A Technique for Tunable Filters with Low Insertion Loss and Narrow Bandwidth

: A technique for tunable filters with low insertion loss and narrow bandwidth is proposed in the form of comb-line structure. Both resonant capacitor with pin-diodes and resonant inductance in the tunable filter were analyzed and the main source of insertion loss was obtained. A series of filters with same pin-diodes, center frequency, absolute bandwidth and low return loss was simulated. The results showed that, by changing the values of the resonant capacitor and inductance, insertion loss of the filter can be greatly restricted. This technique will allow the design of tunable LC filters with low insertion loss and narrow bandwidth.


Introduction
Tunable filter is one of the suitable solutions for intelligent RF applications satisfying multi-band or multimode standards [1]. Compared to a bank of fixed filters, a tunable filter promises greater functionality, better channel selectivity, reduced size, and lower weight since the same hardware can be employed at multiple bands [2]- [5]. However, for tuning over an octave frequency by using pin-diodes switches or varactors, the insertion loss of the tunable filter is larger than normal fixed filters. Up till now, some method has been used to restrict the insertion loss of the tunable filter [6]- [10]. But few research has reported the influence of values of the resonant capacitor with pin-diodes and resonant inductance on the insertions loss of the tunable filter.
In this paper, both resonant capacitor with pin-diodes turned on and resonant inductance in the tunable filter were analyzed and a technique for restricting the insertion loss of tunable filters by changing the values of the resonant capacitor and inductance is reported.

Theoretical Analysis Of The Resonant Circuit With PIN-DIODES
The insertion loss and bandwidth of band-pass filter is shown in (1).
( ) L f is insertion loss, l Q is loaded quality factor, u Q is unloaded quality factor, f is frequency and 0 f is center frequency. The fractional bandwidth of band-pass filter is shown in (2).
According to (1) and (2), it could be concluded that, if the fractional bandwidth of the filter is fixed, the insertion loss mainly depends on u Q of the filter and higher value of u Q means lower insertion loss in the filter.
The original definition of quality factor is: The energy storage in the circuit 2 The energy consumption in the circuit u Q  = (3) In this paper, for the convenience of comparison and discussion, only the tunable filter with pin-diodes all turned on and can be equal to be a resistance was taken into considerations.
The structure of the resonant capacitors with pin-diodes is shown in Figure 1.  (4) and (5).
The structure of the resonant circuit is shown in Figure 2.

Simulation Examples
According to Section 2, a series of tunable comb-line filters with different resonant capacitor and 1% bandwidth were simulated. The models of the tunable filters with the same pin-diode switches but different resonant inductors and capacitors are made and shown in Figure 3. Figure 3 The models of the tunable filters with the same pin-diode switches The pin-diodes are all turned on and can be equal to be a resistance as 0.5 Ω as shown in Fig.3. The value of the capacitors varies from 2 pf to 4 pf and the radius of the resonant metal rib varies from 1 mm to 5 mm which keeps the center frequency of the filters at about 210 MHz. The material of the metal rib is set as aluminum.
By changing the coupling window and the height of the tap-line, the tunable filters with pin-diodes get the same values of bandwidth, return loss and center frequency. However, the values of the insertion loss are different. The simulation results are shown in Figure 4 and table 1. Figure 4 The simulation results of the tunable filters with pin-diodes switches 2MHz -25dB -6.8dB It could be concluded that, as the value of the capacitors varies from 2 pf to 4 pf and the radius of the resonant metal rib varies from 1 mm to 5 mm, the insertion loss of the filters with the same pin-diodes, center frequency, absolute bandwidth and low return loss increases from -4.2 dB to -6.8 dB. Smaller resonant capacitor means higher u Q and lower insertion loss of the tunable filter with pin-diodes switches all turned on, which support the conclusion in section 2.

Conclusion
A technique for Tunable filters with low insertion loss and narrow bandwidth across the tuning range is proposed in the form of comb-line structure. The effect of values of resistant in pin-diodes, resonant capacitor and inductor on insertion loss in tunable filter has been analyzed and a series of tunable filter with the same pin-diodes, center frequency, absolute bandwidth, low return loss but different resonant capacitors and inductors were simulated. It could be concluded that, as the value of the capacitors varies from 2 pf to 4 pf, the insertion loss of the filters with the same pin-diodes increases from -4.2 dB to -6.8 dB. Both the theory analysis and simulation result show that the small value of resonant capacitor means higher u Q and lower insertion loss in the filter with pin-diodes turned on.