. Section 6 presents and compares the efficiency results of the proposed rectifier designs, and ultimately selects the best rectifier.

2       Wireless Power Transfer

Wireless power transfer (WPT) allows for transfer of power from a transmitter to an electrical load without a direct wired connection or exposed contacts. (Mulders et al., 2022) By generating a time-varying electromagnetic field, the transmitter is able to send power through an airgap, and with the correct design, the receiver is able to convert the energy from the electromagnetic field into usable electric power. WPT has many types; each works at a different range and efficiency, and each comes with its own unique set of advantages and disadvantages. (Mulders et al., 2022)

As technology has shifted towards low power wireless application, radio frequency power transfer has significantly increased in popularity. Radio waves are able to transmit power over long distances, in the order of meters. This is known as far-field wireless power transfer. Because of this, recent research focuses on optimizing radio frequency power transfer for biomedical implants. On the other hand, radio frequency (RF) energy has a quite low power density. The power density of RF energy varies between 0.2 nW/cm² to 1 uW/cm². (Sié et al., 2020) This results in power on the order of microwatts on the receiver side, which is providentially sufficient for most biomedical implants.

A basic radio frequency power transfer system consists of a transmitter circuit, where DC power is converted to RF waves usually in the low Gigahertz range for biomedical applications. The RF waves are then transmitted across the medium. On the receiver side, an antenna receives the radio waves, which will then be converted back to DC in order to power the load.

The efficiency of such a system can be measured at many points in the circuit. The first and foremost efficiency that may be measured is the signal generator efficiency – how accurately the signal generated meets the microwave power transmission requirements. Another measured efficiency is the efficiency at the transmitting antenna and receiving antenna. This is measured as the ratio of RF power received at the receiver side to the power outputted at the transmitter side. Note that equation (1) represents this relationship, but in the dB domain, where  is the power transmitted and  is the power received, both in dB.

An advantage of RF power transfer is the flexibility at the transmitter and receiver side. RF power can be harvested even from RF transmitter sources not created for the purpose of WPT. (X. Lu & Wang, 2015) The receiving antenna can harvest the unused power from any RF transmitter in a process commonly referred to as energy harvesting. (Muncuk et al., 2018) Energy harvesting is cost-effective, sustainable, convenient, and reliable. These qualities render it a very advantageous and expedient option for future technologies.   

To increase the power received, a dedicated RF power source can be created to transmit power directly to the receiver circuit. Even so, there are many sources of losses that may decrease the efficiency of such a power transfer system, including: matching, conduction, and dielectric losses in the transmitter circuit, pathloss, shadowing, and antenna properties in the medium of transmission, and matching, conduction, and dielectric losses at the receiver circuit. The receiver side is particularly difficult to design due to the size constraints and safety measures and standards.

3       System Parameters

For the purpose of this paper, a pacemaker has been selected, which operates in the ultra-low (<100uW) power region. It is placed onto the heart in order to stimulate the heart muscles and regulate the heartbeat (Roy et al., 2021). The batteries of traditional pacemakers are surgically replaced every 6-10 years, which costs money as well as having associated risks such as infection, pain, and possible complications.

The selected WPT, as mentioned previously, is radio frequency wireless power transfer, which is characterized by a low power density. Therefore, the receiver circuit, placed inside the human body, must be carefully optimized in order to decrease the losses and increase the efficiency.

4       Rectifiers in WPT System

Further focusing on the receiver circuit reveals that typical rectifier circuits fail in high-frequency applications. A rectifier, otherwise known as an AC-to-DC converter, simply converts the received AC power signal into a DC power signal.

Rectification process could be categorized into two main types: passive rectification and active rectification. Passive rectifiers are usually made of p-n junction diodes, Schottky diodes, or MOSFET based diodes. On the other hand, active rectifiers consist of active diodes, which can be defined simply as a MOSFET connected to a comparator. Active rectifiers are bulky and require an external voltage source, which renders them obsolete for a low-power wireless power transfer.

The simplest form of passive rectification is a typical p-n junction diode. A p-n junction diode is a semi-conductor element that allows current to flow only in one direction blocking the other quantity opposing it. These diodes have a threshold voltage typically starting at 0.5 V and higher. However, since a p-n junction diode has a relatively high threshold voltage for low voltage applications, another alternative such as Schottky diode is used. Schottky diodes are known to have a low threshold voltage ranging from 100 mV to 450 mV. (Y., & K. W. Lu, 2017) As opposed to the discrete typical p-n junction diode or Schottky diode, MOSFET based diodes are preferred since full on-chip integration is realizable.

Figure 1. (

a) P-N junction diode, (b) Schottky diode (c) NMOS diode (d) PMOS diode

Therefore, they are able to dramatically reduce the receiver circuit size. MOSFET based diodes are made by connecting the drain terminal to the gate terminal of NMOS or PMOS transistors. In PMOS diodes, the source terminal represents the anode of a diode and gate terminal is the cathode of the diode. In NMOS diodes, the gate terminal is the anode, and the source terminal is the cathode. The direction of the current is indicated by the arrow direction of the MOS transistor. The described configurations of diodes are summarized in Figure 1.

Several parameters can be calculated to help measure and rank rectifiers: voltage conversion ratio in (2) and power conversion efficiency in (3) .

Where  is the average output voltage, and  is the output average power.

The most well-known rectifier is a full-wave bridge rectifier, displayed in Figure 2. This rectifier is typically utilized in medium to high power applications, and it is one of the most basic full-wave rectifier configurations.

The diode full wave bridge rectifier has four main diodes (D1, D2, D3, and D4). In positive half cycle, D1 and D4 are forward biased, and they are conducting current,  while D2 and D3 are OFF because they are reversely biased. A diode will be forward biased when . If , none of the diodes will be ON. For an ideal

Figure 2. Full wave bridge rectifier

diode, where , the output voltage in each half cycle is equal to . However, in practical applications, losses exist due to voltage drop across the conducting diodes. Hence, the output voltage in the positive half cycle is equal to (2).

Where  and  represent the voltage drop across diodes 1 and 4 respectively. During negative half cycle, the output voltage is equivalent to (3).

Typical configurations of MOSFET based rectifiers and their performance for this application (i.e., high frequency applications ultra low power applications) are explored in the following section.

 Figure 3. DMOS full-wave rectifier

5       Proposed MOS Rectifiers

.  

I.V_th  

  (b)

Figure 5. External V_th cancelation (EVC) full wave rectifier

Figure 6. EVC rectifier smoothed output voltage = 1.27 V

One disadvantage of this circuit is the use of non-passive elements which are batteries. The objective is to construct a passive rectifier circuit for an ultra-low power system. To achieve this, batteries are replaced by an equivalent circuit capable of performing the same function which is the internal voltage cancelation technique.

III.   Internal V_th Cancelation Rectifier

In the previous technique, batteries were used to compensate for the voltage drop across the main path transistors. However, those batteries could be replaced by an equivalent circuitry using a transistor, a capacitor, and a resistor (Kotani & Ito, 2009) (Dai et al., 2015). This technique is called the internal threshold voltage cancelation (IVC) technique as shown in Figure 7. The biasing voltage of the gate

Figure 7. Internal Vth cancelation (IVC) full wave rectifier

terminal for MOS transistors, is generated internally from the output DC voltage (Kotani & Ito, 2009). The principle of this circuit is that the capacitor will charge up with a voltage equivalent to  in which it will be used as a biasing voltage for the two main PMOS transistors  and . While for NMOS transistors, the capacitor will have a voltage of . However, the use of transistors M_P and M_N results in the generation of leakage current in the circuit. Therefore, resistors with big resistance value are connected to reduce losses caused by leakage current (Nakamoto et al., 2007). Initially, the capacitor is charged up and when the voltage across the parallel diode- connected M_P and M_N exceeds their threshold voltages and turn ON,  becomes equal to  for the PMOS transistors and  for the NMOS transistor. Furthermore, to ensure that  is enough to bias the main path transistors,  should be approximately equal to . Figure 8 displays the output of the internally biased rectifier schematic in Figure 7. The output voltage is approximately 0.81 V for the same sinusoidal input signal.

Nevertheless, IVC scheme employs extra elements to offer a biasing voltage for the MOS transistors. In addition, to reduce the leakage current, big resistors should be

Figure 8. IVC rectifier smoothed output voltage = 0.81 V

implemented meaning more area is needed. Thus, it is more common to use other techniques such as self-voltage cancelation mechanism to avoid additional parts in the circuit.

IV.  Self  V_th Cancelation Rectifier

Self-voltage cancelation technique shown in Figure 9 is a topology that depends on biasing the gate of main path transistors using the highest and lowest voltages in the circuit (Kotani & Ito, 2009). PMOS transistor turn ON when , hence PMOS gate terminal is connected to the lowest voltage in the circuit, which is the

ground. However, NMOS are conducting current in forward mode when . Therefore, NMOS gate terminal is connected to the highest DC voltage which is . Comparing this technique to EVC and IVC, it has a much simpler connection since it does not require any additional elements to bias the MOS transistors. Furthermore, SVC mechanism is characterized by higher efficiency at lower DC levels (i.e., at lower input levels) (Roy et al., 2021). This is due to the fact that the threshold voltage of the MOS transistor decreases by the same value of the DC output voltage. Therefore, it is efficient to be used in ultra-low power applications. However, one of the drawbacks to using SVC technique is that increasing the DC

Figure 9. Self V_th cancelation (SVC) full wave rectifier

output voltage value may decrease the effective  of the transistor to a very small value or even make it negative. This results in high leakage current and reduces the power conversion efficiency (Gomez-Casseres et al., 2016). Therefore, for systems where the input is not stable and may increase abruptly, it is not preferable to use SVC scheme. Instead, other circuit topologies are implemented such as cross coupled PMOS rectifier, and fully cross coupled rectifier or differential voltage cancelation (DVC) rectifier. The SVC rectifier smoothed output voltage is shown in Figure 10 (a). Figure 10 (b) displays the rectifier’s efficiency over a range of input power in dBm confirming the performance of SVC rectifier at lower and higher input power levels.

V.     Cross Coupled PMOS Rectifier

Cross coupled PMOS rectifier (CCP) circuit is a widely used rectifier type in high frequency applications due to its high efficiency. CCP rectifier is similar to a DMOS full wave rectifier, but with a difference where gate terminals of the upper PMOS transistors are cross connected to the input voltage. The lower part of the rectifier consists of two diode connected NMOS transistors as displayed in Figure 11.

In the positive half cycle, when , M1 transistor is OFF, but when , both input and output nodes are connected through M1. In order to

(a)

(b)

Figure 10. SVC rectifier (a) Smoothed output voltage = 0.97 V (b) PCE over different input power levels in dBm

establish a closed path for the current, M1 should be ON, and this will happen when  or . In the negative half cycle, main path transistors are M2 and M3. The source-drain voltage of M1 (PMOS) transistor is equal to (7). Whereas drain-source voltage of M4 MOS transistor is equal to (5).

Figure 11. Cross coupled PMOS full wave rectifier

Figure 12. CCP rectifier Smoothed output voltage = 1.38 V

in (7), where  is a relatively large value, hence, it will result in reduction of the overall value of  and higher PCE is obtained (Kotani & Ito, 2009).

Cross coupled PMOS transistor results in higher output voltage equal to 1.38 V as shown in Figure 12.

VI.  Differential V_th Cancelation Rectifier

Differential full wave rectifier is one of the highly efficient rectifier circuits used in passive high frequency applications (Mair et al., 2019b). The rectifier scheme is shown in Figure 13.

In this circuit topology, gate terminals of the main path transistors are fully cross coupled and connected to the input signal. In other words, the gates of the four MOS transistors are driven by a differential input

Figure 13. Differential V_th cancelation (DVC) full wave rectifier

Figure 14. DVC rectifier smoothed output voltage = 1.7 V

signal. PMOS and NMOS transistors would turn ON when , and their source-drain voltage is equal to (7). In the positive interval of the input, when  is less than the threshold voltage of the two functioning p-channel MOS and n-channel MOS transistors, there would be no current flow through the load. When the value of  exceeds the threshold voltage of both M1 and M4, a current flow is realized in the load. 

This connection decreases the source-drain voltage of all the four main path transistors; hence it is more efficient than the cross coupled PMOS rectifier discussed previously. Figure 14 displays the output of the rectifier with the smoothing capacitor and it is approximately 1.7 V which is higher than 50% of the input signal peak voltage.

6       Results

In this section, a comparison between the previously mentioned rectifier topologies is carried out. Firstly, simulations are done using LTSpice software with a 90 nm CMOS process technology. The designed parameters for the rectifiers are  = 900nm/180nm for NMOS transistors and  = 1800nm/180nm for PMOS transistors. Additionally, a smoothing circuit is employed to reduce voltage ripples in the output voltage. The smoothing circuit is simply a capacitor parallel to a resistor. Their values have been chosen and computed to provide the required smoothing effect, where . Furthermore, the operating frequency for RF wirelessly powered biomedical implants is at low giga hertz range (Haerinia & Shadid, 2020b) which is equal to 1.47 GHz in the simulations.

Note that rectifier’s efficiency is calculated as in (8).

However, internal threshold voltage cancelation rectifier has the lowest output

Figure 15. Rectifier efficiency at different amplitudes of the sinusoidal input signal

voltage equal to 0.81V (Figure 8), with an efficiency of 21.04% at  = 3V as shown in Figure 15.

Moreover, self threshold voltage cancelation rectifier also suffers from lower efficiency when increasing input levels as presented in Figure 16 resulting in 7.58% of PCE at  = 3V. This is due to the fact that self-biased rectifiers at high input levels will make the drain-source voltage of the transistors close to zero which means high leakage current, hence, lower efficiency (Roy et al., 2021).

Therefore, for implantable biomedical devices, differential threshold voltage cancelation rectifiers are considered a good option to use in the RF system due to their high PCE. In addition, differential rectifier depends on biasing the transistors without the need for any additional elements, contributing to smaller area on chip; one of the main considerations in any biomedical implant. Another option to consider is cross coupled PMOS rectifier.

7       Conclusion

This paper explored several different designs for a highly efficient AC-to-DC converter suitable for a wireless power transfer system operating at the lower gigahertz frequency of 1.47 GHz. Note that due to the challenged of operating MOSFETs under such high frequency

Figure 16. Rectifiers efficiency at different input power levels

conditions, the rectifier circuits have to be adjusted and their connections rewired to ensure satisfactory operation.

Simulation results revealed differential threshold voltage cancelation rectifier  to have the highest efficiency under the conditions of this particular system, at an efficiency of 48%. On the other hand, rectifiers with self and internal threshold voltage  cancelation  techniques consistently had the lowest efficiency, rendering them impractical for  a wireless power transfer system for biomedical implants.

All in all, the best and most efficient rectifier still suffers a loss of about half. Therefore, further experimentation reveals the potential for combining several threshold voltage cancelations techniques in order to yield even higher efficiencies.

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