Abstract
This paper presents a compact quadrature coupler with a tunable frequency and power-dividing ratio. Wide tunable frequency and power-dividing ratio are achieved by using the novel tunable unit instead of the transmission line sections in a traditional varactor-based quadrature coupler. Closed-form equations are derived for design parameters. For verification, a quadrature coupler is designed based on the given parameters, which demonstrate the tunable frequency of 2.0 GHz to 6.0 GHz and the tunable power-dividing ratio of -20 dB to 7.2 dB at 3 GHz. Finally, a microstrip tunable quadrature coupler is fabricated and measured. The measurements agree well with simulations. Under the frequency-tunable state, the measured 3-dB working frequency of this coupler can be continuously adjusted from 2.0 GHz to 4.7 GHz. And during the adjustment process, the return loss and isolation are always >15 dB. In the power-dividing ratio-tunable state, the adjustment range of the measured power-dividing ratio is from -14 to 6.0 dB at 3 GHz. Moreover, the return loss and isolation are always maintained at >20 dB.
1. Introduction
Modern communication systems, such as the global positioning system (GPS) and wireless local area network (WLAN), need high-performance components working across different communication standards. In addition, in light of today’s crowded radio spectrum and the multistandard RF (radio frequency) frontends in modern telecommunication systems demanding high-performance devices, reconfigurable RF/microwave circuits have become a very important topic of research. As an essential component, various frequency-tunable [1–5] and power-dividing ratio-tunable [6–9] quadrature couplers emerged. In [6], the coupler not only has a narrow adjustment range of power-dividing ratio but also belongs to a double-layer structure. The tunable couplers in [7, 9] are designed by connecting the phase shifters between two traditional couplers. Therefore, this kind of coupler expands the adjustment range of the power-dividing ratio at the expense of circuit size.
Compared with the above single-function tunable couplers, the frequency- and power-dividing ratio tunable couplers [10–12] can integrate multiple functions into a single device or circuit, which is more in line with the development trend of modern communication systems. For the coupler in [10], the 3-dB power-dividing ratio output cannot be achieved in the frequency-tunable mode. The coupler in [11] has a wide adjustment range, but its size is large. Moreover, in [12], the coupler has a narrow adjustment range. To sum up, it is urgent to design a frequency- and power-dividing ratio-tunable quadrature coupler with a small size and wide adjustment range.
In this paper, a compact quadrature coupler, with tunable frequency and the power-dividing ratio is proposed. In Section 2 gives a method for designing the novel tunable unit which can be equivalent to the transmission line sections in a traditional varactor-based quadrature coupler across the entire frequency range. And this coupler has a high degree of symmetry and thus the canonical even- and odd-mode analysis can be simply applied. The presented tunable coupler has several advantages, such as compact design, wide tunable frequency and power-dividing ratio, and closed-form equations available for the systematic design with the prescribed specification. For demonstration, a quadrature coupler is presented based on the given design equations. And it demonstrates the tunable frequency of 2.0–6.0-GHz with an equal power-dividing ratio, and the power-dividing ratio is tuned from -20 dB to 7.2 dB (from 3E-2.5 to 5.3) at 3 GHz in Section 3. Then, a compact microstrip quadrature coupler with tunable frequency and power-dividing ratio is fabricated and measured in Section 4. Good isolation and return loss are obtained for all states. Finally, the conclusion is given in Section 5.
2. Tunable Quadrature Coupler Circuit and Analysis
Figure 1 shows the schematic of the frequency and power-dividing ratio tunable quadrature coupler with electrical length variable transmission-line sections. It basically consists of two transmission lines with a variable electrical length of θ1 and a fixed characteristic impedance of Z1. Two tunable capacitors, C1, are placed in parallel at both ends of the transmission line to tune the operation passband.
2.1. Circuit Analysis
The structure presented in Figure 1 is bisymmetric along the symmetry lines and . Thus, it can be analyzed by using the even-odd mode decomposition technique. If port 1 is specified as an input port, ports 2 and 3 are two outputs, and port 4 is the isolated port. Therefore, the corresponding S-parameters of this coupler should satisfy the following conditions across the entire tuning range: where is defined as the output power-dividing ratio. According to the even-odd mode method, the intrinsic admittances Yee, Yeo, Yoe, and Yoo under different excitation combinations can be obtained as
Thus, the S-parameters of the coupler can be easily obtained as follows: where Z0 represents the port impedance. Combining (1) and ((3a)), ((3b)), ((3c)), and ((3d)), we obtain
By inserting (2a) and (2b) into (4), the following equation is obtained
Subsequently, the value of can be given as
Then, by inserting (2c), (2d), and (8) into (5), the value of can be evaluated as
Finally, by substituting (8) and (9) into (6), the output power dividing ratio of can be expressed as
2.2. Electrical Length Variable Transmission-Line Section
It can be seen from (10) that the power-dividing ratio R is only affected by the electrical length of θ1. In other words, when the power-dividing ratio is determined, the value of the electrical length θ1 should remain constant over the entire adjustable range. To achieve this goal, as shown in Figure 2(b), a novel tunable unit is proposed to replace the electrical length variable transmission-line section (Z1, θ1), which is shown in Figure 2(a). It is basically composed of a low-pass filter and a high-pass filter connected in parallel. The low-pass filter includes two transmission lines (Z2, θ2) and a varactor C2 loaded in shunt to the middle of two transmission lines. Moreover, the high-pass filter consists of the two shunt short-circuited stubs (Z3, θ3) and a varactor diode C3 in a series connection between the two short-circuited stubs.
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When this tunable unit is equivalent to the electrical length variable transmission-line section (Z1, θ1), the Y-matrix of the tunable unit [Y]TU should satisfy the following condition across the entire tuning range:
To calculate the Y-matrix of a novel tunable unit ([Y]TU), the A matrix of this unit is first found and then converted to a Y-matrix. By following Equation (11), the capacitors C2 and C3 can be derived as
2.3. Selection of Design Parameters
According to (8), (9), and ((12a) and (12b)), one can calculate all the design parameters of the quadrature coupler. From Equation (8), it can be known that the value of is equal to Z0 under all conditions. When the center frequency f0 is given, the choice of C1, C2, and C3 are determined by Equations (9) and ((12a) and (12b)). In this paper, for the convenience of calculation, f0 is set at 1 GHz. C1 changes as the frequency for different θ1 or power-dividing ratio R with Z0 = 50 Ω, which is shown in Figure 3. It can be seen from Figure 3 that the value of C1 decreases with the operating frequency. When the electrical length θ1 or power-dividing ratio R is given, the capacitance C1 is mainly determined by the operating frequency. And the variation value of C1 between different power-dividing ratios is relatively small.
In the case of Ω and (i.e. the power-dividing ratio ), and assuming Ω, the change of C2 and C3 versus frequency for different θ2 and θ3 are shown in Figures 4(a) and 4(b). As shown in Figures 4(a) and 4(b), the capacitors C2 and C3 decrease with the operating frequency. Taking into account the controllable range of the varactor, and the tuning frequency, the value of θ2 and θ3 are chosen as 1.5° and 7°, respectively. When θ2 and θ3 are determined, the change of C2 and C3 versus frequency for different Z2 and Z3, are shown in Figures 4(c) and 4(d). To achieve a wide frequency tuning range as much as possible within a realizable range of the varactor, the value of Z2 and Z3 is chosen as 150 Ω. The final structure of the compact quadrature coupler with tunable frequency and the power-dividing ratio is shown in Figure 2(c).
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3. Coupler Design and Microstrip Realization
According to the proposed method, a quadrature coupler with a tunable frequency from 2 GHz to 6 GHz for an equal power ratio and the power-dividing ratio tunable between -20 dB and 7.2 dB at 3 GHz is designed.
3.1. Design Procedure
The design process of this quadrature coupler is summed up as follows:
Step 1. On the basis of the discussions in Section 2.1, given , frequency-tuning range and Z0, the values of C1 and θ1 are determined by (9) and (10).
Step 2. When Ω and (i.e. the power-dividing ratio R =1), one selects Z2, Z3, θ2, and θ3 as 150 Ω, 150 Ω, 1.5°, and 7° at 1.0 GHz, respectively, according to the discussion in Section 2.2. Using ((12a)) and ((12b)), the values of C2 and C3 can be obtained.
Step 3. Based on the above steps, using the commercial EM (electromagnetism) software ADS (advanced design system), the initial design parameters can be optimized.
Following the above design procedure, the calculated circuit parameters of a quadrature coupler are listed in Table 1.
3.2. Microstrip Tunable Quadrature Coupler Realization
The configuration of the proposed microstrip tunable quadrature coupler is shown in Figure 5. The tuning components C1, C2, and C3 are all implemented by MA46H201 high-Q GaAs diodes from MACOM. The equivalent circuit of varactor used in ADS simulation is shown in Figure 6. The package capacitance Cs, package inductance Ls and parasitic resistance Rs of varactor are 0.15 pF, 0.45 nH, and 1 ohm, respectively. The Cblock (100 pF) is realized by ATC 600S series capacitors. The bias resistor Rbias is 180 kΩ.
4. Simulated and Measured Results
To verify the effectiveness of the above design, a quadrature coupler with tunable frequency and power-dividing ratio was manufactured and measured. This tunable quadrature coupler was fabricated on a Rogers RT/Duroid 5880 with and mm. According to Table 1, the parameters for the design and manufacturing of the circuit in this coupler are set. And the final configuration of this microstrip tunable quadrature coupler is shown in Figure 5. The dimensions marked in Figure 5 are as mm, mm, mm, mm, mm, mm, mm, mm, and mm. ADS performs all of the simulation parameters. The vector network analyzer used for measuring is Rohde & Schwarz ZNB-8, which covers the frequency range of 1.0 GHz to 6.0 GHz.
4.1. Performance of the Tunable Frequency with
Figure 7 shows the simulated and measured -parameters of the proposed quadrature coupler with . The simulations are in good agreement with the measurements. When the biasing voltages (i.e., Vbias1,2,3) of varactors change in the range of 0–20 V, the center frequency of the proposed tunable coupler can be continuously adjusted from 2.0 to 4.7 GHz. Moreover, the center frequency is limited by the range of varactors. For all states, the measured return loss and isolation are better than 15 dB. Correspondingly, the return-loss bandwidth is greater than 50 MHz at this center frequency. The measured insertion loss varies from 4.3 to 5.9 dB. The difference between the simulated and measured insertion loss is within 1.0 dB, which is mainly attributed to the limited welding process and the resistive loss from the transmission lines. Moreover, the phase difference between the simulated and measured coupler is shown in Figure 8. For all states, the measured phase imbalances at the center frequency are less than 5°.
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Figure 9 shows an image of the manufactured tunable quadrature coupler. The circuit size is , where λg is the guided wavelength at the lowest center frequency.
4.2. Performance of the Tunable Power-Dividing Ratio
As discussed in Section 2.2, the power-dividing ratio is only affected by the electrical length of θ1. By changing the value of θ1, tunable R can be achieved at each state. For demonstration, this tunable coupler is simulated and measured at 3 GHz.
Figures 10 and 11 show simulated and measured results of this proposed quadrature coupler for different power-dividing ratios. The simulations are in good agreement with the measurements. The power-dividing ratio can be tuned from -14 to 6.0 dB at 3 GHz, which is limited by the range of varactors. The measured return loss and isolation are better than 20 dB. Correspondingly, the return-loss bandwidth is greater than 100 MHz at this center frequency. Moreover, the phase difference between the simulated and measured coupler is shown in Figures 10(c) and 11(c). The measured phase imbalances at each state are less than 5°.
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4.3. Comparison
A performance comparison between this fabricated tunable quadrature coupler and the quadrature couplers reported in the literature, is given in Table 2. It should be noted that the tunable frequency and power ratio of the coupler in [12] are realized by more than 8 tunable elements. And compared with a coupler in [11], the performance of the proposed quadrature coupler is basically the same, but the proposed coupler is smaller in size and easier to analyze. As shown in Table 2, this tunable quadrature coupler offers a tunable frequency, a tunable power-dividing ratio, and a compact size.
5. Conclusion
A compact quadrature coupler with wide tunable frequency and a power-dividing ratio is achieved by using the novel tunable unit to replace the transmission line sections in traditional varactor-based quadrature couplers. Closed-form equations are derived for design parameters. In order to verify the quadrature coupler that has a tunable frequency and tunable power-dividing ratio, the coupler with only three types of varactor is designed and fabricated. Good isolation and return loss are obtained for all states.
Data Availability
The data that support the findings of this study are available on request from the corresponding author. The data are not publicly available due to privacy or ethical restrictions.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
This work is supported by the National Natural Science Foundation of China (62201324) and Natural Science Foundation of Shandong Province (ZR2022QA101 and ZR2022QF065).