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Abstract
A membrane-based coplanar-stripline (CPS) transmission-line platform has recently enabled implementation of diverse THz system-on-chip (TSoC) components. In this paper, we demonstrate an elliptic-function THz low-pass filter (TLPF) using cascaded λ/4 resonators between the right-angle bending of a CPS transmission line defined on a 1 μm-thin membrane. We investigated the effect of bending the CPS transmission line with different angles that introduces a frequency response similar to a simple LC low-pass filter (LPF) and facilitates the design of a desired roll-off performance using traditional methods. ANSYS HFSS was used to provide a full-wave analysis and characterize the effective parameters of the TLPF with a designed cutoff-frequency around 0.6 THz. Using 7 sections of right-angle CPS bending with total length 1.4 mm, we demonstrate experimentally an elliptic-function TLPF characterized by a low-ripple at passband, a roll-off transition with zero transmission near the cutoff frequency and a wide stopband with −60 dB rejection.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Low-pass filters are required in many systems to suppress noise and spurious signals above a certain frequency. In microwave spectrum, LPFs have been implemented by different transmission line structures such as suspended stripline [1,2], coplanar waveguide (CPW) [3–6], CPS [7–9] and many microstrip structures: step impedance [10–12], photonic bandgap [13], split-ring resonator (SRR) [14], defected-ground structure [15–18], p-shaped resonator [19], inductively-compensated parallel-coupled lines [20], two-layer orthogonal cross-over microstrip lines [21], triangle-shaped resonators [22], and half and quarter-wavelength resonators [23].
For THz spectrum, numerous TLPFs had been presented based on different technologies such as: metamaterials [24,25], graphene-based plasmonic [26,27], SRR [28], tapered parallel-plate waveguide [29], CPW [30,31] and compact suspended microstrip resonators [32]. This research introduces a novel TLPF based on cascaded $\lambda /4$ resonators between CPS bends. We demonstrate this TLPF based on the attractive membrane platform introduced in [33], which consists of the CPS transmission line on a 1 $\mu$m-thin silicon-nitride ($Si_3N_4$) membrane and uses thin photoconductive switches (PCSs) to generate and detect THz-bandwidth pulses with low-loss and low-dispersion up to 1.5 THz [33].
There are other interesting THz waveguide fabrication techniques such as micro-machining [34–36], but the membrane platform in [33] offers higher precision, manufacturability and performance. In addition, we offer a balanced CPS transmission line which is desirable for many applications [37–39], and is compatible with a multitude of different components (such as filters, power dividers, couplers, stubs, impedance transformers, etc.) which can be combined in series or parallel configurations. The wide bandwidth offered by the membrane platform (i.e. up to at least 1.5 THz) enables potential future applications such as high-speed millimeter-wave circuits and compact waveguide-based THz spectroscopy systems.
2. Background
Ideally, a LPF suppresses signals with a frequency above a cutoff frequency ($f_c$) and has a unity gain for the signals below $f_c$ with a linear phase response. Practically, a LPF presents attenuation and ripples in the passband spectrum. Moreover, it has a transition bandwidth from passband to stopband and also modifies the phase response at this transition bandwidth which introduces a group delay (phase dispersion).
There are four well-known designs of LPF: Bessel, Butterworth (maximum flat), Chebyshev and elliptic (or Cauer) filter. Each filter has pros and cons related to the features of transmission amplitude response, phase response and the corresponding group delay [40–43]. The main features of the amplitude response associated with the type of LPF are the amplitude of the ripples (at the passband and stopband) and the slope of transition around the cutoff frequency.
The phase response of a Bessel LPF is linear (in other words, flat group delay) but the transition between passband and stopband is very wide. While the Butterworth LPF has a flat amplitude response near unity gain, without ripples (in the passband and stopband), it has a wide transition bandwidth from passband to stopband. Chebyshev LPFs provide a steeper transition between passband and stopband at the expense of the ripples in the passband. The three aforementioned filters are defined as all-pole filters (i.e. no zeros except at infinity). Elliptic-function LPFs show zero transmission (very high attenuation) near the cutoff frequency and display a higher roll-off transition than other types of filters, but exhibit ripple in both of the passband and stopband [40–45].
Transmission line bends are one way to realize reactive elements. Numerous studies on transmission line bends have been performed. Most of these studies described the bends as a transmission line discontinuity which provides better use of the circuit area and connects different components with minimum loss [46,47]. The equivalent circuit of a transmission line bend can be represented as a combination of capacitors and inductors. The capacitance effect is due to the charge accumulation around the outer bend of the transmission line, while the inductance effect is introduced by current flow constriction [48]. Adding this reactance to the impedance of the transmission line equivalent circuit could modify the amplitude and phase response of the circuit in a manner similar to basic LPF circuits. Now that we have a THz waveguide platform suitable for fabricating complex CPS-related features [33], we are inspired to study the effect of bending CPS transmission lines to explore its utility in THz filter design.
3. Simulation
We used a 1 $\mu$m-thin $Si_3N_4$ membrane as a TSoC platform to generate, propagate with low loss and low dispersion and detect THz pulses using CPS transmission line [33]. ANSYS HFSS software was used to study and simulate the proposed TLPF design using both frequency and time-domain solvers [49].
The frequency-domain solver is used to estimate the electrical behaviour of the structure (calculate S-parameters, Z-parameters, losses, attenuation) and visualize 3D electromagnetic field propagation and radiation. Moreover, the frequency-domain solver provides insight into the design parameters and optimum dimensions of the structure using a continuous wave (CW) excitation over a wide sweep-spectrum.
The time-domain solver simulates the propagated field with narrow pulse excitation (similar to the pulse generated from the active PCSs) and analyze the spectrum of the transmitted and received pulses after propagation through the optimized design obtained from the frequency-domain solver.
The following material properties are used in the frequency-domain simulations. For Silicon Nitride: $\epsilon _r$ = 7.6, $\mu _r$ = 1, $\sigma$ = 0 S/m, and $tan \delta _e$ = 0.00526 [50]. For the perfect electric conductor (PEC) stripline: the standard bulk conductivity $\sigma _{au}= 1 \times 10^{30}$ S/m with negligible surface roughness. We used the perfect electric conductor in the frequency-domain simulation to focus on the frequency-response of the filter, we will consider the conductor loss of the gold in the time-domain simulations with standard bulk conductivity $\sigma _{PEC}= 4.1 \times 10^7$ S/m with negligible surface roughness.
3.1 Frequency domain solver
First, HFSS frequency-domain solver was used to enhance the performance of the TSoC platform by obtaining the optimal geometry of the CPS transmission line to minimize the propagation loss and increase the amplitude of the received pulse (compared to the pulse measured in [33]). A stripline width $W_\circ = 45\mu$m and separation $S_\circ = 70\mu$m reduces the CPS-losses from 2 dB/mm to less than 0.8 dB/mm (more details are presented in Appendix A).
Figure 1 illustrates the structure of the TLPF using CPS transmission line on a $1\mu$m-thin $Si_3N_4$ membrane. The TLPF consists of a CPS transmission line with stripline width $W_\circ$ and separation $S_\circ$ and N sections of CPS bend. The main parameters that control the cutoff frequency and ripple-level in passband and stopband are the resonator length L, the angle of bend $\alpha = 2\theta$ and the width of section X; the distance between successive bends, L, introduces a $\lambda /4$ resonator that can be modified either by varying the bending angle $\alpha =2\theta$ (which modifies the reactive equivalent of the CPS bend) or by changing the section length 2X.
Then, we studied the transmission coefficient, $S_{21}$, for different bend angles. Next, we applied the roll-off concept by forming a series of N consecutive bending sections. Figure 2 shows $S_{21}$ for a different number of bending sections (N = 3, 5, 7 and 9). It is clear that increasing the number of sections increases the roll-off response of the filter and reduces the ripple-level in the stopband. However, increasing N introduces a higher attenuation in the passband (due to the longer structure). The transfer function of the elliptic low-pass filter depends on numerous parameters such as the order of the filter ($n$), the cutoff frequency, the passband-ripple level ($L_{Ar}$) and the stopband-ripple level ($L_{As}$). We calculated the transfer function of the elliptic-function LPF using Matlab to compare it with the results of the ANSYS HFSS simulations. The red dotted lines in Fig. 2 represents the transfer functions of elliptic LPF with the following parameters: ($n=3$, $L_{Ar}=0.15$ dB and $L_{As}=25$ dB), ($n=4$, $L_{Ar}=0.15$ dB and $L_{As}=38$ dB), ($n=5$, $L_{Ar}=0.1$ dB and $L_{As}=45$ dB) and ($n=6$, $L_{Ar}=0.1$ dB and $L_{As}=40$ dB) respectively. We noticed that increasing 2 sections (e.g. N=5 to N=7) correspond to increasing the order of the LPF (i.e. from $4^{th}$ to $5^{th}$ order). It should be noted that we used the Matlab calculation to show that the results of ANSYS HFSS simulations are close to the transfer function of an elliptic-function LPF.
Next, we studied the effect of changing the angle of bend ($\alpha$ = $45^\circ , 60^\circ , 90^\circ , 120^\circ$ and $150^\circ$), which directly affects the capacitance at the corners of CPS bends. We modified the length of the section (i.e. 2X) to maintain the length of the resonator, L, constant while changing the angle as shown in Fig. 3; We noticed that the sharper angle (i.e. $\alpha = 45^\circ$ and $60^\circ$) introduces a higher roll-off transition and higher ripple-level at the passband. Increasing the angle results in a shift in the cutoff frequency (e.g. changing the angle from $60^\circ$ to $90^\circ$ shifts the cutoff frequency by 0.05 THz). This is expected since the larger bending angle reduces the capacitance at the corner of bends.
Furthermore, we could modify the cutoff frequency without increasing the ripple level by changing the length X with a constant angle. Figure 4 shows that changing X could modify the cutoff frequency and maintain low ripple level at the passband at the expense of the roll-off between passband and stopband.
Finally, we use a frequency-domain solver to visualize the field propagation at passband and stopband. The optimum structure that provides a roll-off amplitude response with minimum ripple at the passband was selected to be N = 7, length X = 100$\mu$m and bending angle $\alpha = 90^\circ$. Figure 5(a) shows the wave propagation at passing frequency and Fig. 5(b) at rejection frequency. It is clear that the higher-frequency wave (i.e. shorter wavelength) radiates at the corners of the bends and the selected number of sections is sufficient to totally suppress the wave. On the contrary, the lower-frequency spectrum (i.e. longer wavelength) propagates through the design without effect.
3.2 Time domain solver
The time-domain solver is used to simulate the entire structure similar to the fabricated one that includes the tapering, CPS, TLPF, and Bias-T using a 200 nm-thick gold stripline. Also, We excite this structure with a sub-picosecond pulse similar to the generated pulse from the active PCS (i.e. to be comparable with the experimental results).
To investigate the response of TLPF, we compared the received pulses of the entire TLPF structure (i.e. tapering, CPS, TLPF, and Bias-T) with the same structure without the TLPF (i.e. the reference structure) to isolate the effect of the TLPF. For computational efficiency, the length of the simulated structures are 4 mm while the fabricated structure is 10 mm. The overall attenuation of the 10 mm-long is estimated be around $8 - 9$ dB for frequencies up to 0.6 THz. The length of the TLPF is 1.4 mm which introduces around 1.1 dB loss that was included in the total loss.
We excited the two simulated structures with the same sub-picosecond pulse and calculated the electric field of the pulse after propagation through the two structures. Figure 6(a) plots the normalized pulses of the two structures. The TLPF pulse is broadened due to the rejected spectrum and delayed due to the longer propagation-path (through the bending route). Figure 6(b) illustrates the Fast Fourier Transform (FFT) of the input and received pulses of the two structures, the TLPF suppress the spectral power above the cutoff frequency (0.6 THz). Due to the non-uniform spectrum of the input pulse, we compared the spectral power of the received-pulses from the TLPF and CPS structures to emphasize the amplitude response of the filter as shown in Fig. 6(c). It should be noted that the total loss of the two structures (due to the conductor and dielectric loss) is similar (especially at the passband spectrum).
Fig. 6. (a) Received pulses for CPS only and TLPF. (b) The FFT of received pulses. (c) The difference between the FFT of the received-pulses from the TLPF and CPS structures.
4. Experiment and results
Figure 7(a) shows the fabricated TSoC, as one of many circuits, using a quarter of a double-sided polished (DSP) Silicon wafer (thickness = 500 $\mu$m and radius = 10 cm) mounted on a printed circuit board (PCB) which connects the input voltage bias to the transmitter and the output detected-signal from the receiving PCS. We process the following fabrication steps to obtain our membrane-based TSoC. First, a 1 $\mu$m-thin $Si_3N_4$ layer was deposited on the upper face of the Si wafer using Low-pressure chemical vapour deposition (LPCVD) technology. Next, the Potassium Hydroxide (KOH) etching process was performed to the lower face of the wafer to remove defined areas of Si wafer (defined by photolithography) and open windows to reach to the membrane surface (as shown in Fig. 7(b)). Then, the surface-mount devices were defined on the upper face of the Si wafer using photolithography. A 200 nm layer of gold (Au) was deposited using the physical vapour deposition (PVD) technology. A 15 nm layer of Titanium (Ti) was used as an adhesion layer between the membrane and the deposited gold.
Fig. 7. (a) The fabricated TSoC using 1 $\mu$m-thin $Si_3N_4$ membrane on a quarter of Si wafer. (b) Back-side of the TSoC showing the membrane window. (c) Illustration of the CPS-TLPF structure on thin membrane. (d) Rendering of the transmitting PCS bonded to the CPS. (e) Microscope image of the PCS during the placement process with the needles of the micro-manipulator. (f) Microscope image of the TLPF structure. (g) Microscope image of Bias-T configuration. (h) Microscope image of receiving PCS bonded to the CPS.
Figure 7(c) shows the structure of the TLPF structure integrated onto the CPS transmission line deposited on the membrane. We placed two 0.4 $\mu$m-thin LTG-GaAs PCSs directly on both sides of the CPS transmission line to generate and detect low-loss, low-dispersion THz-bandwidth pulses (as shown in Fig. 7(d)). The dimensions of these devices are $20\mu m \times 40\mu m$ to assure minimum radiation from the PCS during the excitation at higher frequencies [33]. Figure 7(e) shows a microscopic image of the transmitting PCS during the placement process using the needles of the micro-manipulator (we processed the same step for the receiving PCS shown in Fig. 7(h)). It should be noted that the pressure of the needle during the placement-process and the mechanical loading of the metal structure may limit the use of thinner membranes (i.e. less than 1 $\mu$m) that would provide lower loss and dispersion. These PCSs were bonded to each end of the CPS by Van der Waals (VDW) bonding using a drop of deionized (DI) water. While alignment of the LTG-GaAs devices on the CPS may introduce some small variability in performance, this was not observed. More important is assuring that the PCS’s gold-pads are bonded to the CPS. We test this VDW-bonding by connecting a DC voltage across the CPS stripline and measuring the dark resistance of the LTG-GaAs device. If it is not connected then we would measure an open circuit. DC bias voltage applied to the transmitter is isolated from the receiving PCS by a Bias-T (Fig. 7(g)), as discussed in Appendix A.
The experimental setup shown in Fig. 8 is similar to the standard THz time-domain spectroscopy (TDS) measurement setup used for the generation and detection of THz pulses. A femtosecond laser pulse (pulse width = 90 fs, wavelength = 780 $\pm$ 3 nm, repetition rate = 80 MHz and average optical power = 20 mW) propagates through a beam splitter; one beam is directed to the transmitter of TSoC through an optical chopper, the other goes through a mechanical optical delay line and then focuses on the receiving PCS. The transmitting PCS is connected to the DC bias voltage (20 V). The receiver is similar to the transmitter but without DC bias and is connected to a lock-in amplifier which is referenced to the optical chopper in the transmitter optical path. The received pulse is reconstructed by sweeping the physical path length difference between transmitter and receiver. Providing that the receiver substrate (LTG-GaAs) has a minimal carrier lifetime ($\tau _c\approx$ 0.5 ps), it becomes possible to resolve THz-bandwidth signals [51–54].
Figure 9(a) illustrates the measured current, the peak current of 15 nA and relatively wide pulse width due to the wide rejected spectrum; this high peak current (compared with the detected pulse in [33]) is the result of enhancements of optimizing the geometry of the CPS and Bias-T configuration. Figure 9(b) shows the calculated spectral power of the measured pulse.
Fig. 9. The experimental result of the received THz-bandwidth pulse after propagation through the CPS-TLPF structure on a thin membrane. (a) The detected THz-bandwidth pulse. (b) the spectral power of the received pulse. (c) The spectral power of the received pulses and the simulation result.
The challenge of experimentally measuring accurate absolute amplitudes (or attenuation) in these types of THz experiments where direct measurement probes do not exist is well known. Based on simulations, which are in good agreement with spectral experimental results, and the discussion in Section 3.2 and Appendix A, we estimate that the attenuation of the optimal-geometry CPS (i.e. $W = 45\mu m$ and $S = 70\mu m$) is less than 0.8 dB/mm, and that the total loss of the 10-mm-long structure is roughly 8 – 9 dB. We then normalized the spectral responses of the measurements and the simulation such that the maximum was 0 dB (as shown in Fig. 9(c)). The calculated spectral response illustrates that the TLPF provides a roll-off transition (between passband and stopband) in addition to a wide spectrum of −60 dB rejection of the THz pulse.
5. Conclusion
In this paper, we demonstrated experimentally an elliptical-function THz low-pass filter using the CPS transmission line on a 1 $\mu$m-thin $Si_3N_4$ membrane, and exploiting the reactance arising from bending the CPS transmission lines. Different parameters of the structure were studied to shape the amplitude response of the TLPF, such as cutoff frequency, passband ripples, and roll-off transition between the passband and stopband. The experimental measurements showed good consistency with simulation using ANSYS HFSS. We achieved a low ripple at passband, a roll-off transition with zero transmission near the cutoff frequency of 0.6 THz and a −60 dB rejection for a wide spectrum.
This TLPF is one example of the many types of filters that will be essential in the design of future THz systems, including terabit communication systems, inspection and imaging systems and spectrometers. As in any microwave system, such filters are needed to separate/select frequency bands, multiplex and demultiplex signals, minimize noise, equalize power, eliminate spurious signals, control phase, etc. Future work will extend the principles demonstrated in this work on the membrane platform to other examples of filters operable at THz frequencies.
Appendix A - Enhancement of the THz System-on-Chip
We worked to enhance the performance of the TSoC membrane introduced in [33]. The main enhancements are: optimize the geometry of the CPS transmission line, optimize a tapering structure (Fig. 10(a)) and design a Bias-T configuration (Fig. 10(b)).
It is important to obtain the optimal geometry of the CPS transmission line which provides a minimum attenuation. We explored the dependence of the CPS transmission line on the geometry of separation, S, and width, W. ANSYS HFSS was used to obtain the optimal geometry of the CPS transmission line. Figure 11 illustrates the S-parameters of two CPS geometries (using gold conductors with thickness of 200 nm); the structure A with geometry $W_i = S_i = 10\mu m$ and structure B with the optimal geometry ($W = 45\mu m$ and $S = 70\mu m$). The enhancement of the transmission coefficient, $S_{21}$ is obvious (i.e. minimum attenuation) and the reflection coefficient is still low. The the optimal geometry introduces attenuation of 0.8 - 0.9 dB/mm at 0.25 - 0.5 THz as shown in Fig. 11(c).
Fig. 11. Comparison between two CPS geometries; structure A with geometry $W_i = S_i = 10\mu m$ and structure B with the optimal geometry ($W = 45\mu m$ and $S = 70\mu m$): (a) The transmission coefficient. (b) The reflection coefficient. (c) The attenuation coefficient.
The main problem of the wide CPS-geometry is that the photoconductive switch is incompatible with these dimensions and will produce radiation during the excitation process. A tapering structure is added to minimize the radiation during excitation by using the small CPS cross-section ($W_i = S_i = 10\mu m$) at the input and output ports, then gradually taper to the wide CPS-geometry ($W_\circ = 45 \mu m$ and $S_\circ = 70 \mu m$) to reduce the propagation losses.
The main disadvantage of the taper structure is the impedance mismatch between different geometries CPS transmission lines. To illustrate the impact of taper length ($L_T$), ANSYS HFSS was used to simulate the transmission and reflection coefficients for five CPS structures with different tapering-lengths: $L_T$ = 100, 250, 500, 750, and 1000 $\mu$m (labelled C, D, E, F and G, respectively). The aforementioned structures A and B (no taper) are included for comparison. Figure 12(a) plots the simulations results. The $S_{21}$ and $S_{11}$ are shown for the 7 structures with the same total length of 2.5 mm. The optimum tapering length that provides a low attenuation with minimum reflection around 0.5 mm to 0.75 mm.
Fig. 12. (a) Structures of CPS transmission lines with different tapering lengths. (b) The transmission coefficients $S_{21}$. (c) The reflection coefficient $S_{11}$.
In addition, we designed a Bias-T configuration which consists of an interdigitated capacitor and meander inductor; the inductor passes the DC bias to the transmitting PCS through the CPS without affecting the propagation of generated THz pulse, while the capacitor blocks the DC bias to reach the receiving PCS without distorting the THz pulse.
The interdigitated capacitor consists of 8 interdigitated electrodes with length of 45 $\mu$m and the separations between the electrodes were limited by the photolithography resolution (i.e. 1-3 $\mu$m). We designed the electrodes near a more conservative resolution of 3 $\mu$m. These dimensions introduces some resonant frequencies, the lowest resonant frequency is around 1.5 THz (i.e. which is higher than the spectral component of the output signal).
Funding
Natural Sciences and Engineering Research Council of Canada (NSERC).
Acknowledgement
The authors would like to thank Prof. Jens Bornemann for his valuable discussions. We acknowledge 4D LABS (Simon Fraser University) for fabricating the TSoC structure.
Disclosures
The authors declare no conflicts of interest.
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