Compact High-Directivity Contra-Directional Coupler

Abstract

This paper presents a novel design of a compact contra-directional coupler with high directivity for high-power monitoring in high frequency. Microstrip parallel coupled lines are widely used for directional couplers; however, they show poor directivity inherently. Their directivity has been improved by many works. However, the suggested approaches often result in other limitations, such as a weak structure for high-power monitoring, or a larger size to be integrated with other circuits. The design approach proposed in this study starts from a ring-type four-port network to avoid weak components that are vulnerable to high power, and uses a 60° electrical length of coupled line for a compact size. The design equations for the initial dimensions are derived from the ring-type four-port network model. The weak coupling of the 20 dB coupler was designed and measured. The measurement shows 20 dB directivity from 12.8 GHz to 14.8 GHz, covering the Ku-band satellite uplink communication and peak directivity of about 45 dB. The coupler’s active area is 4 mm by 5.5 mm; this is a compact size compared with other works.

1. Introduction

Microstrip parallel coupled-line directional couplers are widely used in microwave and millimeter-wave circuits. The power detection and VSWR (voltage standing wave ratio) detection circuits in high-power systems are important areas. The microstrip structure is the most popular choice for this application because it is compact and flexible for integration into other circuits. Power and VSWR detection in high-power systems should have weak coupling to feed sufficiently low power to the detector component. The directivity should be high so that the load impedance of the high-power systems will have a minimal effect on the power detection, and the forward and reverse power can be detected as independently as possible. Lastly, the circuit should be small and compact to ensure minimum loss in the power systems and easy integration. However, the microstrip parallel coupled-line directional coupler with weak coupling shows poor directivity, due to the inherent difference between the phase velocities of its even- and odd-mode in the microstrip transmission line.

Many studies have been carried out to overcome poor directivity. One group of approaches is to compensate for the difference in even- and odd-mode phase velocities. Wiggly lines [1,2,3] were proposed, and they increased the odd-mode electrical length to compensate for the difference. Another compensation method is overlaying a dielectric on a microstrip line [4,5,6] to make an inhomogeneous microstrip transmission line, much like a homogeneous line. Those methods are intuitively clear and reasonable; however, there is a lack of a straightforward design equation which requires more rigorous analysis and trial and error. Moreover, adding an external dielectric material on the PCB is an additional burden for practical implementation. In [7,8,9,10], an interdigital capacitor or thin periodic stubs are inserted between two coupled lines, and in [11,12,13], short stub distributed inductors are placed in the middle of a coupled line, while [14] uses both inductive and capacitive stubs. Some approaches use a feedback path [15,16]. However, all of these used thin and sharp structures that are vulnerable to high power, and as such, they are not suitable for high-power systems. Ref. [17] proposed multiple coupled-lines approaches, and [18,19,20,21] added capacitive and inductive stubs for compensation. Other multiple coupled-lines approaches involve inserting a non-coupling line between the couplers [22,23,24,25]. The multiple coupled-lines approaches show broadband characteristics; however, they are cumbersome for integration into power systems due to their larger size and greater corresponding loss. There are also lumped-element compensation methods, where [26,27] use capacitors at the end of couplers, and [28] uses periodic capacitors inside couplers. However, the lumped-component approaches are unsuitable for microwave and millimeter-wave applications. Refs. [29,30] used distributed version of capacitors at the end of couplers. [31,32] modulated the port impedance with an inductor at the coupler ports, but there are more suitable approaches for power systems.

Most microwave and millimeter-wave power systems operate in a specific frequency band. In light of this, the present study emphasizes high-directivity, compact size and a correspondingly low insertion loss characteristic, rather than wideband operation. To this end, this paper proposes a high-directivity compact microwave directional coupler suitable for integration into high-power systems. This paper derived the design equation for compact, weak coupling and high-directivity couplers for high-power systems, where the coupled line length can be selected arbitrarily. The proposed design is demonstrated in a specific frequency band for Ku-band satellite up-link applications. For the coupled line, 60° electrical length is selected for compact size. The coupling is more than 20 dB, and the resulting layout does not have a sharp and narrow matching section; thus, it is resilient for high-power applications. Furthermore, it has a directivity higher than 40 dB.

2. Materials and Methods

2.1. Design of Directional Coupler

Microstrip parallel coupled lines are commonly used for directional couplers due to their simple structures and ease of use with other circuits. The parallel coupled-line coupler operation can be decomposed into even- and odd-mode operations, as in Figure 1. However, the microstrip transmission line has an inherently inhomogeneous structure, where dielectric material exists only between the signal line and the ground. Therefore, the even- and odd-mode operations have a different effective dielectric constant, resulting in different phase velocities and causing directivity degradation. Many works have been carried out to compensate for the difference. However, they usually have a structure that is vulnerable to high power or of a cumbersome size for integration with other circuits, as well as additional losses, as introduced before.

Another way of implementing a directional coupler is using ring-type four-port structures, such as well-known branch line couplers or rat race couplers. However, these structures have limitations in implementing arbitrary coupling, especially weak coupling. In [33], the general ring-type four-port with lumped-distributed elements is well analyzed with even- and odd-modes of the T matrix for contra-, trans-, and co-directional coupler conditions. However, the lumped element is not readily available in microwave and millimeter waves. Moreover, there is coupling between transmission lines as the circuit size becomes smaller when the frequency increases.

In this study, the original general ring-type four-port model in Figure 2a,b is modified by replacing the isolated four transmission lines ($Z_3,{\theta }_3)$ with a parallel coupled line ($Z_{3e,o},{\theta }_{3e,o})$ as in Figure 2c,d. Instead of compensating for the difference in even- and odd-mode phase velocities as in many other works, we used the different even- and odd-mode electrical lengths obtained by a circuit simulation of the coupled line.

In Figure 2, $Z_i$ and ${\theta }_i$ are the characteristic impedances and electrical lengths of the transmission lines; $X_{12}$, $B_i$, and $B_{pi}$ are the lumped reactance and susceptances; $Z_{0i}$ is the port impedance; $a_i$ and $b_i$ are power waves for the T matrix analysis; $Z_{ie,o} \left(i=1,2\right)$ and ${\theta }_{ie,o} \left(i=1,2\right)$ are the impedances introduced by parallel coupled lumped elements. $B_i$; and $Z_{3e,o}$ are the even- and odd-mode impedances and electrical lengths of the replaced parallel coupled line. In the modified version of the general ring-type four-port model, the series reactances $X_{12}$ are removed, and the original isolated transmission lines are replaced with a coupled line with different even- and odd-mode electrical lengths.

The corresponding T matrix for the even- and odd-mode equivalent circuit in Figure 2d is modified as in Equations (1)–(4) from the original equations, where $Y_{ie,o} \left(i=1,2\right)$ are the admittance form of $Z_{ie,o}$; $Y_{3e,o}$ is the even- and odd-mode admittances of the parallel coupled line; and $Y_{02}$ is the admittance form of $Z_{02}$. Each element in the T matrix is updated in Equations (5)–(11), where $b_{1e,o}$ is the normalized input even- or odd-mode susceptance, and $b_{2e,o}$ is the normalized output even- or odd-mode susceptance; $y_{ie,o}=j{b}_{ie,o}$, where $y_{ie,o}$ is the normalization of $Y_{ie,o}$; $y_{ie,o}=Y_{ie,o}/\sqrt{Y_{01}{Y}_{02}}$.

$$\left[T_{e,o}\right]=\left[T_{1e,o}\right]\left[T_{3e,o}\right]\left[T_{2e,o}\right]$$

(1)

$$\left[T_{1e,o}\right]=\frac{1}{2}\sqrt{\frac{Z_{3e,o}}{Z_{01}}}\left[\begin{array}{cc}1+Z_{01}\cdot \left(Y_{3e,o}+Y_{1e,o}\right)& 1-Z_{01}\cdot \left(Y_{3e,o}-Y_{1e,o}\right)\\ 1-Z_{01}\cdot \left(Y_{3e,o}+Y_{1e,o}\right)& 1+Z_{01}\cdot \left(Y_{3e,o}-Y_{1e,o}\right)\end{array}\right]$$

(2)

$$\left[T_{3e,o}\right]=\left[\begin{array}{cc}exp\left(j{\theta }_{3e,o}\right)& 0\\ 0& exp\left(-j{\theta }_{3e,o}\right)\end{array}\right]$$

(3)

$$\left[T_{2e,o}\right]=\frac{1}{2}\sqrt{\frac{Z_{02}}{Z_{3e,o}}}\left[\begin{array}{cc}1+Z_{3e,o}\cdot \left(Y_{02}+Y_{2e,o}\right)& 1-Z_{3e,o}\cdot \left(Y_{02}-Y_{2e,o}\right)\\ 1-Z_{3e,o}\cdot \left(Y_{02}+Y_{2e,o}\right)& 1+Z_{3e,o}\cdot \left(Y_{02}-Y_{2e,o}\right)\end{array}\right]$$

(4)

$$\Re T_{11e,o}=\frac{1}{4\sqrt{n}}\left[\left(n+1\right)\cdot A_{e,o}-B_{e,o}\cdot \left(b_{1e,o}+n{b}_{2e,o}\right)\right]$$

(5)

$$\Im T_{11e,o}=\frac{1}{4}\left[\left(b_{1e,o}+b_{2e,o}\right)\cdot A_{e,o}+B_{e,o}\cdot \left(1-b_{1e,o}{b}_{2e,o}\right)+C_{e,o}\right]$$

(6)

$$\Re T_{12e,o}=\frac{1}{4\sqrt{n}}\left[\left(n-1\right)\cdot A_{e,o}+B_{e,o}\cdot \left(b_{1e,o}-n{b}_{2e,o}\right)\right]$$

(7)

$$\Im T_{12e,o}=\frac{1}{4}\left[\left(b_{1e,o}+b_{2e,o}\right)\cdot A_{e,o}-B_{e,o}\cdot \left(1+b_{1e,o}{b}_{2e,o}\right)+C_{e,o}\right]$$

(8)

$$A_{e,o}=2cos{\theta }_{3e,o}$$

(9)

$$B_{e,o}=2z_{3e,o}sin{\theta }_{3e,o} , n=\frac{Z_{02}}{Z_{01}}$$

(10)

$$C_{e,o}=\frac{2}{z_{3e,o}}sin{\theta }_{3e,o}$$

(11)

With algebraic manipulation of Equations (5)–(11) and the contra-directional condition of Equations (12) and (13) [33], we can express the even/odd and input/output susceptances $b_{ie,o}$ as in Equations (14)–(17), Appendix A. We assumed the input and output impedances are identical, where $n=1$.

$$T_{11e}=T_{11o}$$

(12)

$$T_{12e}=-T_{12o},\hspace{1em}\hspace{1em}\Re T_{12e}=\Re T_{12o}=0$$

(13)

$$b_{1e}=\frac{A_e+\sqrt{A_e^2-B_e\cdot \left(B_o-C_e\right)}}{B_e},\hspace{1em}\hspace{1em}n=1$$

(14)

$$b_{1o}=\frac{B_e}{B_o}{b}_{1e}-\frac{A_e-A_o}{B_o}$$

(15)

$$b_{2e}=b_{1e}$$

(16)

$$b_{2o}=b_{1o}$$

(17)

With the susceptances $b_{ie,o}$, we can construct the lumped-distributed equivalent circuit and its even- and odd-mode equivalent circuits, as in Figure 3, where $C_{ie}$ is the even-mode equivalent capacitance as in Equation (18), and $C_{io}\prime$ is the internal coupling capacitance between two parallel coupled lines. The internal coupling capacitance is expressed with even- and odd-mode capacitances, as in Equation (20).

$$C_{ie,o}=\frac{b_{ie,o}}{{\omega }_0\sqrt{Z_{01}{Z}_{02}}}$$

(18)

$$C_{io}=2C_{io}\prime +C_{ie}$$

(19)

$$C_{io}\prime =\frac{C_{io}-C_{ie}}{2}$$

(20)

We realized the lumped-distributed equivalent circuit in Figure 3 with the distributed circuit in Figure 4. Two inner and outer stubs in Figure 4b implement the capacitance in the even mode, as in Figure 3b. The capacitance in the odd-mode in Figure 3c consists of the even-mode capacitance and the additional capacitance from two times the gap capacitor $2C_{ig}$ in Figure 4c. By comparing the even-mode equivalent circuit of the shunt capacitor, as in Figure 3b, and its distributed open stub realization, as in Figure 4b, the electrical length of the outer stub can be expressed as in Equations (21) and (22). $Y_s$ is the characteristic admittance of the stubs, and ${\theta }_{ie,o}$ is the electrical length of the stubs (i = 1 or 2). $Y_{in}$ in Figure 4c is the admittance after transforming the gap capacitance $2C_{ig}$, and is expressed in Equation (23). $Y_{in}$ can be decomposed into the admittance from the original open stub and the additional capacitance transformed from the gap capacitance, $2C_{ig}$, by the inner stub. By algebraic manipulation, $Y_{in}$ is expressed as the sum of the original open stub term and the additional transformed term, as in Equations (24) and (25). We can express the gap capacitance $C_{ig}$ as in Equations (26) and (27) by equating the transformed admittance term in Equations (24) and (25) and the equivalent capacitance $C_{io}\prime$ in Figure 3c.

$$j\omega C_{ie}=j{Y}_{s}tan\left({\theta }_{ie}\right)+j{Y}_{s}tan\left({\theta }_{io}\right)$$

(21)

$${\theta }_{ie}=atan\left(\frac{{\omega }_0{C}_{ie}-Y_{s}tan\left({\theta }_{io}\right)}{Y_s}\right)$$

(22)

$$Y_{in}{|}_{Y_L=j{\omega }_{0}2C_{ig}}=Y_s\frac{j{\omega }_{0}2C_{ig}+j{Y}_{s}tan\left({\theta }_{io}\right)}{Y_s-{\omega }_{0}2C_{ig}tan\left({\theta }_{io}\right)}$$

(23)

$$Y_{in}{|}_{Y_L=j{\omega }_{0}2C_{ig}}=j{Y}_{s}tan\left({\theta }_{io}\right)+j{Y}_s{\omega }_{0}2C_{ig}\frac{tan{\left({\theta }_{io}\right)}^2+1}{Y_s-{\omega }_{0}2C_{ig}tan\left({\theta }_{io}\right)}$$

(24)

$$Y_{in}{|}_{Y_L=j{\omega }_{0}2C_{ig}}=Y_{in}{|}_{Y_L=0}+j{Y}_s{\omega }_{0}2C_{ig}\frac{tan{\left({\theta }_{io}\right)}^2+1}{Y_s-{\omega }_{0}2C_{ig}tan\left({\theta }_{io}\right)}$$

(25)

$$j{Y}_s{\omega }_{0}2C_{ig}\frac{tan{\left({\theta }_{io}\right)}^2+1}{Y_s-{\omega }_{0}2C_{ig}tan\left({\theta }_{io}\right)}=j{\omega }_{0}2C_{io}\prime$$

(26)

$$C_{ig}=\frac{C_{io}\prime Y_s}{Y_{s}tan{\left({\theta }_{io}\right)}^2+2{\omega }_0{C}_{io}\prime tan\left({\theta }_{io}\right)+Y_s}$$

(27)

In the physical realization in Figure 5, the gap $g_i$ can be expressed in Equation (28), where $\lambda$ is the wavelength of the stub in the microstrip line. The gap capacitor can be expressed in Equation (29) [34]⁠. Hence, using Equations (27) and (29), we can solve the inner stub electrical length ${\theta }_{io}$ as in Equation (30). The outer stub’s electrical length ${\theta }_{ie}$ can be obtained by inserting ${\theta }_{io}$ into Equation (22). The physical length of the inner and outer stub can be obtained from Equation (31). All the initial physical dimensions in Figure 5 are now obtained.

Table 1. The framework of the design process.

Start

2. Determine the coupling factor and electrical length of CPL $\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}C=\frac{{10}^{C_{dB}}}{20}.{\theta }_3<\frac{\lambda }{4}$

3. Calculate the even- and odd-mode impedance of CPL $\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{Z}_e=\sqrt{\frac{1+C}{1-C}}{Z}_0,\hspace{1em}\hspace{1em}{Z}_o=\sqrt{\frac{1-C}{1+C}}{Z}_0$

4. Simulate the even- and odd-mode phase of the CPL $\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{\theta }_{3e},\hspace{1em}{\theta }_{3o}$

5. Calculate the normalized input/output, even- and odd-mode susceptances $\hspace{1em}\hspace{1em}\hspace{1em}{b}_{1e}=b_{2e}=\frac{A_e+\sqrt{A_e^2-B_e\cdot \left(B_o-C_e\right)}}{B_e} , b_{1\mathrm{o}}=b_{2\mathrm{o}}=\frac{B_e}{B_o}{b}_{1e}-\frac{A_e-A_o}{B_o}$

6. Calculate the lumped capacitances $\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{C}_{1e}=C_{2e}=\frac{b_{ie}}{{\omega }_0{Z}_0} , C_{1o}^{\prime }=C_{2o}^{\prime }=\frac{C_{io}-C_{ie}}{2}$

7. Calculate the electrical length of the distributed stubs, given Ys $\hspace{1em}{\theta }_{1o}={\theta }_{2o}=solve\left(C_{ig}\left({\theta }_{io}\right)=C_{is}\left({\theta }_{io}\right)\right),{\theta }_{1e}={\theta }_{2e}=atan\left(\frac{{\omega }_0{C}_{ie}-Y_{s}tan\left({\theta }_{io}\right)}{Y_s}\right)$

8. Calculate the physical dimensions of the stub lengths and the gap $\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{l}_{1o}=l_{2o}=\frac{{\theta }_{io}}{2\pi }\lambda ,l_{1e}=l_{2e}=\frac{{\theta }_{ie}}{2\pi }\lambda ,g_i=s_{cpl}-2l_{io}$

9. Stop

summarizes the design process.

$$g_i=s_{cpl}-2l_{io}=s_{cpl}-2\cdot \left(\frac{{\theta }_{io}}{2\pi }\lambda \right)$$

(28)

$$C_{is}\left(g_i\right)=500\cdot h\cdot exp\left(-1.86\frac{g_i}{h}\right)\cdot Q_1\cdot \left(1+4.19\left(1-exp\left(-0.785\sqrt{\frac{h}{W_1}\frac{W_2}{W_1}}\right)\right)\right)$$

(29)

$${\theta }_{io}=solve\left(C_{ig}\left({\theta }_{io}\right)=C_{is}\left({\theta }_{io}\right)\right)$$

(30)

$$l_{io}=\frac{{\theta }_{io}}{2\pi }\lambda ,l_{ie}=\frac{{\theta }_{ie}}{2\pi }\lambda$$

(31)

2.2. Implementation of Directional Coupler

We implemented the coupler with RF35HTC 20 mil 1 oz substrate with the described design method in the frequency covering 13 to 14.5 GHz, which is used in the uplink of Ku-band satellite communication. A width of 1mm was selected for the four stubs, and the corresponding admittance $Y_s$ was calculated with the transmission line calculation software from the open-source circuit simulator, Qucs [30]. For the initial design parameters of the parallel coupled line, we chose 25 dB coupling, and 60° electrical length. By Equation (32), we calculated the even- and odd-mode impedances and obtained the physical dimensions of the microstrip line coupler using the transmission line calculation software Qucs.

$$Z_e=\sqrt{\frac{1+C}{1-C}}{Z}_0, Z_o=\sqrt{\frac{1-C}{1+C}}{Z}_0, where C=\frac{{10}^{C_{dB}}}{20}.$$

(32)

The even- and odd-mode operations in Figure 1 are simulated in the circuit simulator, as in Figure 6. For the odd-mode excitation, out-of-phase ideal couplers (Coupler1 and Coupler2) in the upper circuit in Figure 6 are used at the input and output of the microstrip parallel coupled line under test. For the even-mode excitation, in-phase couplers are placed as in the lower circuit of Figure 6.

The simulation results are shown in Figure 7. The even-mode electrical length is longer than the odd-mode length. The ratio between them is about 95.5% over the wide frequency range. With the calculated even- and odd-mode impedances, the simulated electrical lengths, and Equations (14)–(17), the susceptances, $b_{ie}$ and $b_{io}$, are calculated as Equation (33). With the calculated susceptances and Equation (18) through Equation (31), the initial dimensions of the physical coupler in Figure 5 ($l_{ie}$, $l_{io}$, and $g_i$) are calculated as Equation (34).

$$b_{ie}=1.1142,\hspace{1em}{b}_{io}=1.3339$$

(33)

$$l_{ie}=0.291 \mathrm{mm}, l_{io}=1.539 \mathrm{mm}, g_i=0.6355 \mathrm{mm}$$

(34)

From the microstrip coupled-line coupler dimensions, and the initial physical dimensions in Equation (34), the coupler was laid out and simulated with a 3D electromagnetic simulator, MWS, from CST. The additional 50 Ohm lines were added for measurement, as in Figure 8a. There are additional discontinuities from the initial design, such as the additional microstrip around and across the physical layout. Therefore, the initial dimensions are adjusted to compensate for the discontinuities during the 3D simulation. The resulting final detailed dimensions of the coupler are listed in

Table 2. Detailed dimensions of the coupler in Figure 8b.

Dimension Designation	Dimension (mm)	Position
$l_c$	2.0	Coupled-line length
$w_c$	1.1	Coupled-line width
$l_e$	0.5	Main-line stub length
$l_e\prime$	0.7	Coupled-line stub length
$l_o$	0.425	Inner stub length
$w_s$	1.0	Stub width
$s_c$	1.1	Coupled-line space
$g_i$	0.25	The gap between inner stubs
$w_0$	1.15	50 Ohm line width

, and Figure 8b shows the corresponding dimension designation.

3. Results

The proposed coupler was designed and fabricated with Taconic RF-35HT 20 mil PCB. Figure 9 shows the fabricated and assembled PCB with the external coaxial connectors. The insertion loss, coupling, return loss and isolation are measured with Agilent ENA E5071C after coaxial calibration. A comparison of the measurement and simulation results is shown in Figure 10. The coupling is about 20 dB, and well-matched with the simulation result. The directivity is better than 20 dB in bandwidth from 12.8 GHz to 14.8 GHz, and the peak directivity is better than 40 dB. The worst return loss is about 17 dB within the band.

Table 3. Performance comparison.

Works	Freq. (20 dB dir.) (GHz)	Size (mm)	$\mathbf{FoM}.(\mathit{S}/\mathit{\lambda })$ $(\mathbf{mm})$	Cpl. (dB)	Dir. (min.) (dB)	Dir. (peak) (dB)	High-Power Structure
[9]	1.2~2.8 *	18.9 × 5.4	0.80	30	20	28	No (thin interdigital stub)
[11]	0.8~1.03	53.4 × 23.2	3.78	10	20	52	No (thin short stub)
[13]	2.22~2.65	18 × 17	2.50	20	20	56	No (thin short stub)
[20]	2~18 *	52 × 8	13.87	20	15	25	Yes
[21]	2~50	8.5 × 1.5	1.74	16	9	31	No (sharp shape, thin gap)
[24]	10~11 **	13 × 6	2.73	6.5	28	30	Yes
[25]	1.7~1.91	60 × 34.5	12.56	20	20	30	Yes
[29]	0.8~2.8 *	30 × 6.5	1.17	20	20	40	No (thin stub)
[30]	2.05~2.6	25 × 16	3.10	10	20	37	Yes
[31]	1.0~2.1	19 × 7.5	0.74	10	20	50	No (inductor at port)
[32]	0.31~1.18	42 × 20	2.09	10	20	43	No (inductor at port)
[30]	2.05~2.6	25 × 16	3.10	10	20	37	Yes
This work	12.8~14.8	5.5 × 4	1.01	20	20	45	Yes

* 3 dB insertion loss bandwidth. ** available maximum bandwidth in the paper.

shows a comparison of the performance of this work with others. Most of the previous studies were conducted in relatively lower frequency ranges. Therefore, a figure of merit is introduced in this paper, for the size comparison between the couplers in different operating frequencies, as $S/\lambda$. The parallel coupled-line length decreases inversely in proportion with the increase in frequency; however, the height change with frequency change is negligible, because the change of the 50 Ohm line width and the coupling gap is negligible. The active coupler area $S$ was divided by the wavelength $\lambda$ to compensate for the coupler length variation in the different frequencies. Additionally, weak structures vulnerable to high power, such as a thin interdigital capacitor, were identified. The 20 dB directivity frequency ranges are shown, except when the 20 dB directivity bandwidth is much wider than the 3 dB bandwidth, or when the 20 dB bandwidth is not identifiable in the paper.

From a comparison of the figure of merits, this work shows the most compact size among the structures without weak components which are vulnerable to high power, and it is still very compact compared with all the other works. It also shows high peak directivity of 45 dB.

4. Discussion

Most power systems operate in a relatively narrow band (for example, the Ku-band satellite uplink operates at 14~14.5 GHz), because the active power component does not have wideband performance. However, the previous studies on microstrip directional couplers have been mainly focused on increasing their directivity without considering structures that are suitable for high-power applications, or on increasing the bandwidth to be much wider than that of most high-power systems.

In this paper, we proposed a compact weak coupling high-directivity coupler suitable for high power without any weak structure. In order to achieve this, the design is approached from the general ring-type four-port with an uncompensated parallel-coupled line, not from the parallel-coupled line with a compensation structure vulnerable to high power. Additionally, all derivations of the design are presented.

The measured results, especially the return loss, could be improved if the connectors are de-embedded with a more complex calibration method, such as four-port TRL calibration. However, the return loss is sufficient for applications, and the results of the proposed coupler show wide enough bandwidth for Ku-band satellite uplink high-power applications, and the most compact size for high power, even with high directivity at weak coupling. The proposed design can be integrated very effectively into the most practical microwave and millimeter-wave power systems.