Microstrip Tunable Bandpass Filter with the Colinear Resonators

. This paper presents the lumped element circuit and transmission line equivalent circuit for a varactor-tuned bandpass filter. The filter consists of transmission lines, fixed capacitors, and a varactor diode. The colinear resonant sections, in this filter, are not configured in parallel, as they are in a conventional combline filter. For this reason the overall area of the filter is reduced. The passband of the filter can be tuned from 0.69 GHz to 1.20 GHz by varying the capacitance of the varactor diode. The insertion loss of this filter changes from 1.2dB to 2.1dB across this bandwidth.


Introduction
T u n a b l eb a n d p a s s l t e r sw i l lp l a ya ni m p o r t a n tr o l ei nt h e future communication [ -]. Compact, highly selective, and tunable lters with low insertion loss are widely required. Di erent tuning technologies have been developed, including varactor diode, mechanical tuning, microelectromechanical (MEMS) component, and p-i-n diode [ -]. One of the most popular techniques for achieving continuous tuning by electrical means within a bandpass lter is to use a varactor diode. Hunter and Rhodes [ ] report a tunable combline bandpass lter which can be tuned from . GHz to . GHz Most of the designs reported to date are based around coupledlines.Primarilythesestructuresarecoupledtogether m a g n e t i c a l l y . er a d i a t i o nl o s so ft h ec o u p l e dl i n ei sh i g h when the coupling is weak. In some application, it is not easy to establish the coupling matrix. is is the case for coplanar waveguide (CPW), for example. is paper presents a novel tunable bandpass lter with colinear resonators. e lter is not based around parallel coupled lines. e overall area of this lter is smaller than the conventional combline lter. Equivalent circuits of the new lter are analyzed.

Equivalent Circuit
Figure shows the proposed lter. e lter consists of microstrip lines, xed capacitors, and a varactor diode. e main resonator is composed of a varactor diode and microstrip line 2 . A lumped element equivalent circuit has been derived for this lter. e equivalent circuit is shown in Figure . e basic resonator is represented by 2 and capacitance of the varactor ( 2 ). e external coupling is controlled by the " " shaped circuit located on either side of this resonator. e circuit element values are presented in Table . e parameters of the lumped element equivalent circuit are calculated in MATLAB . , as shown in Figure .I tc a n be observed from Figure that the centre frequency of the passband can be tuned from . GHz to . GHz by varying the capacitance of 2 from pf to pf. e absolute dB bandwidth of this lter is 100 ± 2 MHz across the tuning range. According to computer simulation the return loss is better than dB across the entire tuning range.
Figure shows a transmission line equivalent circuit developed from the lumped element equivalent circuit. e capacitors retain their value and position in the transmission line circuit. e inductors 1 , 2 ,a n d 3 in the lumped element circuit are replaced by sections of transmission line TX 1 ,TX 2 ,a n dTX 3 , respectively. Transmission through the lter, that is, 21 , can be deduced with reference to the ABCD matrix.
e ABCD matrix for the series capacitor 1 is where 1 , 1 are the characteristic impedance and admittance of the transmission line, is the transmission line phase constant, and 1 is the length of the transmission line. (dB) e ABCD matrix of the parallel capacitor 12 is 3 = 10 cap12 1 , ( ) where cap12 = 12 . e ABCD matrices of the other capacitors and transmission lines follow in the same way, respectively.
According to matrix algebra the ABCD matrix of the whole circuit shown in Figure can be described as follows: = 1 2 3 4 5 6 7 8 = .
( ) e parameter matrix can be derived from the ABCD matrix as follows: e lengths of the transmission line sections TX 1 ,TX 2 , and TX 3 were set to . , . , and . wavelengths at GHz, respectively. Normally one would expect the length of the input and output lines of a lter to be identical. In this case,however,thelengthsofTX 1 and TX 3 are di erent. is is mainly caused by the asymmetry of the main resonator (formed by TX 2 and 2 ). e length of TX 3 is set shorter than that of TX 1 . is makes the passband bandwidth constant, across the entire tuning range. e characteristic impedance of TX 1 and TX 3 is set to Ω. echaracteristicimpedance International Journal of Antennas and Propagation of TX 2 , however, is set to Ω. is is necessary in order to achieve a high inductance value from a short length of transmission line. Figure s h o w st h ec a l c u l a t e dr e s u l t sf r o m( )u s i n g MATLAB . . It can be observed that the centre frequency of the passband can be tuned from . GHz to . GHz by varying the capacitance of 2 from pf to pf. e absolute dB bandwidth of this lter varies from MHz to MHz a c r o s st h et u n i n gr a n g e . e d Bb a n d w i d t hi sn e a r l yc o nstantasthecenterfrequencyofthepassbandischanged.

Microstrip Line Filter Design
A microstrip line tunable bandpass lter is developed based on transmission line circuit shown in Figure . estructure of the lter is shown in Figure . 0 and 4 are Ω transmission lines. Both of these lines are . mm wide and mm long. However the length of 0 and 4 has no impact on the performance of this design. 1 , 2 ,a n d 3 are resonant sections. elengthandwidthofthese resonantsectionsare optimized to provide constant bandwidth across the whole tuning range. 1 is . mm wide and . mm long. 2 is . mm wide and mm long. A mm by mm pad is introduced at the end of 2 nearest 1 . is pad provides a surface on which to solder the varactor diode. 3 is . mm wide and . mm long. e resonator within this lter is . mm long (i.e., nearly e /4 at . GHz). Two chip capacitors, labeled 1 and 3 (ATC S, = 3.3 pf),areusedtoconnectthe transmission lines 0 and 4 to 1 and 3 together. A second pair of chip capacitors, labeled 12 and 23 (ATC S, = 6.8 pf),areusedtoconnect 1 and 2 to the grounding vias.
Two kΩ RF-choke resistors are used to connect the resonator to the bias line. e lter is fabricated on a Taconic TLY-substrate (i.e., ℎ = 1.14 mm, = 2.33,a n dt a n = . ). An MV surface mount varactor diode, from MDT Corporation, was used in the prototype circuit. e relationshipbetweenthevoltageandthecapacitanceisgiven in Table . e equivalent series resistance of the varactor is . Ω.
e parameters of the microstrip line lter can be calculated using ( ), as mentioned earlier.
e ABCD matrix of the varactor diode can be represented as follows:

Figures (a) and (b)
show the scattering parameters obtained through simulation using CST MWS. e lter's passband centre frequency can be tuned from . GHz to . GHz by varying the reverse voltage applied to the varactor diode ( 2 ). e absolute dB bandwidth of this lter varies from MHz to MHz as the lter is tuned. e insertion loss is nearly . dB, and the return loss is better than dB across the whole tuning range. e capacitances of 12 and 23 control the loadedfactor of the lter (see Figure ). Increasing the capacitance increases the loaded -factor. In order to minimize the total number of varactors required and hence the overall insertion loss we demonstrate a -pole tunable bandpass lter. In a multipole bandpass lter these capacitors would provide a convenient way by which to vary the coupling coe cient over a wider range of values. It is also possible to control the bandwidth of the passband by tuning the coupling capacitance.

Measurement Results
Figure shows a prototype of the tunable bandpass lter. Two SMA connectors are soldered on each side of the lter. e reverse voltage is applied across the bias lines depicted in Figure .Agilen t VN Aisusedinthismeasuremen t. Figure (a) shows measured 21 results. e centre frequency of the passband can be tuned from . GHz to . GHz. e insertion loss varies from . dB to . dB as the lter is tuned throughout this range. e insertion loss is suppressed below − dB from . GHz to . GHz. According to the measurement results the dB bandwidth of the lter changes from MHz to MHz, as the lter is tuned throughout its full range. Compared with the simulation results, the measurement results indicate that the passband bandwidth o fthe l t erbeco mesna rr o w erasthe l t erist unedt o wa r ds higher frequencies. e insertion loss observed through the measurement is also higher than that predicted by simulation. ese di erences are mainly due to an increase in the parasitic resistance and inductance of the xed capacitors and the varactor diode. e simulation results show that the tuning range is restricted by the variation in the capacitance of the varactor diodes.
International Journal of Antennas and Propagation

Conclusion
is paper presents a new form of tunable bandpass lter with colinear resonators. Unlike many of the other tunable lters in the literature the lter is not based around coupled lines. e equivalent circuits of the new lter are analyzed. Experimental results show that the passband centre frequency can be tuned from . GHz to . GHz by varying the capacitance of the varactor from . pf to . pf.