Recently, with the evolution of the silicon-CMOS-device process technology, highly integrated silicon ICs (integrated circuits) including RF (radio frequency) and baseband blocking have been developed [1-8]; however, passive components such as the coupler, the divider, and filters have been fabricated outside of the silicon ICs due to their large sizes and the high conductive loss of the silicon substrate, the latter of which has impeded the realization of a fully-integrated silicon front-end. To solve this problem, a short-wavelength transmission line for which a periodically arrayed grounded-strip structure (PAGS) is employed, which enables the realization of miniaturized on-chip passive components on the silicon substrate [2-5], has been developed.

For the application of this solution to the RFIC (radio- frequency integrated circuits), the impedance-matching components as well as the transmission line should be realized on the silicon substrate; in particular, PAGS-employing open and short stubs that are on the silicon substrate should be intensively studied because they are the essential matching components in the millimeter-wave as well as the microwave frequency. An intensive study of the PAGS-employing open and short stubs has not yet been performed, however, so in this work, these stubs were studied after they were fabricated on the silicon substrate. The basic RF characteristics were subsequently studied for an applicability regarding the RF-matching components on the silicon RFIC, and a highly miniaturized harmonic-rejection filter was also realized on the silicon substrate through the use of the PAGS-employing open and short stubs.

Figure 1 shows the structure of the PAGS-employing coplanar waveguide [4,5] wherein the PAGS exists at the interface between the SiO₂ film and the silicon substrate, and it is electrically connected to the top-side ground planes (GND planes) through the contacts; therefore, the PAGS was grounded through the GND planes. As is well-known, the capacitance C_a (shown in Fig. 1)-per-unit-length of the conventional coplanar waveguide (CPW) that is without the PAGS is only periodical, while an additional capacitance C_b, as well as the C_a, applies for the PAGS-employing CPW due to a coupling between the line and the PAGS. As shown in Fig. 1, the C_b is a capacitance between the line and the PAGS; that is, the total capacitance of the PAGS-employing CPW corresponds to the C_a + C_b, but it corresponds to only the C_a for the conventional CPW that is without the PAGS. The PAGS-employing CPW therefore exhibited a wavelength (λ_g) that is much shorter than that of the conventional one because the λ_g is inversely proportional to the periodical capacitance; that is, λ_g = 1/[f·(LC)^0.5] [4,5]. In this work, the PAGS-employing open and short stubs were fabricated on the silicon substrate.

Figure 2 shows a photograph and the layout of the PAGS-employing open and short stubs on the silicon substrate that were fabricated with a height of 600 μm; here, L, W, and T are all 20 μm.

Figure 3 shows the return loss (S₁₁) of the open stub, and for a comparison, the open stub for which the conventional CPW is employed was also fabricated on the silicon substrate, and its return loss is also plotted in Fig. 3. In the conventional CPW, the line and the GND planes are placed on the silicon substrate; therefore, in the structure of the conventional CPW, the SiO₂ film and the PAGS do not exist [9,10].

In the case of the ideal lossless open stub, its S₁₁ moves clock-wise from the open point along the outermost circle as the frequency is increased because its absolute S₁₁ value is 1 at all of the frequencies. As shown in Fig. 3, the S₁₁ trace of the PAGS-employing open stub is comparatively similar to that of the ideal lossless open stub. Alternatively, as the frequency is heightened, the S₁₁ of the open stub for which the conventional CPW is employed moves inward, whereby it deviates from the outermost part due to an attenuation that originates from the loss of the silicon substrate.

The quality (Q) factors of the PAGS-employing stubs on the silicon substrate were also investigated. There are several methods for the calculation of the Q factor [9,10]. In this work, the transmission-line Q factor was derived from a resonant tank that was built using a one-quarter-wavelength-long line at the resonance frequency f0. The Q factor was extracted according to the ratio of the - 3 dB bandwidth to the f0; that is, Q = f₀/△f__3dB.

Figure 4 shows the two-port insertion loss (S₂₁) of the quarterwavelength PAGS-employing open and short stubs on the silicon substrate; for a comparison, the S₂₁ of the open stub for which the conventional CPW is employed on the silicon substrate was also plotted. The Q factors of the stubs are summarized in Table 1. If the size of the periodic structure changed, the frequency response also changed. Concretely, the size of the metal strip in the PAGS (T in Fig. 1) decreased as the center frequency shifted to a higher frequency range because the wavelength of the PAGS structure becomes longer due to the reduction of the periodic capacitance.

As shown in Table 1, the PAGS-employing open and short stubs show Q factors that are much higher than that of the open stub for which the conventional CPW is employed on the silicon substrate. The above results indicate that the PAGS-employing open and short stubs can be applied to the matching components of the millimeter-wave frequencies as well as those of the microwave frequencies due to the low loss. Even though the PAGS-employing open and short stubs were fabricated on the silicon substrate with a high conductivity, they show a comparatively high Q. The comparatively high Q of the PAGS-employing stubs originates from the C_b, which is shown in Fig. 1. Figure 5 shows the equivalent circuit of the PAGS-employing transmission line where Ri is the resistance that originates from the current between the line and the ground, which is caused by the high conductivity of the silicon substrate. The conventional CPW shows a very low Q due to the R_i. As shown in Fig. 5, however, the C_b is connected in parallel with the R_i in the PAGS-employing transmission line; therefore, in the PAGS-employing transmission line, the C_b serves as a bypass capacitor, and R_i can be ignored due to the C_b because the capacitance value of the latter is very high at the operating frequency, as follows:

For this reason, in spite of the high conductivity of the silicon substrate, the PAGS-employing open and short stubs showed a comparatively high Q factor.

By using the PAGS-employing open and short stubs on the silicon substrate, miniaturized band-rejection filters were fabricated. As is well-known, a λ/4 open stub is employed for the band-rejection filter, and it suppresses the signal at which the frequency of the length of the open stub equals λ/4. To realize the band-rejection filter, the PAGS-employing λ/4 open stub was fabricated on the silicon substrate, which is shown in Fig. 2, and the use of the PAGS led to a great reduction of the size of the band-rejection filter. The lengths of the open-stub filter that are required for rejections of specific frequencies is shown in Fig. 6; here, the length of the PAGS-employing open-stub filter is much shorter than that of the open-stub filter for which the conventional CPW is employed because the PAGS-employing transmission line shows a wavelength that is much shorter than that of the conventional one [4,5]. The above results indicate that band-rejection filters can be highly miniaturized through the use of the PAGS. The measured band-rejection characteristics of the PAGS-employing open-stub filters of a variety of lengths on the silicon substrate are shown in Fig. 7.

By using the PAGS-employing open and short stubs, a highly miniaturized harmonic-rejection filter was also realized on the silicon substrate, and it is shown in Fig. 8. As shown in this figure, the harmonic-rejection filter consists of the PAGS-employing λ/4 open and short stubs, and a grounded line is located between the open and short stubs for the isolation of the two stubs; therefore, the filter suppresses the signals with the frequencies of the length of the open stub that equals (2n-1) × λ/4 and the length of the short stub that equals nλ/2. For the harmonic-rejection filter that is shown in Fig. 8, the length of the open stub is 1 mm, which is (2n-1) × λ/4 at (2n-1) × 13 GHz, and the open stub suppresses the signals with frequencies of (2n-1) × 13 GHz (13 GHz, 39 GHz, 65 GHz, etc). The length of the short stub is also 1 mm, which is nλ/2 at 2n × 13 GHz, and the short stub suppresses the signals with frequencies of 2n × 13 GHz (26 GHz, 52 GHz, 78 GHz, etc). The harmonic-rejection filter that is shown in Fig. 8 therefore suppresses the signals with frequencies of n × 13 GHz (13 GHz, 26 GHz, 39 GHz, 52 GHz, etc).

Figure 9 shows the measured insertion losses of the harmonic-rejection filter. As shown in this figure, even though the minimum points of the V-shape graphs slightly shifted from the center frequencies, a comparatively sound suppression characteristic is observed in the frequencies of n × 13 GHz. Concretely, the insertion losses of the filter are - 18 dB, - 13 dB, and - 15 dB at 13 GHz, 26 GHz, and 39 GHz, respectively. The above filter can be used as an on-chip-LO (local oscillator) harmonic-signal-rejection filter for the DBS (direct-broadcasting satellite) system, because the LO frequency of the DBS system is 13 GHz.

In this work, the harmonic-rejection filter was designed to suppress signals with the frequencies of n × 13 GHz; therefore, the length of each PAGS-employing stub is 1 mm, the line width is 20 μm, and the total size of the PAGS-employing filter is 0.1 mm², the latter of which is only 7% of that of the filter for which the conventional CPW is employed on the silicon substrate. Based on these findings, if the filter that suppresses the signals with the frequencies of n × 13 GHz is fabricated using the conventional CPW on the silicon substrate with a height of 600 μm, the line-width and the line-length of the stub are 0.22 mm and 2.04 mm, respectively, and the total size of the filter is 1.428 mm². The sizes of the filters are summarized in Table 2.

The above results indicate that the bulky off-chip filter of a wireless communication system can be integrated on the silicon substrate through the use of the PAGS-employing stubs.

In this work, PAGS-employing open and short stubs were fabricated on the silicon substrate, and their basic RF characteristics regarding an applicability for the RF-matching components were studied. According to the results, for which a comparison with the conventional stubs on the silicon substrate was made, the PAGS-employing open and short stubs showed a much lower loss. Concretely, the Q values of the PAGS-employing open and short stubs are 9 and 10.2, respectively, while the Q value of the conventional open stub is 2.5. The comparatively high Q values of the PAGS-employing stubs originate from the high coupling capacitance between the line and the PAGS. To improve the PAGS-employing RF device, however, the Q value should be further increased, and this can be achieved by improving the device process or by designing the device structure optimally, and these should be studied in a future work.

Using the PAGS-employing open and short stubs, a highly miniaturized harmonic-rejection filter was also fabricated on the silicon substrate. The filter showed a comparatively sound harmonic-suppression characteristic at n × 13 GHz, and its size is 0.1 mm², which is only 7% of the size of the conventional filter on the silicon substrate.