Design of a 75–140 GHz high-pass printed circuit board dichroic filter Open Access

As a future and eco-friendly energy source, researches on nuclear fusion are world-widely investigated. In Daejeon, Korea, the KSTAR (Korea Superconducting Tokamak Advanced Research) machine has been operational since 2007. In order to understand the physics of MHD (Magneto-Hydro-Dynamics) and turbulence phenomena in tokamak plasmas, MIR (Microwave Imaging Reflectometry) and ECEI (Electron Cyclotron Emission Imaging) measurement systems have been utilized.

The magnetic field inside the vessel of a tokamak, which is inversely proportional to plasma radius, causes the rotation of plasma electrons, and electromagnetic waves are radiated (ECE: electron cyclotron emission). The frequency of the radiated electromagnetic (EM)000 wave is proportional to the magnitude of the magnetic field, and the intensity of the radiated EM wave is proportional to the local electron temperature of the plasma. The ECEI system resolves the frequency channels of the radiated wave and measures the intensity of the wave for each frequency channel, thereby determining radial plasma electron temperature to provide real time 2-D cross-sectional imaging of the plasma temperature.

Currently, in KSTAR, the ECEI system measures the radiated W/F-band signals (75-130 GHz) from plasma, and a high-pass dichroic filter is used to block lower frequency components, ensuring a single-sided heterodyne mixing of RF and LO signals for the system.¹ The dichroic filter is located between the lens array, which focuses W/F-band signals, and is located in front of the W/F-band antenna-detector array. The dichroic filter should block the lower frequency components sufficiently and preferably have wide passband.

Dichroic filters, typically, were in the form of a high-pass filter (HPF), a low-pass filter (LPF), or a reflector. For example, dichroic filters were used to pass selective frequencies in satellite communications² and to bandpass the desired frequencies in multipliers.³ These dichroic filters were used to protect the measurement system and tailored for the specific purposes. In the KSTAR ECEI/MIR system, a dichroic filter and a notch filter are used to protect the system and select the required EM spectrum from the tokamak radiated signals.⁴ 

The current dichroic filter for the KSTAR ECEI system is made of a 6-mm thick metal plate. A triangular lattice array of circular holes is patterned on the metal plate, but there is a limitation on the reduction of hole spacing, which limits passband. The proposed Printed Circuit Board (PCB) dichroic filter, which uses commercial PCB process, significantly enhances the passband frequencies with lower insertion loss and reduces weight and expense with flexible design and fabrication options.

Various types of FSS (Frequency Selective Surface) filters are shown in Fig. 1 in forms of LPF (Low-Pass Filter), HPF (High-Pass Filter), BSF (Band-Stop Filter), and BPF (Bandpass Filter). A dichroic filter is a type of FSS filter, and the high-pass dichroic filter for the KSTAR ECEI system is shown in Fig. 1(b), where rectangular or circular hole array can be used.⁵ 

For the design of a dichroic filter, using analytical methods of Floquet modes and waveguide modes, the transmission coefficients T and the reflection coefficient R can be obtained,⁶ 

where β is the phase constant and ℓ is thickness of the substrate. A (a function of hole spacing) and B (a function of hole size) can be obtained by using the expression described below.

Among various dichroic filter designs, a circular hole array in an equilateral triangle lattice is used, and A and B are given in Eqs. (3) and (4), respectively,⁷ 

for a > 0.28d and d < 0.57λ,

where λ is the wavelength of the EM wave passing through the dichroic filter, d is distance between the centers of the circular holes, a is the radius of the circular hole, J₁ is the 1st kind of Bessel function, and $J 1 ′$ is the derivative of the 1st kind of Bessel function.

Since the circular hole array is used, the main mode of the circular aperture waveguide is TE₁₁, and we can obtain the phase constant β as

The cutoff frequency of the TE₁₁ mode of the circular aperture waveguide can be obtained as⁸ 

where c = 3 × 10⁸ m/s.

At higher frequencies above the specific frequency, there is a frequency region of increased insertion loss. This increased insertion loss happens when the incident EM wavelength is smaller than hole spacing (d)⁹ and is diffracted and the power is distributed to the first side lobe.⁷ This diffraction frequency can be obtained using Eq. (7), and this frequency increases as the hole spacing (d) decreases,

The existing dichroic filter for the KSTAR ECEI system uses the 6-mm metal plate with a circular hole array. It is heavy and the thick metal causes limitation on the fine metal fabrication process. The proposed PCB dichroic filter used the inexpensive commercial PCB fabrication technique. As shown in Fig. 2, a triangular lattice array of circular holes is perforated on the FR-4 substrate, and the whole substrates are metal plated.

The operating frequencies of the KSTAR ECEI system is W-band (75-110 GHz) and F-band (90-140 GHz) frequencies. The radius of the circular hole can be determined by the desired cutoff frequency of the dichroic filter. Using Eq. (6), the radius of the hole (a) can be calculated as 1.256 mm with the cutoff frequency (fc) of 70 GHz and 1.172 mm with fc = 75 GHz.

In order to maximize the operating bandwidth of the dichroic filter, the distance of the circular holes or the hole spacing (d) should be minimized. This hole spacing, thereby the bandwidth of the filter, is typically limited by the PCB fabrication tolerance.

For the KSTAR ECEI system, a sharp filter skirt property is required: i.e., ∼40 dB attenuation at the rejection region. EM simulations show that steeper skirt characteristics and higher attenuation at the rejection region can be obtained as substrate thickness increases as shown in Fig. 3. In this paper, the thickness of the substrate is chosen as 6-mm by considering the actual PCB fabrication limits.¹⁰ 

In order to compare the performance of the proposed PCB dichroic filter with the metal dichroic filter, the type 1 design has chosen parameters of the circular hole radius a = 1.125 mm, the hole spacing d = 3.375 mm, and the substrate thickness ℓ = 6 mm. The optimized PCB dichroic filter design (type 2 design) has parameters of a = 1.25 mm, d = 3 mm, and ℓ = 6 mm. The performance of the filters has been simulated using the 3D EM software: i.e., the FSS unit cell FD (Frequency Domain) solver in the CST Microwave Studio for a single unit cell of the metal plated FR-4 substrate as can be seen in Fig. 4. In simulation, tetrahedral meshes and two Floquet ports (Zmax, Zmin) were used.

The performance of the type 1 filter is shown in Fig. 5. The calculated and simulated values of the cutoff frequency and the filter skit property are in agreement. The diffraction frequency fdiff, which is determined by d, is 102.6 GHz, and the high insertion loss of 8.17 dB above fdiff occurs due to diffraction.

The performance of the optimized type 2 filter is shown in Fig. 6. The cutoff frequency and the skirt property are the same as type 1, but the passband of the filter is broad enough to cover the W/F-band (75-140 GHz) suitable for the ECEI measurements in KSTAR. Smaller hole spacing results in higher fdiff (115.5 GHz) and lower insertion loss of 4.1 dB.

The proposed PCB dichroic filters were fabricated using the commercial PCB process. Once the triangular-lattice circular hole array is patterned on the FR-4 substrate, the whole substrate is plated by copper including inside walls of the holes and then gold-plated to protect the metal surface. Figs. 7(a) and 7(b) show the portions of the PCB dichroic filters.

The performance of the dichroic filters was measured using a test setup with the network analyzer. As shown in Fig. 8, the Tx and Rx antennas were aligned in height, and the network analyzer was calibrated.

Figure 9 compares the property of the type 1 dichroic filter for calculation, EM simulation, and measurement results. The measured cutoff frequency is down-shifted by 3.5 GHz due to tolerance of the circular hole diameter, but the filter skirt properties are similar to those of calculation and simulation. The average insertion loss in the passband is 0.15 dB, while the insertion loss above fdiff is 7.4 dB, which is similar to the calculated value. Figure 10 compares the measured insertion losses between the type 1 PCB dichroic filter and the metal dichroic filter with the same dimensions.

Figure 11 shows the comparison of the type 2 dichroic filter properties for calculated, simulated, and measured data. The cutoff frequency, the filter skirt property, fdiff, and insertion losses are in good agreement. For both type 1 and type 2 filters, the measured cutoff frequencies of the fabricated filters were shifted by ∼3 GHz since the cutoff frequency is sensitively affected by the fabrication tolerances, while other filter properties are similar. With the EM simulation, the cutoff frequency and passband properties are in agreement with the calculations, but appreciable discrepancies of insertion loss exist above fdiff. This discrepancy might have happened since, with the EM simulation using a single unit cell, the transmitted power in all front lobes are counted, while, with the calculation and measurement, the transmitted power is counted only for the main lobe in the front side.

In order to experimentally verify the filter skirt properties with the variation of filter substrate thickness as shown in Fig. 3, two identical dichroic filters with 6-mm thickness were aligned along holes and clipped together. Figure 12 compares the filter properties of a single PCB filter (ℓ = 6 mm) and a two-layered PCB filter (ℓ = 12 mm), and the skirt property is shown to be steeper with the thicker PCB filter. At 66 GHz, the insertion loss of the single PCB filter is 15.9 dB, while the insertion of the two-layered PCB filter is 33.1 dB. The cutoff frequency for both cases is 70 GHz, and fdiff is 115.5 GHz.

In this paper, a new high-performing W/F-band PCB dichroic filter, which can be used for the KSTAR ECE imaging system, is proposed. It is fabricated with the inexpensive commercial PCB process. The design of the proposed PCB filter is flexible and its properties well exceed the existing metal-based dichroic filter. The PCB dichroic filter consists of a triangular lattice of circular hole array on a dielectric substrate, and the whole substrate is metal plated to act as a high-pass filter. It has advantages over the metal-based filter in bandwidth, insertion loss, fabrication cost, and weight. The existing metal-based filter has relatively narrow bandwidth (∼20 GHz) due to fabrication limit in minimizing the hole spacing with thick metal plate (ℓ = 6 mm), while with the proposed PCB filter the bandwidth can be over 60 GHz by flexibly adjusting the hole spacing. The filter skirt property can also be improved by adopting a thicker PCB substrate. In this paper, the proposed PCB filter is designed and optimized with theoretical calculation, verified with EM simulation and measurements.

This research was supported by the National R&D Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. NRF-2015M1A7A1A02002291).

This study was supported by the BK21 Plus project funded by the Ministry of Education, Korea (No. 21A20131600011).