Concept

The concept of the proposed tunable microstrip bandpass filter basically involves a BST varactor (or DTC) loaded quarter-wavelength (λ/4 length) resonator, as depicted in Fig. 1. One end of the resonator is shorted to the RF ground, while the other end is loaded with the varactor. The change in the DC bias voltage (or control signal for DTC) changes the capacitance value, tuning the resonant frequency. By suitably coupling such resonators together and by suitably tapping the input and output, one can realize tunable microstrip bandpass filters.

Figure 1. Tunable microstrip resonator using BST varactor (or DTC).

Figure 2 shows the schematic of the BST varactor-based second-order tunable bandpass filter designed using Keysight ADS. Gap coupling is used for inter-resonator coupling, whereas tap coupling is used for input–output coupling. BST varactor (1.7–9.7 pF: 24–1 V) which has a minimum Q of around 50, is employed. A second-order filter has three design parameters (variables), namely resonator length, input–output tapping location, and the gap between the resonators. The gap corresponds to the inter-resonator coupling, while the tapping location corresponds to the input–output coupling. Inter-resonator coupling co-efficient can be determined using equation (1), which incorporates operating bandwidth (BW), normalized coupling coefficient (M_i,j), and the resonant frequency (f_r). Equations (2) and (3) relate input coupling (R_S) and output coupling (R_L) to the normalized coupling coefficients [Reference Cameron, Kudsia and Mansour12, Reference Gowrish and Koul13]. A coupled microstrip transmission line model in Keysight ADS is used for the simulation. Since there are only three design parameters, the filter is designed using manual tuning of the parameters. The gap between the resonators determines the bandwidth obtained, and the return loss can be improved using the tapping location. Figure 3 shows the DTC (pSemi: PE64102) based second-order tunable bandpass filter implemented using a similar methodology.

(1)\begin{equation}{k_{i,j}} = \,\left( {{BW}*{M_{i,j}}} \right)/{f_{\mathrm{r}}}\end{equation}

(2)\begin{equation}{R_S} = \,\left( {{M_{s,1}}*{M_{s,1}}*{BW}} \right)/{f_{\mathrm{r}}}\end{equation}

(3)\begin{equation}{R_L} = \,\left( {{M_{N,L}}*{M_{N,L}}*{BW}} \right)/{f_{\mathrm{r}}}\end{equation}

Figure 2. (a) Schematic and photograph of the tunable microstrip bandpass filter using BST varactors. (b) Simulated reflection coefficient and transmission coefficient of the tunable bandpass filter using BST varactors: capacitance variation from 2 to 8 pF. (c) Simulated transmission group delay (capacitance variation from 2 to 8 pF) and spurious response (at 8 pF) [BST varactor-based bandpass filter].

Figure 3. (a) Schematic and photograph of the tunable microstrip bandpass filter using DTCs. (b) Simulated reflection coefficient and transmission coefficient of the tunable bandpass filter using DTCs: capacitance variation from 2.8 to 8 pF. (c) Simulated transmission group delay and spurious response (at 8 pF) [DTC-based bandpass filter].

Design methodology

Since RT5880 (dielectric constant of 2.2 and loss tangent of 0.0009) is a low loss substrate, and provides good performance, and hence is employed to design and fabricate the tunable microstrip bandpass filter shown in Figs. 2 and 3. The resonators and feeding line for the tunable bandpass filter are designed using 50 Ω transmission lines. The line width for the resonators and feedline is calculated using the design equations for microstrip technology. For a given characteristics impedance “Z ₀”, dielectric constant and substrate height “d”; the line width “W” can be calculated using the following equations [Reference Pozar14]:

(4)\begin{equation}\frac{W}{d} = \left\{ \begin{array}{*{20}{c}} \frac{8 e^A}{e^{2A} - 2}\,\mathrm{for}\frac{W}{d} \lt 2 \\[3pt] \frac{2}{\pi }\left[ B - 1 - \ln \left( {2B - 1} \right)\right. \\[3pt] \left.+ \frac{e_{\mathrm{r}} - 1}{2 e_{\mathrm{r}}}\left\{ \ln \left( {B - 1} \right) + 0.39 - \frac{0.61}{e_{\mathrm{r}}} \right\} \right]\,\mathrm{for}\frac{W}{d} \lt 2 \end{array} \right.\end{equation}

where

(5)\begin{equation}A = \,\frac{{{Z_{{o}}}}}{{60}}\sqrt {\frac{{{e_{{r}}} + 1}}{2}} + \frac{{{e_{{r}}} - 1}}{{{e_{{r}}} + 1}}\left( {0.23 + \frac{{0.11}}{{{e_{{r}}}}}} \right)\end{equation}

(6)\begin{equation}B = \frac{{377\pi }}{{2{Z_{{o}}}\sqrt {{e_{{r}}}} }}\end{equation}

Length of the resonators is taken equal to quarter wavelength of the center frequency of operating band. However, the actual length in design is optimized to achieve the optimum performance. Copper is used as the metal layer with gold plating. Plated through hole via is used for RF short. A common DC bias voltage is applied to both the BST varactors, as depicted in Fig. 2(a). Similarly, common control signals using Arduino Due microcontroller (Vdd, Clock, Select, and Data) are applied to both the DTCs as shown in Fig. 3(a). Both BST varactors and DTCs have inherent RF and DC isolation, and hence no RF choke and no DC blocking capacitors are required.

Simulation results are plotted in Figs. 2 and 3. The measured reflection coefficient (S₁₁) and transmission coefficient (S₂₁) for the BST varactor-based bandpass filter are plotted in Fig. 4. The measured reflection coefficient (S₁₁) is better than −10 dB from 900 to 1275 MHz, thus achieving a tuning range of 35%. The transmission coefficient (S₂₁) varies from 2.6 (at 1275 MHz) to 3.1 dB (at 900 MHz). The measured absolute bandwidth is nearly constant and varies around 68 MHz by ±5%. The transmission group delay variation and spurious response are shown in Fig. 5. It can be observed that there is no spurious response till 3 GHz. It is worth mentioning here that BST varactors have excellent linearity (IIP3 > 50 dBm) and have low leakage current (<100 nA).

Figure 4. Measured reflection coefficient and transmission coefficient of the tunable bandpass filter using BST varactors: bias voltage variation from 7 to 24 V.

Figure 5. Measured transmission group delay (bias voltage variation from 7 to 24 V) and spurious response (at 7 V) [BST varactor-based bandpass filter].

The measured reflection coefficient and transmission coefficient for the DTC-based bandpass filter are plotted in Fig. 6. The measured reflection coefficient (S₁₁) is better than −10 dB from 850 to 1225 MHz, thus achieving a tuning range of 36%. The transmission coefficient (S₂₁) varies from 1.5 dB (at 1225 MHz) to 3.1 dB (at 850 MHz). The measured absolute bandwidth is nearly constant and varies around 93 MHz by ±5%. The transmission group delay variation and spurious response are shown in Fig. 7. It is worth mentioning here that DTCs have excellent linearity (IIP3 > 60 dBm). Table 1 compares the proposed tunable microstrip bandpass filters with those reported in the literature.

Figure 6. Measured reflection coefficient and transmission coefficient of the tunable bandpass filter using DTCs (state 0 → S0: 00000000, state 7 → S7: 00000111).

Figure 7. Measured transmission group delay and spurious response (at S7) [DTC-based bandpass filter].

Table 1. Comparison of tunable microstrip bandpass filters

λ= free-space wavelength; IP3 = third-order intercept point; NM = not mentioned; SI = stepped impedance; TW = this work.