A Power Combiner–Splitter Based on a Rat-Race Coupler for an IQ Mixer in Synthetic Aperture Radar Applications

Abstract

Synthetic aperture radar (SAR) is a powerful tool in remote sensing applications that can produce high-resolution images and operate in any weather condition. It is composed of many RF components, such as the IQ mixer, which mixes the base chirp signal (IF) with the carrier signal (LO) and increases the bandwidth of the transmitted signal to twice the maximum frequency of the base chirp signal, reducing the workload of Programmable Field Gate Arrays (FPGA) and increasing the resolution of the SAR system. This research proposes a power combiner–splitter design that will be used as a supporting component to construct the IQ mixer in SAR applications based on a rat-race coupler. The measurement results show that the coupler has good S-parameter values. $S_{11}$, $S_{22}$, and $S_{33}$ have a low reflection value below −17 dB, $S_{13}$ has a high isolation value below −22 dB, and $S_{21}$ and $S_{31}$ have a low attenuation value below −4 dB with amplitude unbalance below 0.1 dB and phase unbalance below 1$°$. The 150 MHz requirement bandwidth for the RF signal is also achieved.

1. Introduction

Synthetic Aperture Radar (SAR) is a powerful instrument in remote sensing applications because of its ability to produce high-resolution images, to be operated day and night, penetrate vegetation and soil, and that it does not require sunlight [1]. This is possible because the SAR system independently generates and sends an electromagnetic signal to obtain information about objects through reflection [2], compared with the conventional optic method, which has the limitation of an operation period only during the day and clear weather.

The RF subsystem is one of the subsystems that make up the SAR system. It plays a significant role in controlling analog signal processing such as synthesizing, mixing, filtering, and amplifying [3]. The mixing process by the IQ mixer is one of the crucial stages in the RF subsystem because the base chirp signal, which has a maximum frequency of 75 MHz, will be mixed with the carrier signal, which has a fixed frequency of 5.5 GHz. The mixing process uses the single side band (SSB) modulation method that can suppress unwanted sideband (image) without filter, also known as sideband suppression [4]. This method, combined with the modified base chirp signal, will reduce the workload of the Field Programmable Gate Array (FPGA), increase the bandwidth of the transmitted signal, and improve the image resolution produced by the SAR system [5].

The sideband suppression capability of the IQ mixer depends on the amplitude and phase unbalances between two signals that meet on the output port of the power combiner. The unbalance, either amplitude or phase, is the accumulation from the transmission line that the signal passes through, including the connector [4]. Therefore, all components that compose the IQ mixer, such as the LO phase shifter, matched mixer, and power combiner, are expected to have good performance to reduce the accumulated unbalance.

The IQ mixer, as shown in Figure 1, is composed of three components: a quadrature LO phase shifter, two matched mixers, and a power combiner–splitter [4]. The quadrature LO phase shifter has a role in providing two carrier signals that have a phase difference of 90°. The matched mixer’s function is to mix the base chirp signal, which is a pair of quadrature signals (I and Q), with a carrier signal. The power combiner–splitter has a role in combining the signals resulting from the mixing process if it works on the transmitter side (upconversion) or dividing the incoming RF signal if it works on the receiver side (downconversion). The three components that make up the IQ mixer can be made as passive components and can be realized using microstrip and wet etching fabrication methods [6].

Among the three components, the power combiner–splitter has a critical issue in maintaining the balance of power and phase. In general, there are three techniques to design a power combiner, including T-junction, resistive power combiner, and Wilkinson power divider (WPD) [7,8,9]. The T-junction offers a simple technique to divide power only by transmission lines with different impedances to divide the power. However, this technique does not maintain isolation between ports [8]. Meanwhile, other resistive power combining techniques offer the ability to work at low frequencies, including DC signals. However, it has high attenuation due to the use of resistors to divide the power [9].

For the IQ mixer in a SAR system, the power combiner–splitter is working at low power, requiring good unbalance and isolation [4]. Therefore, another technique of the Wilkinson power divider is preferable because it has simplicity in design and offers high isolation by using a resistor between the two output ports [10]. Some research on the Wilkinson power divider has been conducted for various applications. It can be designed to have unequal output power [7], modified to operate on multiple band frequencies [11,12], and widely used for radar [13] and communication [14] systems. It can also be fabricated using the MMIC method [15] or conventional printed method [16].

Nevertheless, the use of a resistor in the design affects the measurement result, such as shifting the maximum frequency response or deviation on amplitude unbalance. This condition can come from the asymmetric position of the resistor, the deviation of the actual resistor value, and the different sizes between the resistor area and the transmission line at the connection [17]. Another factor can come from the improper placement of the resistor which, if the resistor is close to the discontinuity of the transmission line, can contribute to an increase in the attenuation [18,19]. Therefore, the use of resistors can be minimized to improve the quality of the component.

The role of the resistor in WPD is to improve the isolation between two output ports [20]. A similar characteristic can be achieved by adopting a coupler component combined with a signal cancellation technique by adjusting the transmission line length to obtain a specific phase difference. The condition can be conducted with one input port, two output ports, and one isolated port. These requirements can be obtained in a ring-shaped coupler, also known as a rat-race coupler [21].

This paper proposes the design of a power combiner–splitter by utilizing a rat-race (anti-phase) hybrid coupler as a supporting component for designing a microstrip IQ mixer. The rat-race coupler has a pair of in-phase ports that can be used to combine two signals or split a signal into two signals with equal power and phase, as shown in Figure 2. The isolation on the rat-race coupler is obtained through the signal cancellation on the isolation port, compared to WPD, which uses a resistor. The coupler is modified to become square-shaped to reduce its height for optimum space utility and simplicity in the final design integration. The additional port (port 5) is also installed to balance the influence of port 4, make it symmetric, and improve the balance response from the output ports. The coupler is then fabricated using the microstrip wet etching method, and the measurement result shows that the proposed design has fulfilled all the specification requirements.

2. Design and Simulation

The power combiner–splitter will be manufactured using a RT/duroid 5880 substrate that has a thickness (h) of 0.51 mm and permittivity (${ϵ}_r$) of 2.2, a dissipation factor ($tan \delta$) of 0.0009, and a conductor thickness (t) of 0.035 mm. The substrate that has a low thickness or higher permittivity is preferable because it can lead to a shorter transmission line [18]. The summary of the substrate properties is shown in

Table 1. Properties of substrate RT/duroid 5880.

Property	Typical Value
Permittivity (${ϵ}_r$)	2.2
Dissipation factor ($tan \delta$)	0.0009
Substrate thickness (h)	0.51 mm
Conductor thickness (t)	0.035 mm

.

Figure 2 depicts the conventional design of a rat race coupler when used as a signal combiner and splitter. The rat-race coupler has four main ports as input–output signal interfaces. Port number 2 has an equal distance to port number 1 and port number 3. Therefore, the coupler can be used as a combiner or splitter signal [21]. On the transmitter side (upconversion), port number 1 and port number 3 will become the input, and port number 2 will become the output. On the receiver side (downconversion), port number 2 will have a role as an input port, and port number 1 and port number 3 will become the output port. Meanwhile, port number 4 will remain terminated. The coupler is mainly built by the transmission line, which has an impedance value of $Z_0\sqrt{2}$ [22].

The summarized specification requirement of the power combiner–splitter is shown in

Table 2. Specification requirement of the power combiner–splitter.

Specification	Requirement Value
S11	<−10 dB
S22	<−10 dB
S33	<−10 dB
S32	>−4 dB
S12	>−4 dB
S31	<−15 dB
Amplitude Unbalance	<0.6 dB
Phase Unbalance	<−5° dB

. It is desired to have S-parameter values $S_{11}$, $S_{22}$, and $S_{33}$ less than −10 dB, $S_{12}$ and $S_{32}$ less than −4 dB, and $S_{13}$ less than −15 dB [9]. The amplitude unbalanced is preferred to be less than 0.6 dB, and the phase unbalance is less than 5°.

The coupler is designed to work at an LO frequency of 5.5 GHz, with a 150 MHz requirement of bandwidth RF signal and the maximum base chirp frequency being 75 MHz. The width and length of the coupler are acquired based on Equations (1)–(3) and are summarized in

Table 3. Width and length of the coupler transmission line.

Impedance	Width	Length ($\frac{1}{4}\mathit{\lambda }$)
$Z_0$ = 50 $\Omega$	1.6 mm	10.4 mm
$Z_0$$\sqrt{2}$ = 35.15 $\Omega$	0.9 mm	10.6 mm

. Equation (1) is used to obtain the effective permittivity value (${ϵ}_e$), Equation (2) is used to obtain the impedance value (Z), and Equation (3) is used to obtain the transmission line length ($\frac{1}{4}\lambda$) [18].

$${ϵ}_e=\frac{{ϵ}_r+1}{2}+\frac{{ϵ}_r-1}{2}{(1+\frac{12h}{w})}^{-0.5}-0.217({ϵ}_r-1)\frac{t}{\sqrt{wh}}$$

(1)

$$Z=\frac{120\pi {ϵ}_e^{-0.5}}{\frac{w}{h}+1.393+0.0667ln(1.444+\frac{w}{h})}$$

(2)

$$\lambda =\frac{c}{f\sqrt{{ϵ}_e}}$$

(3)

The width and length values in Table 3 and the layout in Figure 2 are used as a basis for designing the coupler. The design needs further adjustment to obtain an optimum response at a frequency of 5.5 GHz. Increasing the length of the transmission line will shift the optimum response of the component to the lower frequency, and decreasing the length of the transmission line will shift the response of the component to the higher frequency. At the same time, the width of the transmission line is not changed to maintain the impedance value. Because of the discontinuity in the design, such as a mitered corner or intersection between two transmission lines, the electrical length of the transmission will be slightly different compared to the calculation. The simulation results are also observed to understand the response behavior of the simulated design. The final dimension after adjustment is shown in Figure 3; the length values are in mm. It has four ports with a distance equal to $\frac{1}{4}\lambda$, except for port 1 to port 4, which has a distance of $\frac{3}{4}\lambda$. The model is simulated using CST Microwave Studio 2019, a computer-aided design (CAD) software that can simulate the component in a 3D model.

Figure 4 and Figure 5 show the simulation results of the conventional rat-race coupler. The amplitude unbalance of the coupler has shown a good result for the required bandwidth (150 MHz). The phase unbalanced also meets the requirement specification below 5$°$. Nevertheless, since the distance between port number 2 to port number 1 and port number 3 is equal, the S-parameter of $S_{21}$ and $S_{31}$ are expected to have similar patterns and values on wideband frequency. Instead, the result shows that the output signal pattern is different. Based on our analysis, the presence of port number 4 as an isolation port affects the signal imbalance at the other ports. Therefore, to balance the influence of port number 4, we suggest adding port number 5. The position of port number 5 mirrors the position of port number 4. Hence, the rat-race coupler shape becomes symmetric, as shown in Figure 6. This configuration is then simulated and shows an improvement in the imbalance value for the entire simulated frequency (10 GHz), as shown in Figure 7 and Figure 8.

Figure 7 and Figure 8 show the simulation result of phase imbalance and amplitude imbalance of the coupler after modification. It shows a significant improvement that the unbalanced values are close to zero. The graphics of the two measurements are so similar that they look like one single measurement. It shows that even though the physical distance of port number 2 to port number 1 and number 3 are equal, because of the asymmetric design (presence of port 4), the other coupler response of other is altered and becomes unbalanced. The modification of adding port 5 adjusted the response to become equal.

The power combiner is installed between two matched mixers. Therefore, the power combiner with a smaller height is preferable because it will reduce the final size of the IQ mixer when fully integrated. For this purpose (maximum space utility), the shape of the coupler is modified. Instead of a ring-shaped coupler, it is preferred to be square-shaped because the height of the coupler can be adjusted separately from the length.

Figure 9 depicts the final design of the square-shaped coupler; all length values are in mm. It shows a height reduction of 5.9 mm compared to the conventional design, from 20.3 mm to 14.4 mm. Port 4 and port 5 are then terminated with a surface mount device (SMD) resistor of 50 $\Omega$ through a via hole to the ground and placed inside the coupler. The resistor has the same function as a dummy load when doing measurements on terminated unused ports, and its value is similar to the impedance value of the transmission line.

Figure 10 and Figure 11 show the simulation results from the final modified coupler. The coupler can maintain a good response, similar to the previous design configuration. At frequency 5.5 GHz, the phase unbalance value is 0.0037°, and the amplitude unbalance is 0.000006 dB, almost perfectly close to zero. Therefore, this design is considered good enough to be fabricated.

3. Fabrication and Measurement

Figure 12 depicts the fabrication result of the square-shaped coupler. Each port is equipped with an SMA female connector. Ports 1 and 3 are placed on the same side to reduce the error possibility because of the difference in transmission line length due to the defect in the fabrication process. Both ports will be connected to the matched mixer in the final integration to build an IQ mixer. Ports 4 and 5 are terminated by an SMD resistor that has a value of 50 $\Omega$ through a via to the ground. The S-parameter of the coupler was then measured using the N9917A FieldFox Handheld Microwave Analyzers from Keysight (Santa Rosa, CA, USA).

Figure 13, Figure 14, Figure 15 and Figure 16 show the measurement results of the fabricated square-shaped coupler. At the frequency of 5.5 GHz, the coupler has an amplitude unbalance value below 0.1 dB, and a phase unbalance value below 1$°$. The unbalanced specification requirements for the coupler, either the amplitude or phase, have been achieved and can be maintained for the entire measurement frequency (10 GHz).

Figure 13 and Figure 14 show that the response $S_{21}$, $S_{23}$, $S_{12}$, and $S_{32}$ of the coupler is different from the WPD. WPD will have a flat response over wideband frequency. Still, the coupler instead has additional attenuation before frequency 4 GHz and after frequency 6.2 GHz that is similar to a band-pass filter, which is good for interference rejection since the coupler works at a center frequency of 5.5 GHz. The S-parameter values for $S_{11}$ and $S_{22}$ are measured below −17 dB, as shown in Figure 17, which means most of the power signal is well transferred through the coupler. It also has good isolation value with $S_{13}$ measured below −20 dB. Three frequency samples are selected to represent the response of the RF bandwidth (150 MHz), 5.425 GHz, 5.5 GHz, and 5.575 GHz, and summarized in

Table 4. Measurement result of the fabricated coupler.

Parameter	${\mathit{f}}_1$ 5.425 GHz	${\mathit{f}}_2$ 5 GHz	${\mathit{f}}_3$ 5.575 GHz
$S_{12}$	−3.411 dB	−3.443 dB	−3.427 dB
$S_{32}$	−3.453 dB	−3.492 dB	−3.482 dB
Amplitude Unbalance	0.042 dB	0.049 dB	0.055 dB
$S_{11}$	−26.20 dB	−32.79 dB	−26.33 dB
$S_{22}$	−17.35 dB	−18.80 dB	−20.81 dB
$S_{13}$	−24.41 dB	−22.17 dB	−20.43 dB
$S_{12}$	47.60$°$	42.48$°$	37.39$°$
$S_{32}$	47.58$°$	42.41$°$	37.34$°$
Phase Unbalance	0.02$°$	0.07$°$	0.05$°$

.

Table 5. Performance comparison of square-shaped coupler and commercial power combiner.

Part Number	Type	Frequency (GHz)	Amplitude Unbalance (dB)	Phase Unbalance (°)	Insertion Loss (dB)	Isolation (dB)
PD-0R510 [23]	WPD	0.5–10	0.1	1	3.9	22
PD-0109 [24]	WPD	1–9	0.1	1	3.75	22
PE2026 [25]	WPD	2–8	0.06	3	3.4	20
PE2063 [26]	Resistive	DC–12.4	0.4	2	6	-
ZFRSC-123-S+ [27]	Resistive	DC–12	0.11	1.4	9.5	19.5
ZX10R-2-183-S+ [28]	Resistive	DC–12	0.2	2	6.9	26
This Research	Coupler	5.5	0.049	0.07	3.47	22.17

shows the comparison between the measurement result of the square-shaped coupler and the commercial product of power combiner on the market. It shows that the coupler has a better value on amplitude unbalance and phase unbalance. The insertion loss of 3.47 dB also shows a good value compared with another power combiner, especially with the resistive type. The isolation of the coupler also shows a good value of 22.17 dB compared with other components that range from 19 to 26 dB.

Figure 18 depicts the placement of the power combiner–splitter on the final design of the IQ mixer (upconversion). It is installed between two matched mixers. Therefore, the reduction in the height of the coupler also will reduce the size of the IQ mixer. Port number 1 is connected to the output port of the in-phase matched mixer, and port number 3 is connected to the output port of the quadrature-phase matched mixer. Port number 2 will become the output port while port number 4 and port number 5 are terminated by an SMD resistor 50 $\Omega$ to the ground through the via hole.

4. Conclusions

A power combiner–splitter based on a rat-race coupler has been designed, simulated, fabricated, and measured. The coupler is modified to have a square shape for optimal space utility and simplicity in integration with other components. The additional port is added to balance the influence of the isolation port and has been shown to improve stable responses in either magnitude or phase. All of the measurement results show that the coupler already meets the requirement specification. The phase unbalance between port number 1 and port number 3 is less than 1° and the amplitude unbalance is below 0.6 dB, identical for the entire measurement (10 GHz bandwidth). The values of $S_{11}$, $S_{22}$, and $S_{33}$ are below −17 dB, which means that almost all power is well transferred through the coupler, and it also has good isolation with the value of $S_{13}$ below C 22 dB. Therefore, the proposed coupler can be used as a power combiner–splitter to construct the IQ mixer.