A) Harmonic rejection filter

A compact microstrip harmonic rejection filter is introduced for the capacitor-less microwave rectifier. The low-pass filter with the cut-off frequency of 7.3 GHz is composed of one thin microstrip line and two microstrip patches with a dimensions of 8.1 mm × 3.6 mm on a F4B-2 substrate with ε _r = 2.65 and thickness of 1 mm, as shown in Fig. 2. The thin line and the patches operate as a series inductor and two parallel capacitors, respectively. Figure 3 shows the measured results of the low-pass filter. The insertion losses of the filter are 0.3 dB at 5.8 GHz, 15.8 dB at 11.6 GHz, and 8.4 dB at 17.4 GHz, respectively. The fundamental frequency is located in the pass-band, and its harmonics are rejected to the rectifying diode by the harmonic rejection filter. The input and output impedances of the filter are 50 Ω to match the microwave source and load, respectively.

Fig. 2. The proposed harmonic rejection filter.

Fig. 3. The simulated and measured results of the low-pass filter.

B) Impedance matching

An HSMS 286 Schottky diode is applied in the proposed rectifier, which shows capacitive impedance at the operating frequency and input microwave power level. Therefore, an impedance transformer is required to match the complex impedance to 50 Ω.

In the proposed design, the large signal model of the HSMS 286 Schottky diode is applied. The impedance of the diode [Reference Strassner and Chang10] is defined as

(1)$$Z_d = \displaystyle{{\pi R_s } \over {\cos \theta _{on} \left({\displaystyle{{\theta _{on} } \over {\cos \theta _{on} }} - \sin \theta _{on} } \right)+ j\omega R_s C_j \left({\displaystyle{{\pi - \theta _{on} } \over {\cos \theta _{on} }}+\sin \theta _{on} } \right)}}\comma \;$$

where C _j, R _s, and θ _on are the junction capacitance, the series resistance, and the forward-bias turn-on angle, respectively. A λ _g/8 short-ended microstrip line is equivalent to an inductance at the fundamental frequency. Therefore, this microstrip line cancels the imaginary part of diode impedance to enhance the rectifying efficiency at the fundamental frequency [Reference Gao, Yang, Jiang and Zhou9]. The inductive reactance of the microstrip line is defined as

(2)$$jX_L = j2\pi f_0\, L = jZ_0 \tan \lpar \beta l\rpar \comma \;$$

where Z ₀ and β are the characteristic impedance and propagation constant, respectively. The equivalent inductance is L = Z ₀/2πf ₀, while l = λ _g/8. At the second harmonic, the input of the short-ended microstrip line is open which has no effect to the impedance matching circuit.

The MW-to-DC conversion efficiency is greatly dependent on the length of the parallel microstrip line. Figure 4 shows the relation between the conversion efficiency and the length of the parallel microstrip line with the optimum load resistance of the rectifier. In Fig. 4, the maximum conversion efficiency is 76%, when the line's length is 5.32 mm which approximates to λ _g/8. The MW-to-DC conversion efficiency drops obviously while the length deviates from λ _g/8. In the simulated results, the curve is not smooth due to an insufficient number of interpolation which is automatically controlled by ADS software.

Fig. 4. MW-to-DC conversion efficiency according to the length of the parallel microstrip line.

When the diode self-bias DC voltage V ₀ equals to half-diode reverse break-down voltage V _br, the conversion efficiency achieves the maximum value [Reference He and Liu11, Reference Yoo and Chang12]. The complex impedance of the diode HSMS-286 with different DC load resistances are simulated, and the results are shown in Fig. 5 when V ₀ = 3.7 V. The input impedance of the HSMS-286 is equal to 126 Ω at a 120 Ω DC load.

Fig. 5. Complex impedance of an HSMS-286 Schottky diode with various load resistances at 5.8 GHz.

Figure 6 shows the simulated results of the impedance matching circuit used in the proposed rectifier. The matching circuit contains the parallel λ _g/8 short-ended microstrip line and two short series microstrip lines. At 5.8 GHz, the return loss on both input filter and diode port is greater than 13 dB, and the simulated insertion loss is 0.3 dB.

Fig. 6. Simulated insertion and return loss of the impedance matching circuit.

C) Output low-pass filter

Conventional output filter of the rectifier is composed of a λ _g/4 microstrip line and a lumped capacitor. The capacitor is assumed to produce a short circuit at the fundamental frequency and an open circuit after λ _g/4 microstrip line. Normally, a chip capacitor cannot produce zero impedance since its capacitance is not infinity and the loss cannot be neglected at microwave frequency. Thus, an output low-pass filter is proposed to replace the chip capacitor and λ _g/4 microstrip line in schematic, which rejects the fundamental frequency microwave and its harmonics. Figure 7 shows the detailed microstrip structure of the low-pass filter which realized by the artificial transmission lines [Reference Huang, Liu, Chen, Yan and Huang13]. The interdigital structured microstrip is used to suppress the third harmonic.

Fig. 7. Microstrip structure of the output low-pass filter.

The reflection and transmission characteristics of the applied low-pass filter are shown in Fig. 8. The reflection and the transmission coefficients at the fundamental frequency of 5.8 GHz are −0.8 and −27.4 dB, respectively. Furthermore, the reflection and the transmission characteristics are −0.46 and −25.6 dB at the second harmonic, −4.1 and −16.6 dB at the third harmonic, respectively. The low-pass filter obtains a good performance of preventing the fundamental frequency microwave and its higher order harmonics from leaking to the DC output port. Then, the harmonics are reflected back to the diode for power recycling, which may improve the DC-to-MW rectifying efficiency.

Fig. 8. Reflection and transmission characteristics of the low-pass filter.