A High Conversion Gain Envelope Detector with Wide Input Range for Simultaneous Wireless Information and Power Transfer System

: Wireless sensors networks (WSN) have been gradually facilitating the pervasive connectiv-ity of wireless sensor nodes. A greater number of wireless sensors have been used in different aspects of our life. However, limited device battery life restricts the applications of large-scale WSN. This paper presents a batteryless envelope detector with radio frequency energy harvesting (RFEH) for wireless sensor nodes, which enables simultaneous wireless information and power transfer (SWIPT). The envelope detector is designed for small modulation index AM signals with large amplitude variations. Therefore, the envelope detector is supposed to have wide input range while achieving a high conversion gain. We proposed an adaptive biasing technique in order to extend the input range of envelope detector. The input differential pair is adaptively biased through a feedback loop to overcome the variation of bias point when the amplitude of input signal changes. The cross coupled rectiﬁer and DC-DC boost converter with maximum power point tracking (MPPT) are presented against power conversion efﬁciency (PCE) degradation of RF rectiﬁer with the input power varying. The adaptive biased envelope detector is theoretically analyzed by square law MOSFET model. Designed with 0.18 µ m complementary-metal-oxide-semiconductor (CMOS) standard process, the power consumption of proposed envelope detector is 9 µ W. Simulated with a 915 MHz AM input signal with 2 Mbps data rate and 0.05 modulation index, the proposed envelope detector achieves 20.37 dB maximum conversion gain when the amplitude of input signal is 0.5 V, and the PCE of energy harvesting circuits achieves 55.2% when input power is –12.5 dBm. applications.


Introduction
Mutifunctional sensors have been widely used in our daily life. These tiny sensors, which can wirelessly communicate in short ranges, represent significant roles in various areas, such as the predictive maintenance of structures, smart buildings, and safety control in automotive applications [1]. However, battery replacement is arduous work, especially in a large WSN. In some cases, it is even hard to obtain access to these sensors in person. Energy harvesting is an attractive solution of the energy-constrained sensor nodes in WSN to perpetually capture energy from ambient environment and convert to DC supply. By adopting energy harvesting in WSN, the maintenance cost can be reduced with enhanced flexibility in practical deployment [2]. Several kinds of ambient energy sources have been widely used in energy harvesting systems, such as heat, vibration, light, and radio frequency (RF) energy [3][4][5]. From above, RF energy is the most applicable energy source for WSN applications as compared with others due to the ubiquity of RF signals. RF energy harvestor can convert RF power to DC supply power. If the RF energy source is stable, the DC power will be permanently provided by RF energy harvesting system. RF energy has been already used in many applications, such as electric vehicles and implantable medical devices [6,7]. In order to implement RF energy harvesting and wireless data receiving in wireless sensor nodes, one solution is to use two links that are in different frequency bands to separately harvest RF energy and transfer wireless data. Generally, the RF energy signal is much stronger than the RF data signal. These two frequency bands must have enough separation in order to protect RF data signal from the interference. Figure 1 shows the configurations of conventional energy harvestor and data receiver systems. It can be seen that RF energy harvestor and data receiver are two relatively independent systems. There are two sets of antennas and impedance matching networks in the systems. In circuits design, the passive elements, such as antennas and inductors, are very bulky. Moreover, two different frequency bands will occupy more bandwidth, which is a precious resource in current society. Therefore, it is desirable to use a single RF signal in order to implement RF energy harvesting and wireless data receiving [8].  Figure 2 presents our proposed RF energy harvestor and wireless data receiver system, the received RF signal is used both for energy harvesting and data transfer. Amplitude modulation (AM) is preferred in these applications, due to its lower power consumption and less circuit complexity in demodulation [9]. Equation (1) shows the expression of AM signal. Where A is the amplitude of the signal, m is the modulation index, X BB (t) is the baseband signal, and ω c is the carrier frequency.
It is clear that the amplitude of AM signal is A(1 + m) and A(1 − m) when the baseband data is symbol 1 and symbol −1, respectively. Therefore, the power of AM signal can be expressed as Suppose that the power conversion efficiency (PCE) of the WPT os represented as X and the probabilities of symbols 1 and symbol −1 are equal. Thus, the effective PCE (EPCE) of the RF energy harvesting is as following.
Equation (3) indicates that increasing m will degrade the EPCE of RF energy harvesting. In addition, the peak-to-average ratio (PAR) of AM signal is directly decided by the m, as shown in Equation (4) [10].
A big PAR means a large variation of power, which requires regulating processes by battery management circuits and further degrades the PCE of the entire system [11]. Therefore, AM signals with small modulation index is preferred and a sensitive AM demodulator for AM signals with small modulation index is considered to be the prerequisite for realizing the RF energy harvestor with the wireless data receiver system. Figure 3 shows a typical AM demodulator, which is widely used in radio frequency identification (RFID) [12]. However this topology is less sensitive and it can be hardly used for small modulation index AM signals. The conversion gain of the envelope detector is less than 1, because the conventional envelope detector is only composed of passive devices. When the modulation index of AM signals is small, the comparator cannot determine the correct results, due to the effect of noise and offset. Moreover, envelope detectors containing active devices, such as MOSFETs, can provide high conversion gain. The circuit that is depicted in Figure 4 is a common implementation of an active envelope detector [13].
However, the amplitude of AM signal may also change due to other factors besides modulation, such as the distance to the RF signal source and obstructions. Thus, the demodulator must have a relatively wide input range. The amplitude variation of input RF signal may change the bias point of the active devices, resulting in saturation and distortion, which limits the input range.    In order to address the problem mentioned above, we proposed a low power envelope detector with an adaptive biasing technique. The large conversion gain is obtained through the amplification of differential pair, and the biasing voltage of input differential pair is generated through the feedback loop that is based on the input signal, so the envelope detector can work in a wide input range. The RF rectifier and DC-DC boost converter with MPPT are also implemented in order to achieve a higher PCE in wide input power range. The rest of the paper is organized, as follows. Section 2 theoretically analyzes the conversion gain of proposed envelope detector and shows the effectiveness of proposed adaptive biasing technique. Section 3 presents the RF rectifier and DC-DC boost converter with MPPT. Section 4 presents the simulation results. Finally, Section 5 concludes the entire work.  The proposed envelope detector is composed of a common source PMOS differential pair M p1 , M p2 , a NMOS transistor M n1 as a current source, and an error amplifier A 1 . The output signal V o is the baseband signal, which can be further amplified through the baseband amplifier. When the RF signal X AM (t) is applied, while assuming the gate voltage of M p1 is V g1 and expressed as Equation (3). V G is the biased voltage, which is generated by the feedback loop. v g is the amplitude of input signal, m is the modulation index, X BB (t) is the baseband signal, and ω c is the carrier frequency. It is difficult to analyze this kind of circuit, because, usually, the amplitude of input signal v g is large, the MOSFET transistor works on the strong inversion region and weak inversion region in one frequency period. In this paper, we present a theoretical analysis method by using the square law MOSFET model. We first analyze the envelope detector in an open loop condition, and calculate the conversion gain of the baseband signal.

Theoretical Analysis of Proposed Envelope Detector
Because the modulation index of the AM signal m is small, therefore v g mX BB (t) cos ω c t can be seen as small signal, and V G + v g cos ω c t is the quasi-static operating point of M p1 . The output current of M p1 can be expressed as The function f (x) is the I-V function of PMOS transistor, and I Q (ω c t) and g(ω c t) represent the quasi-static current and quasi-static transconductance, respectively. The Fourier expand method is introduced in order to compute the conversion gain of the envelope detector. I n and g n are nth harmonic quasi-static current and nth harmonic quasi-static transconductance, respectively. If the impedance at output node O is R out , then the conversion gain of baseband signal can be obtained.
MOSFET in a strong inversion region conducts much more current than in a weak inversion region or moderate inversion region. In our design, MOSFET in the strong inversion region contributes the most of the current. Therefore, it is reasonable to use the square law MOSFET model for approximations.
Here, I Z = 2µC OX ( W L )(nφ t ) 2 , φ t = (kt)/q is the thermal voltage, which approximately equals to 26 mV in room temperature, µ is the carrier mobility, C OX is the gate oxide capacitance per unit area, and W L is the aspect ratio of the MOSFET. The substrate factor n can be represented as 1 + [γ/(2 V SB + 2φ F )], where φ F is the Fermi voltage. In order to obtain quasi-static transconductance, we use this PMOS model and take the derivative of V gs and represent V g1 as equation 6. We have Here, we define the conduction angle is ). Accordingly, Equations (12) and (13) can be rewritten as Hence, the average current consumption I 0 and the first harmonic transconductance g 1 can be calculated, as follows.
Figures 6 and 7 show the I 0 and g 1 characteristics with W/L = 1 µm/0.5 µm aspect ratios fabricated in the 0.18 µm process based on our calculations. The calculations were done while using Equations (16) and (17), with the condition of I Z = 180 nA, V th = −450 mV, substrate factor n = 1.3, and φ t = 26 mV. The source terminal of transistor is biased at 1.8 V and the source terminal of transistor is grounded. The I 0 and g 1 characteristics indicate that it is difficult to achieve wide input range and high conversion gain under low power consumption at the same time. For example, if we want to have a relatively large conversion gain when v g is small, then the biased voltage V G must be low. However, for the low biased voltage V G , as v g becomes larger, the average current I 0 increases dramatically, which increases the power consumption. Therefore, it is not power efficient to set the biased voltage V G at a fixed value.
In this paper, we propose the adaptive biasing technique, which can generate low bias voltage V G when v g is small to obtain a higher conversion gain and high bias voltage V G when v g is large for low power consideration. It is implemented through the constant biasing current. Figures 8 and 9 show the calculation results of g 1 and V G for I 0 = 1 µA, 2 µA, 4 µA, respectively. It can be shown that, when the MOSFET has constant biasing current, the relatively constant conversion gain can be obtained with low power consumption by properly setting V G , according to v g . As I 0 increases, g 1 will increase accordingly. However, higher I 0 requires higher v g , which limits the input range.   The proposed adaptive biasing technique is implemented through a negative feedback loop. The cut-off frequency of low pass filter R f C L is much lower than the bandwidth of baseband signal, so the gate of transistor M n1 can be seen as AC ground. Therefore, the gate voltage of M n1 approximately equals to V re f through the feedback loop. Thus, the average current of NMOS transistor I n is as follows.
The adaptive biased voltage V G is generated by error amplifier. For example, as the amplitude of input signal v g increases, the average current of PMOS differential pair is increased. Because I n is fixed, the voltage V o will increase. Therefore, the output voltage of error amplifier will increase in order to generate a higher V G , which will decrease the average current of PMOS differential pair. The bias voltage is supposed to only react with the average amplitude of input signal in order to generate a stable biased voltage V G . Therefore, the bandwidth of the feedback loop need to be lower than the bandwidth of baseband signal. The transfer function of the feedback loop can be approximately expressed, as follows.
where A V1 and R O1 are voltage gain and output impedance of the error amplifier A 1 , respectively. In addition, the low bandwidth of the feedback loop results in the low transient response requirements for error amplifier, which can be easily implemented in low power condition. In our design, a folded cascode topology is adopted for error amplifier, which achieves 50 dB DC voltage gain with 100 KHz-3 dB bandwidth under 1 µA current consumption. Table 1 lists the device parameters that are used in the envelope detector. The average current of proposed envelope detector is 5 µA, and the supply voltage is 1.8 V. 1 MΩ is chosen for R f in order to obtain enough conversion gain.   Figure 10 shows the schematic of the proposed RF energy harvesting circuits. It is composed of a cross couple rectifier and a DC-DC boost converter. When compared to diode connection CMOS rectifiers, cross couple rectifiers can achieve much higher PCE. However, the PCE of cross couple rectifiers is highly related to the input power and load impedance. For different input power, the optimum load impedance of rectifier to obtain the highest PCE is different. As the input power changes, the PCE will quickly degrade. Figure 11 shows the simulated PCE of cross coupled rectifier with different load impedances. The rectifier has a NMOS transistor size of 100 µm/0.18 µm and PMOS transistor size of 160 µm/0.18 µm. It can be shown that, if we keep the load impedance of rectifier unchanged, the highest PCE can only be obtained at a specific input power. The optimal load impedance changes from 10 KΩ to 1 KΩ when the input power changes from −17.5 dBm to −2.5 dBm.

RF Energy Harvesting Circuits
In order to improve the PCE with varying input power, we designed a DC-DC boost converter operating in discontinuous conduction mode (DCM) with maximum power point tracking (MPPT). Figure 12 shows the output voltage of cross coupled rectifier when input power varying. It can be seen that, for each input power, there are optimal load impedance and corresponding optimal output voltage V rec,opt . Because the input power varies from −17.5 dBm to −2.5 dBm, the V rec,opt changes slightly from 0.46 V to 0.53 V.
Therefore, we implemented MPPT by properly setting the output voltage of cross coupled rectifier V rec close to V rec,opt . Through the negative feedback loop, V rec is approximately equals to the reference voltages V re f 1 . The reference voltages V re f 1 is set to 0.5 V, corresponding to the input power range from −17.5 dBm to −2.5 dBm. We use off-chip Schottky diode D 1 to reduce voltage drop. In our design, the Schottky diode model is LSM115J, which has only 100 mV forward voltage drop at 400 mA forward current. The capacitor C d is charged by the rectifier, and the reference voltage V re f 2 is clamping voltage, which is 1.8 V for over voltage protection in our design. The start up circuit is designed in order to achieve cold-start. It is composed of a ring oscillator, which can generate a 50% duty cycle square wave under 0.48 V voltage supply. The NMOS transistor M n4 is driven by start up circuit and boost up V out to 1 V. Once V out is beyond 1 V, the start up circuit is disabled, and the DC-DC boost converter operates in DCM. Figure 13 shows the equivalent circuits of DC-DC boost converter in DCM and its current and voltage waveforms. Figure 13a-c illustrate the operation principle of DC-DC boost converter working in DCM. If the input power increases, the switching MOSFET M n3 will be more frequently conducted, as shown in Figure 13d. Therefore, I LAV , the average current of I L , increases. The input impedance of DC-DC boost converter is calculated as V dc /I LAV , so the input impedance will decrease. The load of cross coupled rectifier is the input impedance of DC-DC boost converter. Accordingly, the load impedance of cross coupled rectifier will decrease when the input power becomes larger. By properly setting V re f 1 , the input impedance of the DC-DC boost converter can be approximately equal to the optimum load impedance of rectifier with input power varying. The PCE of cross coupled rectifier can be increased, according to our previous analysis. Table 2 shows the summary information of proposed RF rectifier and DC-DC boost converter.  1 mH V re f 1 500 mV V re f 2 1.8 V

Post-Layout Simulation Results and Discussion
Our proposed batteryless envelope detector with RF energy harvesting circuits was designed with 0.18 µm CMOS standard process. Figure 14 shows the layout of complete system, which has 200 µm × 300 µm active area. Post-layout simulations are performed with 2 Mbps AM modulated signal through Spectre. The RF input signal has 915 MHz carrier frequency with 0.05 modulation index.   Figure 15 shows the simulation results of envelope detector under 1.8 V supply voltage. When the amplitude of input signal increases from 0.25 V to 1 V, the bias voltage V G changes from 0.9 V to 1.7 V. Thanks to the adaptive biased voltage, the average current I 0 is almost constant, changing only from 1.96 µA to 2.08 µA. The variation of average current I 0 is approximately 5 %. Figure 16 shows the conversion gain as a function of the amplitude of the input signal. It achieves 20.23 dB conversion gain at v g = 0.5 V. The conversion gain is higher than 14 dB in the entire input range due to the adaptive biasing technique. Different from our previous theoretical analysis, the simulation results show that the conversion gain decreases when the amplitude of the input signal becomes larger. This is because, when the input signal becomes larger, the output voltage saturates due to the swing limitation.   Figure 17 shows the simulated timing waveforms of proposed envelope detector. V in+ and V in− are the differential input signals, which have a 915 MHz carrier frequency with 2 Mbps AM modulated signal, 0.05 modulation index, and 1 V amplitude. V G is the adaptive biasing voltage of the proposed envelope detector and V O is the envelope detector output. The amplitude of V O increases as V G settling to 1.7 V, which indicates the effectiveness of the proposed adaptive biasing technique.  Figures 18 and 19 illustrate the output power and PCE of the proposed RF energy harvesting circuits. The proposed envelope detector is the load of RF energy harvesting circuits. The output power reaches 9.28 µW with −17.5 dBm input power. It is enough to power our proposed envelope detector, and this is equivalent to PCE of 52.1%. In order to extract the maximum power, as the input power increases, the corresponding load resistor R L is connected in parallel with C L . The value of load resistors R L is labeled in Figure 18. The highest PCE reaches 55.2%, with −12.5 dBm input power and 150 KΩ load resistors.  Figure 20 illustrates the time waveforms of the DC-DC boost converter. The simulation is performed with 100 KΩ load resistor and −10 dBm input power. The start up circuit is enabled after 0.8 ms when the output voltage of RF rectifier V rec reaches 0.5 V. Once the output voltage of DC-DC boost converter V out is beyond 1 V, the DC-DC boost converter works in DCM. Therefore, it maintains V rec near to V rec,opt . As V out increases to 1.8 V, the control circuits will disable the DC-DC boost converter shortly for over voltage protection. Thus, V out is clamped at 1.8 V.  Table 3 summarizes and compares the performances of the proposed batteryless envelope detector with previously published reports. Our proposed envelope detector achieves 0.25-1 V input range and 20.37 dB conversion gain through the adaptive biasing technique, which are improved as compared to previous works. In addition, RF energy harvesting circuits have 55.2% peak PCE and they eliminate the requirement of battery. Therefore, it is a good candidate for SWIPT in WSN applications.

Conclusions
We have proposed a novel batteryless envelope detector with RF energy harvesting. The adaptive biasing technique is introduced to dynamically generate the biasing voltage through the feedback loop in order to obtain a stable conversion gain. Theoretical analysis have been proved that, through the adaptive biasing technique, the proposed envelope detector can achieve both high conversion gain and wide input range. The RF rectifier and DC-DC boost converter with MPPT are also presented. The simulation results indicate that the proposed envelope detector achieves maximum 20.37 dB conversion gain with 915 MHz carrier frequency and 0.05 modulation index, and it maintains over 14 dB when the amplitude of input signal is between 0.25 V and 1 V. When compared to previous works, both input range and conversion gain have been improved. The overall power consumption of the envelope detector is only 9 µW, and it can be powered by RF energy harvesting circuits, which makes it suitable for SWIPT applications.