Tuning of the center frequency

Figure 1 shows the structure of a slot-loaded SIW resonator connected with two weakly coupled 50 Ω microstrip lines. To simplify the simulation, the vias which constitute the walls of a SIW cavity is replaced by metal walls. All the designs in this paper use F4B substrates with a thickness of 0.8 mm, a relative dielectric constant of 2.65, and a loss tangent of 0.001. The width and length of the cavity are both a. There is a slot with a length l ₁ and a width w ₁ on the top metal layer. The slot is a distance p from the center of the cavity. A shorting strip, a distance p ₁ along the slot, acts as a “switch on” in the simulations. In the extreme case where p ₁ is larger than l ₁/2, the strip is removed. This simulates the switch of “OFF” state. The switch can make the slot connected or not which results in different resonant frequencies. The resonant frequency of the TE₁₀₁ mode in a traditional SIW resonator without the slot can be calculated by [Reference Pozar11]

(1)$$f_{TE101} = \displaystyle{c \over {a\sqrt {2\varepsilon _r}}} $$

where c is the velocity of light in the vacuum and ε _r is the relative permittivity of the substrate. The introduction of the slot changes the cavity's field distribution. So the slot-loaded cavity has a lower resonant frequency than f _TE101. In addition to the width of the cavity a, the resonant frequency also depends on the position of the slot p, the slot's length l ₁, width w ₁, and the position of the switch p ₁. In order to reduce the radiation caused by the slot, the width of the slot should not be wide. Here, w ₁ = 1 mm. It is found that when the slot is further away from the center of the cavity, the cavity would has a lower radiation quality factor Q _r and a lower resonant frequency, but a wider tuning range as shown in the simulation in Fig. 2. This is due to more electric current cut by the slot. Q _r is always larger than 180, while the total quality factor of the resonator not including Q _r, by simulation, is estimated to be 500. So the whole Q is comparable with that of a microstrip resonator which ranges from 100 to 200 at around 2.4 GHz in our simulation.

Fig. 1.

A slot-loaded SIW resonator.

Fig. 2.

Effects of p and p ₁ on (a) the quality factor due to the radiation loss and (b) the resonant frequency (a = 53.5 mm, l ₁ = 40 mm, w ₁ = 1 mm).

To achieve more tuning states of the resonant frequency, more strips can be introduced. Figure 3 illustrates the situation of two strips loaded slot as an example, where 0 and 1 represent the trip is removed and added, respectively. Once one more strip is added, the state would have a higher resonant frequency than the state without the strip and vice versa. So the 00 state has the lowest resonant frequency while the 11 state has the highest one. The frequency tuning range is decided by those two states. In 01 and 10 states, the slot loads one strip. According to the above analysis, in the 01 state, the strip is further from the center, the resonator has a lower resonant frequency than that in the 10 state. If the two strips are on symmetric location of the slot, the two states would have the same resonant frequency. However, to get the widest tuning range of the center frequency, one strip should put in the center of the slot.

Fig. 3.

Two strips-loaded slot.

Figure 4 shows the equivalent circuit of the PIN diode in the on-state and off-state. The PIN diode is an MA4P789-1141T with an on-state resistance of 1.5 Ω and an off-state capacitance of 0.35 pF. Its package is SOD323 with a parasitic inductance of 1.2 nH and a package capacitance of 0.12 pF. For the simulation, the package parasitic parameters are also considered. Replacing the shorting strip in Fig. 1 by the model of the PIN diode, the quality factor due to the diode loss can be calculated. For simplify, the bias circuit is not considered. Figure 5 shows the curves of the quality factor due to the diode loss changing with different p and p ₁ when the diode is switched on. As shown, when the slot is far away from the cavity's center or the diode is near the slot's center, Q _d is low. That is due to the fact that more current flows through the diode at those positions. When the diode is switched off, the diode is lossless. The unloaded Q of the cavity is mainly depended on Q _r.

Fig. 4.

The equivalent circuit of the PIN diode.

Fig. 5.

Effects of p and p ₁ on the quality factor due to the diode loss in the on-state.

Center frequency switchable filter

The structure of the proposed center frequency switchable filter is shown in Fig. 6. The filter has two SIW cavities. Each cavity is loaded with two PIN diodes as the switches. So the resonant frequency can have four states. Figure 7 shows an enlarged view of the PIN diode-loaded slot and bias circuit. The inductor and capacitors for the bias circuit are chosen to be 1 µH and 100 pF, respectively. When the PIN diodes are switched on, the resonators have a higher resonant frequency and vice versa.

Fig. 6.

Structure of the center frequency switchable filter (unit: mm).

Fig. 7.

Zoom view of the slot loaded with the PIN diode and bias circuit.

To design such a filter, many parameters control the center frequency, including the size of the cavity, the size and position of the diode-loaded slot. For a given center frequency, the initial value of the cavity's width can be calculated from equation (1). The accurate values of the whole cavity are determined by a full wave simulator. The size and position of the slot is determined by the lowest center frequency. Then the position of the diodes can be decided by other center frequencies. When all the PIN diodes are in on-state, the filter works at the highest center frequency. Then, according to the specified bandwidth and center frequency (the center frequency in the middle of the tuning range is used here), the external Q and the coupling coefficients are calculated. With those values, the size of the coupling slots can be ascertained. A second-order filter with four center frequency tuning states is taken as an example. The specified center frequency of the Chebyshev response filter is 1.85 GHz with a 3 dB bandwidth of 95 MHz. The external Q is calculated to be 30.5 while the coupling coefficient is 0.0362. Figure 8 shows a photograph of the simulated and measured S-parameters of the filter. Figure 9 shows the insertion loss and the bandwidth against the center frequency, where, 0 and 1 represent the off and on states of the PIN diodes biased by the corresponding voltage. The measured lowest and highest center frequencies are 1.78 and 1.91 GHz with a tuning range of 130 MHz. The narrowest and widest bandwidths are 90 and 100 MHz, respectively. The bandwidth variation is as small as ±0.64% without tuning the external Q and internal coupling in this design. The measured insertion losses for all states are between 1.83 and 2.43 dB. According to the insertion loss, return loss, center frequency, and 3-dB bandwidth of the filter, the simulated unloaded Q of the resonator is estimated to be 100–156 while the measured one is estimated to be 92.8–127.5.

Fig. 8.

Simulated and measured S-parameters as well as photograph of the fabricated filter.

Fig. 9.

Simulated and measured insertion loss and bandwidth against the center frequency.

Tuning of the coupling coefficient

The inter-resonator and external couplings are all realized by the slot and coplanar waveguide structure. Figure 10(a) shows a one-pole SIW filter with this kind of coupling structure. The coupling strength depends on the width w _s and length l _s of the coupling slot, as well as the position of the strip p _s. Thus, the coupling can be controlled by changing the position of the strip. Figure 10(b) shows a simulation of the filter's transmission response and extracted Q _e with different p _s. As indicated in Fig. 10(b), a larger p _s leads to a stronger coupling, thus a wider bandwidth. When p _s = 0 mm, Q _e reaches its maximum value and when the strips are removed, Q _e reaches its minimum value. It should also be noted that a larger p _s will result in a shifting of the center frequency to lower values. In order to keep the center frequency unchanged while tuning, we should also vary the resonant frequency using the method described in the “Tuning of the center frequency”.

Fig. 10.

(a) A first order SIW filter with the strip-loaded coupling structure and (b) transmission response with different positions of the strip and extract Q _e (a = 53.5 mm, l _s = 15.35 mm, w _s = 1 mm).

The structure in Fig. 11(a) is used to study the tuning mechanism of the coupling coefficient. The strips on the coupling slot can move along the slot to tune the coupling coefficient. Figure 11(b) shows the extracted coupling coefficient changing with the position of the strips. As shown, the coupling coefficient increases with p _s. When p _s = 0 mm, it has a minimum value of 0.0276. This coupling coefficient decides the available narrowest bandwidth. And when the strips are moved away which equals the off-state of a switch, it gets to the maximum value of 0.0851. This coupling coefficient is corresponding to the widest bandwidth state.

Fig. 11.

(a) Two coupled SIW resonators with the strip-loaded coupling structure and (b) extracted coupling coefficients with different positions of the strip (a = 53.5 mm, l _s = 15.35 mm, w _s = 1 mm, w ₁ = 2.3 mm, l ₁ = 6 mm).

To realize more tuning states of the internal and external coupling, more PIN diodes can be added. As mentioned before, when all the diodes are switched off, Q _e and the coupling coefficient get to the minimum and maximum value, respectively. The filter has the widest bandwidth. To get the narrowest bandwidth, all diodes should be switched on. For only one diode is switched on, if the diode is closer to the coupling window, Q _e gets larger while the coupling coefficient gets smaller. As a result, the filter gets a narrower bandwidth. Once one more diode is switched on, Q _e gets even larger while the coupling coefficient gets even smaller.

Bandwidth switchable filter

Figure 12 shows the structure of the bandwidth switchable filter. According to “Tuning of the coupling coefficient”, when the PIN diodes biased by V ₂ and V ₃ are switched off, the filter would have a lower center frequency than that of the on state. The PIN diodes biased by V ₁ are introduced to change the resonant frequency of each resonator and keep the center frequency unchanged. The filter is designed to have a center frequency at 2.09 GHz with bandwidths of 70 and 107 MHz. The external Q for the wide and narrow bandwidth states are 29.7 and 46.54 while the corresponding coupling coefficients are 0.0372 and 0.0237. The simulated and measured results agree with each other except the measured ones have larger insertion losses, as shown in Fig. 13. A photograph of the fabricated filter is also shown in Fig. 13. The measured return losses are always larger than 20 dB at the center frequency. Table 1 compares the performance of the simulation and measurement in detail.

Fig. 12.

Structure of the bandwidth switchable filter (unit: mm).

Fig. 13.

Simulated and measured S-parameters as well as photograph of the fabricated filter.

Table 1.

Comparison of the simulated and measured results

Table 2 compares the proposed switchable SIW filters in this paper with some previous works. As shown, for the center frequency switchable filter, the bandwidth of our design is more stable. Moreover, the insertion losses of our designs are close or a little lower than those in other designs. Most of the reported works do not have the ability of bandwidth tuning. Our second design provides a potential solution for this problem.

Table 2.

Comparison of various tunable SIW filters