research article reconfigurable ring filter with...

Research ArticleReconfigurable Ring Filter with ControllableFrequency Response

Norfishah Ab Wahab Mohd Khairul Mohd SallehZuhani Ismail Khan and Nur Emileen Abd Rashid

Microwave Technology Centre Faculty of Electrical Engineering Universiti Teknologi MARA (UiTM)40150 Shah Alam Selangor Malaysia

Correspondence should be addressed to Norfishah AbWahab fishahahuyahoocommy

Received 11 March 2014 Revised 16 June 2014 Accepted 17 June 2014 Published 8 July 2014

Academic Editor Run-Cang Sun

Copyright copy 2014 Norfishah AbWahab et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Reconfigurable ring filter based on single-side-access ring topology is presented Using capacitive tuning elements the electricallength of the ring can be manipulated to shift the nominal center frequency to a desired position A synthesis is developed todetermine the values of the capacitive elements To show the advantage of the synthesis it is applied to the reconfigurable filterdesign using RF lumped capacitors The concept is further explored by introducing varactor-diodes to continuously tune thecenter frequency of the ring filter For demonstration two prototypes of reconfigurable ring filters are realized using microstriptechnology simulated andmeasured to validate the proposed conceptThe reconfigured filter using lumped elements is successfullyreconfigured from 2GHz to 9844MHz and miniaturized by 71 compared to the filter directly designed at the same reconfiguredfrequency while for the filter using varactor-diodes the frequency is chosen from 110GHz to 138GHz spreading over 280MHzfrequency range Both designs are found to be compact with acceptable insertion loss and high selectivity

1 Introduction

Modern and integrated communication systems are pushingfor compact low cost with flexible design for front-endelectronic components This led to the evolution of band-pass filtersrsquo construction with various types of topologiesand technologies Amongst these miniaturized and tunablebandpass filters have the potential for further improvementto fit the advancement of technology with rigid specifica-tions in communication systems Numerous techniques havebeen explored and amongst these are high performancereconfigurable filters with simple topology fast tuning speedsharp rejection skirt for high selectivity and compact sizethat received great interests [1ndash4] Well-established tuningmethods made use of devices such as RF microelectricalmechanical systems (MEMS) and ferroelectric-based andmagneto-electric devices using Yttrium Iron Garnet films(YIG) and reactive elements were reported in [1ndash6] Undeni-ably various resonator shapes or topologies can be designed

easily but it is not a simple task to couple these elementson a microstrip resonator The tuning elements must becarefully arranged and coupled to the resonator to minimizethe filter size and losses Furthermore most of the work didnot elaborate or neglect the synthesis part which is importantfor flexible design [7ndash11]

Therefore this paper proposed a simple topology usingsingle-side-access ring resonator as a base cellThe advantageof this single-side-access ring resonator is its compactnessand simple configuration with minimum number of control-ling parameters besides high selectivity characteristic Thering is mounted with capacitive elements and by varyingthe values of capacitive elements the frequency response canbe reconfigured to a desired position A complete synthesisis presented in order to control the position of centerfrequency or transmission zero while capacitance values ofthe capacitive elements and the odd-mode impedance areautomatically calculated using the synthesis To demonstratethe concept two methods are proposed

Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 671369 11 pageshttpdxdoiorg1011552014671369

2 The Scientific World Journal

Cr Cr

Cr

Cr

Zr

Zr

Zrlr

lr

lr

Zoe Zoo

(a)

Frequency (GHz)

Nominalresponse

Shifted response

0

minus10

minus20

minus30

minus40

minus50

S11S12

fominusx fo = 2GHz

S-pa

ram

eter

s (dB

)

(b)

Figure 1 Reconfigurable ring filter electrical length 119897119903 and four shunted capacitors designed at center frequency 119891

119900= 2GHz for 119885

119903= 85Ω

119885119900119890= 70Ω 119885

119900119900= 35Ω and 119862

119903= 1 pF (a) Topology and (b) frequency responses

The first method applies RF lumped capacitors as thetuning element This filter is designed at higher centerfrequency 119891

119900and by varying the value of the capacitor the

nominal center frequency can be shifted to a desired positionwhich is lower than the nominal center frequency at 119891

119900119903 The

advantage of this design is that the position of reconfiguredcenter frequency can be fixed to a desired position whilethe value of the capacitors and the odd-mode impedanceare calculated automatically using the synthesis Impedancematching can be achieved by adjusting the impedance valuesof the ring The filter is miniaturized up to 71 comparedto the ring filter designed directly at the same reconfiguredcenter frequency 119891

119900119903

To further explore the tuning aspect of the reconfigurablefilter varactor-diode with biasing circuit is introduced as thetuning element to electronically tune the center frequencyof the ring filter The advantage of this method is that evenwith a small capacitance values the circuit is capable of tun-ing continuously to create a frequency-agile characteristicFinally both designs are realized on microstrip substratessimulated and measured using EM solvers to demonstratethe idea

2 Design of Reconfigurable Ring Filter

A ring resonator is shunted with four capacitive elements119862119903

at the edges of the ring lines to vary the nominal electricallength 119897

119903 of the ring The variation of electrical length

depends on the variation values of 119862119903to reconfigure the

nominal center frequency to a new position As shown inFigure 1(a) the ring is reconfigured with a set of chosenimpedances as follows ring impedance 119885

119903= 85Ω even-

mode impedance 119885119900119890= 70Ω and odd-mode impedance

119885119900119900= 35Ω while the tuning element known as reconfigured

capacitor 119862119903 is chosen to be equal to 1 pF Figure 1(b) illus-

trates the frequency responses between the reconfigured ringand the nominal ring without the four reactive elements Asobserved the nominal center frequency 119891

119900 is reconfigured

to the left at 119891119900-119909 due to the changes in electrical length of the

ring lines

21 Equivalent Circuit and Synthesis Applying the definitionsand parameters of a 3-port coupled-line section given by[12ndash14] a simplified circuit diagram of the reconfigured ringresonator is constructed as shown in Figure 2(a)

The definitions of transformer 119879 the unit element 119884ueand the coupling capacitor 119884

119888are given in (1) to (5) to

represent the 3-port coupled-line section while the 3119885119903and

reconfigured capacitor 119862119903represent the ring lines and the

tuning elements respectively Running a circuit simulation ofthe diagram in Figure 2(a) with the same value of impedancesgiven earlier in Figure 1(a) where 119891

119900= 2GHz 119885

119903= 85Ω

119885119900119890= 70Ω 119885

119900119900= 35Ω and 119862

119903= 1 pF will give the same

results as shown in Figure 2(b)

119884ue = 11988411 minus11988412

2

11988411

(1)

119884119888= 119895 tan

120587119891tz2119891119900

11988411 (2)

11988411=(1119885119900119900+ 1119885

119900119890)

2 (3)

11988412=(1119885119900119900minus 1119885

119900119890)

2 (4)

119879 =11988411

11988412

(5)

Next the reconfigured equivalent circuit in Figure 2(a) issimplified forming a quadripole admittancematrix119884

119877 of the

closed-loop while transformer 119879 and admittance 119884119888 at the

outer section are as depicted in Figure 3At this stage we need to determine the controlling

parameters that influence the position of transmission zeros

The Scientific World Journal 3

1

Input

32 1 Output

Cr Cr

CrCr

Zr

Zr Zr

1205824

1205824

1205824

1205824

Yc

Yue

T

(a)

Frequency (GHz)

Reconfigured resonance

0

1

Reconfigured transmission

05

S11

S12

fo = 2GHz

minus10

minus20

minus30

minus40

frequency for

S-pa

ram

eter

s (dB

)

zero ftzr

(b)

Figure 2 (a) Equivalent circuit diagram of a reconfigurable ring resonator and (b) reconfigured frequency response

and the characteristic performance of the nominal ringTherefore the quadripole admittance matrix of the closed-loop for the nominal ring is termed as matrix 119884 and can bewritten as follows

119884 = [11988411

11988412

11988412

11988411

]

11988411=(4 cos (120579)2 minus 3 + 4119884ue119885119903 cos (120579)

2

minus 119884ue119885119903) cos 120579

119895119885119903sin 120579 (4 cos (120579)2 minus 1)

11988412= minus

1 + 4119861119884ue119885119903cos (120579)3

minus 119861119884ue119885119903 cos 120579(4cos (120579)2 minus 1) 119895119885

119903sin 120579

(6)

with a term given as follows

119861 =(tan (120579)2 + 1)

radic1 + tan (120579)2 (7)

Hence the position of nominal transmission zero 119891tz can bedetermined by equating the 119884

12= 0 resulting in

1 + 4119862119884ue119885119903cos (120579)3

minus 119862119884ue119885119903 cos 120579 = 0 (8)

Next the electrical length of the nominal transmission zeroat the lower side can be expressed as follows

120579tz = arccos(radic1 minus 119884ue1198851199031 + 119884ue119885119903

) (9)

Similarly the electrical length of the nominal transmissionzero can also be represented as

120579tz =120587119891tz2119891119900

(10)

1

Input

32

1 OutputTYC

YR

Figure 3 Simplified reconfigured equivalent circuit diagram with aquadripole admittance matrix 119884

119877

Therefore applying (10) and (11) and for a given nominaltransmission zero frequency119891tz the admittance unit element119884ue can also be written as

119884ue = minus1

(minus1 + 4 cos ((12) (120587119891tz119891119900))2

)119885119903

(11)

Finally 119885119900119900can be written as

119885119900119900= 119885119900119890(2119885119900119890minus 119884ue

119884ue) (12)

At this stage the nominal ring can be constructed at arbitrarycenter frequency119891

119900 with a chosen set of impedance values of

119885119903and 119885

119900119890 while 119885

119900119900is calculated using (12) The next step

is to synthesize the ring circuit with reconfigured capacitor119862119903 shunted at the four edges of the ring line The purpose

of this procedure is to determine the reconfigured frequencyresponse and at the same time calculate the required valuesof capacitor 119862

119903 using the synthesis

Next we need to identify the controlling parameters thatinfluence the shifting of the frequency By solving the matrixelements of the middle quadripole admittance matrix 119884

119877 of

the reconfigurable ring circuit in Figure 3 one can express interms of ABCD-matrix the circuit as follows

119884119877= [

11988411119903

11988412119903

11988412119903

11988411119903

] (13)


12 07 16Frequency (GHz)

0

minus20

minus40

minus60

minus80884MHz

922MHz955MHz

Cr = 304pFCr = 270pF

Cr = 243pF

S-pa

ram

eter

s-S 1

2(d

B)

(a)

07 14Frequency (GHz)

0

1209

minus20

minus40

Cr = 304pFCr = 270pFCr = 243pF

1132GHz 629dB

1178GHz 703dB

1220GHz 772dB

S-pa

ram

eter

s-S 1

1(d

B)

(b)

Figure 4 Frequency responses for three different positions of transmission zeros 119891tz119903 and capacitor 119862119903 is automatically calculated using

the synthesis (a) 11987812and (b) 119878

11

Table 1 Simulated response of a reconfigurable ring resonator designed at center frequency 119891119900= 2GHz with the value of impedances given

by 119885119903= 85Ω 119885

119900119890= 70Ω and 119885

119900119900= 35Ω

Initial setting of reconfiguredtransmission zero 119891tzr1 (GHz) Calculated 119862

119903(pF) Simulated reconfigured responses

Transmission zero 119891tzr2 (GHz) 119891119900119903(GHz)

100 243 0955 12200900 270 0922 11780800 304 0884 1132

Then by solving the quadripole admittance matrix 119884119877 the

reconfigured capacitor 119862119903 can be deduced This is achieved

by equating 11988412119903

= 0

11988412119903

= 4119885119903

2

1205872

119891tz1199032

119862119903

2

119876minus1

(1 minus cos (120579)2)

minus 119875 cos (120579) + 119876minus1 (4119885119903

2

1205872

119891tz1199032

119862119903

2

+ 1)

+ 44119885119903

2

1205872

119891tz1199032

119862119903

2(12) sin (120579)2 cos (120579)2 = 0

(14)

Finally by manipulating (14) it leads to the determination ofreconfigured capacitor119862

119903 which can be expressed as follows

119862119903= minus

119876cos (120579)2 + 119875 cos (120579) minus 119876 minus 2119876119885119903120587119891tz119903 cos (120579) sin (120579)

119876119885119903

2

1205872119891tz1199032 sin (120579)2

(15)

And introducing the terms below to simplify the aboveequation

119875 = radic1 + tan (120579)2

119876 = minus1

minus1 + 4 cos ((12) (120587119891tz1198910))2

(16)

This also means that by fixing the lower side of nominaltransmission zero position119891tz the impedances can be chosen

arbitrarily for a nominal center frequency119891119900 by the designer

one can estimate the value of 119862119903and odd-mode impedance

119885119900119900

which is calculated automatically by (15) and (12)respectively with respect to the position of reconfiguredtransmission zero 119891tz119903

22 Application of Synthesis to Control the Position of Trans-mission Zero An example of reconfigurable ring filter isdesigned with a chosen set of impedances given as follows119885119903

= 85Ω and 119885119900119890

= 70Ω and given by (12) 119885119900119900

is equal to 35 Ω at a nominal center frequency of 2GHzand transmission zero frequency 119891tz at 16 GHz In thissimulation the synthesis is applied and the reconfiguredtransmission zero 119891tz1199031 is set at three different positionswhich are 1 GHz 09GHz and 08GHz Based on 119891tz1199031 thevalues of the capacitors119862

119903 are automatically calculated using

(15)Figures 4(a) and 4(b) depict the frequency responses for

three different sets of reconfigured transmission zero Withapplication of the synthesis different position of reconfiguredtransmission zero gives different value of 119862

119903 The lower the

position of transmission zero is the higher the 119862119903value will

beTable 1 summarized the values of initial setting of recon-

figured transmission zero frequency 119891tz1199031 calculated capaci-tor119862119903 and simulated reconfigured responses of transmission

zero frequency 119891tz1199032 and reconfigured center frequency


Table 2 Summary of values with adjustment impedances 119885119903= 80Ω and 119885

119900119890= 75Ω while 119885

119900119900is automatically calculated to be equal to

35066Ω

Return loss beforeadjustment (dB) Return loss after adjustment (dB) Position of simulated reconfigured center frequency 119891

119900119903

Before adjustment (GHz) After adjustment (GHz)772 dB 3438 dB 1220 1202703 dB 2508 dB 1178 1160629 dB 1997 dB 1132 1114


0

1209 14 16

Before impedance matchingAfter impedance matching

minus20

minus40

minus60

minus80


S-pa

ram

eter

s-S 1

1(d

B)

Figure 5 Comparison of frequency responses between initial andafter impedances modification for 119878

11

119891119900119903 It can be observed that the simulated reconfigured

transmission zeros119891tz1199032 are not at the same positionwith theinitial setting of reconfigured transmission zeros 119891tz1199031 Thisis due to the fact that as the frequency shifted to the left thenominal bandwidth is not conserved anymore Therefore itis easier and more advantageous to control the reconfiguredcenter frequency than the transmission zeros

It can also be observed that the shifting of frequenciesis accompanied by in-band matching problem Thereforeone needs to be cautious in handling the losses duringthe implementation stage with some adjustment needed tobe done on the impedance values of the ring Figure 5illustrates the performance of return loss before and after theadjustment of impedances 119885

119903and 119885

119900119890 It can be seen that

the return loss has improved exceeding 19 dB when both 119885119903

and 119885119900119890are adjusted for impedance matching as compared

to the earlier response in Figure 4 However one has to takenote that with a different set of impedances the positionof center frequency may change accordingly Finally returnloss and center frequencies before and after adjustments aresummarized in Table 2

23 Tuning and Application of Synthesis In a tunable schemeit is an advantage if one can determine the position ofreconfigured center frequency 119891

119900119903 To achieve this theory of

Frequency (GHz)Nominal

frequencyReconfigured center

frequency

BWS-pa

ram

eter

s (dB

)

BWr

for ftz foftzr fo + (fo minus ftz)

Figure 6 Bandwidth of the nominal and reconfigured filter

relative bandwidth (RBW) is applied here in a function ofnominal center frequency 119891

119900 and transmission zero 119891tz

RBW =BW119891119900

=2 (119891119900minus 119891tz)

119891119900

(17)

where BW is bandwidth of the nominal filterUsing relative bandwidth (RBW) concept in (17) relative

bandwidth of reconfigured filter RBW119903 can be written as

follows

RBW119903=BW119903

119891119900119903

= 2(119891119900119903minus 119891tz119903119891119900119903

) (18)

whereby BW119903is bandwidth of reconfigured filter with BW gt

BW119903as illustrated in Figure 6

Therefore to estimate the position of reconfigured centerfrequency 119891

119900119903 an assumption has to be made on the recon-

figured relative bandwidth RBW119903 For calculation purpose

let us assume that the relative bandwidth RBW is alwaysconsistent at any arbitrary center frequency119891

119900Therefore the

reconfigured relative bandwidth RBW119903 can be assumed to be

approximately equal to relative bandwidth of nominal filter asfollows RBW

119903asymp RBW

By using the expressions in (17) and (18) this can bewritten as follows

RBW119903asymp RBW 997904rArr 2119891

119900

(119891119900minus 119891tz)

119891119900

asymp 2119891119900119903(119891119900119903minus 119891tz119903119891119900119903

)

(19)


03 10

0

0705Frequency (GHz)

x = 1 Cr = 3527pF

x = 0805 Cr = 3328pF

minus20

minus40

minus60

minus80

S-pa

ram

eter

s (dB

)

Figure 7 Application of synthesis frequency responses

Hence by manipulating (19) the reconfigured center fre-quency 119891

119900119903 can be equated as follows

119891119900119903asymp2119891tz119903119891119900119891tz

(20)

Taking into account the reconfigured relative bandwidthRBW119903 is only an approximationwhich is assumed to be equal

to the relative bandwidth RBWTherefore to compensate theapproximation and obtain a symmetrical response 119891

119900119903has to

be factorized with a tuning parameter of 119909 In other words(20) can now be written as follows

119891119900119903asymp 2(

119891tz119903119891119900119891tz

)119909 (21)

Somehow to have a good control on filter design it ispractical for the designer to be able to set the position ofreconfigured center frequency 119891

119900119903 Therefore we introduced

a term 119877119900119888 as a ratio of reconfigured center frequency 119891

119900119903

and nominal center frequency 119891119900 and this can be expressed

as follows

119877119900119888=119891119900119903

119891119900

(22)

Finally we can apply the synthesis and predetermine the posi-tion of reconfigured center frequency 119891

119900119903 with initial tuning

parameter 119909 is assumed to be 1 Example of application ofthe synthesis is simulated with a chosen set of impedancesgiven by 119885

119903= 85Ω and 119885

119900119890= 70Ω and given by (12)

119885119900119900

is equal to 35Ω designed at center frequency 119891119900 of

1 GHz Capacitor 119862119903 is automatically calculated using (15) to

be equal to 3527 pF The nominal position of transmissionzero 119891tz is fixed at 083GHz while tuning parameter 119909 istuned accordingly to obtain a symmetrical response Theresponses according to variation of 119909 are depicted in Figure 7and summarized in Table 3 It can be seen that at initial valueof tuning parameter 119909 = 1 the reconfigured center frequencyfalls at 668MHz while the passband responses exhibit poor

Table 3 Summarized values for reconfigured ring designed atnominal center frequency 119891

119900= 1GHz nominal transmission zero

119891tz = 083GHz and 119877oc = 070

Parameter 119909 100 0805119885119903 119885119900119900(Ω) 8500 3500 7500 3462

119885119900119890(Ω) 70 70

Reconfigured centerfrequency 119891

119900119903(GHz) 0668 0700

Calculated 119862119903(pF) 353 3328

Table 4 Summary of frequency responses on ideal circuit designedat 2GHz 119877oc = 05

119909 = 1 119909 = 13

Simulated 119891119900119903

0871 GHz 0984GHz119885119903 119885119900119890 119885119900119900(Ω) 85 70 35 99 92 32

Calculated 119862119903

252 pF 275 pF

matching level When tuning parameter 119909 is tuned to 0805the center frequency is reconfigured to 07GHz To improvethe matching level the impedances are modified as followsby fixing 119885

119900119890 119885119903is modified to 75Ω while 119885

119900119900is recalculated

using (12) and equal to 3462Ω while the value of capacitor119862119903 is given by (15) to be equal to 3328 pF

3 1st Design Using Lumped Capacitors

For demonstration a ring filter using four RF lumped capac-itors as tuning element to reconfigure its center frequencyis proposed The circuit is designed at 119891

119900= 2GHz with

transmission zero119891tz fixed at 16 GHzwhile the reconfiguredcenter frequency 119891

119900119903 is set at 1 GHz The impedances of the

ring resonator are given with values of 119885119903= 85Ω and 119885

119900119890=

70Ω and 119885119900119900

given by (12) equals 35 Ω while capacitor 119862119903

is given by (15) to be equal to 252 pF At initial stage let ussimulate the ideal circuit with parameters set as follows 119909 = 1and 119877

119900119888= 05 As shown in Figure 8 the frequency response

shifted to the left with lower- and upper-side transmissionzeros which are found at 675MHz and 948MHz respectivelywhile the reconfigured center frequency 119891

119900119888 is found at

0871 GHz with attenuation of 293 dB levelHowever this ideal circuit must be tuned to obtain the

position of reconfigured center frequency 119891119900119903 at 1 GHz

This can be achieved by tuning parameter 119909 from 1 to 13For impedance matching 119885

119903is modified to 99Ω 119885

119900119890is

equal to 92Ω and 119885119900119900

is automatically calculated using(12) to be equal to 32Ω while capacitor 119862

119903is given by

(15) to be equal to 275 pF As observed in Figure 8 theposition of reconfigured center frequency 119891

119900119903 is shifted to

0984GHzwith attenuation level improved to be 1737 dBThemodified lower- and upper-side transmission zeros are foundat 780MHz and 1103GHz respectively Table 4 summarizedthe reconfigured center frequencies and capacitance valuesaccording to tuning parameter 119909 The calculated 119862

119903is used


0

05 14 Frequency (GHz)

minus20

minus40

minus60

minus80

S 12-p

aram

eter

s (dB

)

x = 1 Cr = 252pF

x = 13 Cr = 275pF

fo = 10

(a)

Frequency (GHz)

0

07 12

S 11-p

aram

eter

s (dB

)

x = 1 Cr = 252pF

x = 13 Cr = 275pF

minus20

minus40fo = 10

(b)

Figure 8 Simulated frequency responses of the reconfigurable ring resonator on ideal circuit using RF lumped capacitors designed at 2GHz119891tz = 16GHz with 119877

119900119888= 05

Ground Ground

Ground

Ground

RF inRF out

L1

L2

Wr

Wc s

(a) (b)

Figure 9 (a) Final layout of the reconfigurable ring bandpass filter (b) fabricated photo

as an estimation to choose a suitable value of the capacitorfor the implementation of reconfigurable filter on microstripsubstrate

31 Implementation and Results During implementation ofthe filter on microstrip substrate once again the value of thereconfigured capacitor 119862

119903needs to be adjusted This is due

to the effect of connecting pads (to connect the four lumpedcapacitors to the ring resonator) via holes bonding wiressoldering and the availability of the RF lumped capacitorvalue available in the market Based on the calculation of119862119903in the previous discussion RF lumped capacitor with

22 pF is chosen The final layout of the circuit is illustratedin Figure 9(a) with dimensions tabulated in Table 5

The circuit is then implemented using microstrip tech-nology on substrate Tachonic with characteristics given by120576119903= 45 ℎ = 163mm and tan 120575 = 00035 As proved by

work a picture of fabricated reconfigurable ring filter is put

Table 5 Dimensions of the reconfigurable ring filter on Tachonic

Length1198711

(mm)

Length1198712(mm)

Ring width119882119903(mm)

Coupling width119882119888(mm)

Coupling gap119904 (mm)

2400 1895 227 190 040

on view as shown in Figure 9(b) with dimensions tabulatedin Table 5

The simulated and measured frequency responses aredepicted in Figures 10(a) and 10(b) respectively As observedthe simulated reconfigured center frequency attenuates at0985GHz with return loss of 1672 dB and insertion loss of205 dB Two transmissions zeros are found at 921MHz and109GHz with fractional bandwidth of 173 The measure-ment results show that the reconfigured center frequency fallsat 0984GHz and attenuates at 2078 dB level with insertionloss about 3 dB while the two transmission zeros are found


Simulated responseMeasured response

08 12

0

Frequency (GHz)

minus10

minus20

minus30

minus40

minus50

minus60

S 12-p

aram

eter

s (dB

)

(a)

Frequency (GHz)

0

08 12

minus10

minus20

minus30

minus40

minus50

S 11-p

aram

eter

s (dB

)


(b)

Figure 10 Final responses on microstrip for reconfigurable filter using four capacitors (a) simulated and measured 11987811 (b) simulated and

measured 11987812

(a) (b)

Figure 11 Comparison between filters (a) reconfigurable ring filter designed at 2GHz and (b) single mode directly designed at 1 GHz

Table 6 Dimensions of the two filters on Tachonic

Ring filter 119891119900(MHz) Insertion loss (dB) Length (um) Width (um) Total dimension (um2)

Reconfigured at 1 GHz 9844 300 6504 3005 195430Directly designed at 1 GHz 9900 187 12294 5464 671717

at 9494MHz and 1104GHz with fractional bandwidth of203

Finally the reconfigurable filter is compared in terms ofsize with ring filter directly designed at 1 GHz As illustratedin Figures 11(a) and 11(b) the size of reconfigurable ring filteris greatly reduced and miniaturization has been achieved upto 71 compared to the ring filter directly designed at 1 GHzThe dimensions of the two filters are summarized in Table 6

4 2nd Design Using Varactor-Diodes

The reconfigurable filter of the ring resonator is furtherexplored for tunable filter application using four varactor-diodes to electronically and continuously tune the centerfrequency Each varactor-diode is mounted on themicrostripring resonator circuit via biasing circuit which consists of RF

choke resistor 119877dc and DC block capacitor 119862dc DC biasedvoltage is applied to every diode via the resistor 119877dc Thusthe 119877dc has to be large enough to minimize signal leakageSubsequently the capacitor 119862dc has to be sufficient enoughto function as DC block to block the DC bias from flowing tothe resonator Finally every biasing circuit is designed withresistor 119877dc equal to 20 kΩ and capacitor 119862dc equal to 1 nFThe varactors are grounded via hole by drilling themicrostripsubstrate and the connections are made from varactors to theground plane using bond wires

41 Implementation and Results For implementation thevaractor-diode model Skyworks SMV1800 is chosen withspecifications given as follows tuning capacitance (119862

119869) =

145 pF package capacitance (119862119875) = 09 pF bulk resistance


RF inRF out

Varactor

Via hole

VaractorVia hole

Varactor

Via hole

Varactor

Via hole

Vdc

Vdc

Vdc

Rdc

Rdc

Rdc Rdc

Cdc

Cdc

Cdc Cdc

Wr

Lr

Lr1

Wcs

+minus

+minus

+minus

(a) (b)

Figure 12 (a) Layout of the electronically reconfigurable ring bandpass filter using four Skyworks SMV 1800 varactors for impedances119885119903= 80Ω 119885

119900119890= 75Ω and 119885

119900119900= 30Ω (b) photo of fabricated filter

Table 7 Dimensions of ring filter designed at 2GHz and biasing components

Length 119871119903(mm) Length 119871

1199031(mm) Coupling width119882

119888(mm) Width ring119882

119903(mm) Gap s (mm) 119877dc (kΩ) 119862dc (nF)

2250 2020 230 140 024 2000 100

Table 8 Measured responses of reconfigurable ring filter designed at 2GHz

DC supply voltage Poles (GHz) Transmission zeros (GHz) Insertion loss (dB) Return loss (dB) FBW 10 volt 110 096 123 312 2896 930 volt 138 119 160 156 1862 10

(119877119878) = 25 ohm and package inductance (119871

119878) = 08 nH

[15]This model is chosen because of the range of capacitanceeffect of the varactor which is sufficient to tune the filterfrom 2GHz to a desired minimum center frequency of 1 GHz(using (15) 119862

119903is approximately equal to 2 pF)

The electronically reconfigurable circuit is designed at2GHz with a chosen set of impedances given by 119885

119903= 80Ω

119885119900119890= 75Ω and 119885

119900119900= 30Ω The proposed reconfigurable

ring bandpass filter is designed using four varactors with bias-ing circuits which are loaded at the edge of the ring resonatorto create capacitance effect to the ring resonator The circuitis implemented using microstrip technology and substrateTachonic with characteristics given by 120576

119903= 45 ℎ = 163mm

and tan 120575 = 00035 The final layout of the filter is depictedin Figure 12(a) with dimensions summarized in Table 7 and apicture of the prototype microstrip reconfigurable bandpassfilter is shown in Figure 12(b) as proved by work

For a successful reconfigurable filter design there hasto be a trade-off between tunability dynamic range andloss to ensure high filter performance Therefore acceptablelevels of the frequency responses are chosen in the rangefrom 10V to 30V only From the simulation it shows thatwhen DC bias voltage is at 10V the insertion loss is 289 dBand the return loss is 2249 dB found at 109GHz Thetwo transmission zeros exist at 986MHz and 117 GHz with

fractional bandwidth of 4 When DC bias voltage is at 30Vthe center frequency is found at 137GHz with insertionloss at 105 dB and return loss at 2398 dB Two transmissionzeros are obtained at 122GHz and 151 GHz respectivelygiving a fractional bandwidth of 5The simulated frequencyresponses are illustrated in Figures 13(a) and 13(b)

The measured results are shown in Figures 14(a) and14(b) The passband characteristics have an insertion lossof 312 dB and return loss of 2896 at 110GHz when theforward bias is at 10V Two transmission zeros are obtainedat 960MHz and 123GHz respectively with fractional band-width of 9 At forward bias of 30V the insertion loss is156 dB while the return loss is 1862 dB at 138GHz Twotransmission zeros are obtained at 119 GHz and 160GHzwith fractional bandwidth of 10

In general it is difficult to control both frequencyresponses and bandwidths along the tuning range Assummarized in Table 8 the measured fractional bandwidth(FBW) is about 10 which is doubled as compared tothe simulated FBW in Figure 13 Some possible techniquesfor better control of bandwidth such as coupling of thenonresonant transmission line of the filter could be employedfor future improvement [16] In terms of tunability the centerfrequencies are spreading over 280MHz which gives 25achievable tuning range while the insertion losses from 30V


12

0


minus20

minus40

10 volts14 volts18 volts 22 volts

26 volts30 volts

S-pa

ram

eter

s (dB

) (S 1

2)

(a)

12

0


minus20

minus40

10 volts

14 volts

18 volts

22 volts26 volts

30 volts

S-pa

ram

eter

s (dB

) (S 1

1)

(b)

Figure 13 Tuning range from 10V to 30V of the electronically bandpass filter for (a) simulated 11987812and (b) simulated 119878

11

10Frequency (GHz)

0

1812 14 1608

10 volts14 volts

18 volts 22 volts26 volts30 volts

S-pa

ram

eter

s (dB

) (S 1

2) minus10

minus20

minus30

minus40

minus50

(a)

Frequency (GHz)

0

1810 12 14 16

10 volts14 volts

18 volts22 volts26 volts

30 volts

minus20

minus40

S-pa

ram

eter

s (dB

) (S 1

1)

(b)

Figure 14 Measured frequency responses for tuning range from 10V to 30V (a) 11987812and (b) 119878

11

to 10V are in the range of 156 dB to 312 dB which are withinthe acceptable specification As can be observed there aredifferences between the simulated and measured insertionlosses This can be attributed to tolerances in the componentvalues and fabrication process

5 Conclusion

This paper explored the use of ring-based resonator topologyto develop reconfigurable ring filters This study had proventhat the nominal center frequency of the ring filter can betuned by introducing capacitive elements which had createdvariation of electrical length to the ring lines Synthesis waspresented to control the position of reconfigurable centerfrequency or transmission zero while the value of capacitiveelements and the odd-mode impedance are automatically

calculated For demonstration two reconfigurable filters wereproposed using two different tuning techniques The firstprototype made use of four lumped capacitors and thenominal center frequencywas successfully reconfigured from2GHz to 9844MHz with narrow fractional bandwidth of203 In terms of size this filter was successfully reducedby 71 compared to the filter designed directly at 1 GHzThe second prototype made use of hyperabrupt junctionvaractor-diodes Skywork SMV1800 and the nominal centerfrequency was tuned in the chosen range of 110GHz to138GHz spreading over 280MHz frequency range withachievable tuning range of 25 and fractional bandwidthbelow 10 The frequency responses for both filters hadshown good passband response high selectivity with twofinite transmission zeros and narrow bandwidth throughoutthe tuning range Finally both prototypes were simulated andmeasured to validate the concept


Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The authors would like to thank Ministry of EducationMalaysia and Research Management Institute (RMI) Uni-versiti Teknologi MARA with Grant no 600-RMI-NRGS53(32013) for funding this project

References

[1] R Saal and E Ulbrich ldquoOn the design of filters by synthesisrdquoIRE Transactions on Circuit Theory vol 5 pp 284ndash327 1958

[2] G Matthaei L Young and E M T Jones MicrowaveImpedance-Matching Networks and Coupling Structures ArtechHouse Norwood Mass USA 1985

[3] I C Hunter and J D Rhodes ldquoElectronically tuneablemicrowave bandpass filtersrdquo IEEE Transactions on MicrowaveTheory and Techniques vol 30 no 9 pp 135ndash136 1982

[4] J Long C Li W Cui J Huangfu and L Ran ldquoA tunablemicrostrip bandpass filter with two independently adjustabletransmission zerosrdquo IEEE Microwave and Wireless ComponentsLetters vol 21 no 2 pp 74ndash76 2011

[5] S W Fok P Cheong K W Tam and R P Martins ldquoA novelmicrostrip square-loop dual-mode bandpass filter with simulta-neous size reduction and spurious response suppressionrdquo IEEETransactions on Microwave Theory and Techniques vol 54 no5 pp 2033ndash2040 2006

[6] S L Delprat J Oh F Xu et al ldquoFully distributed tunablebandpass filter based on Ba

05Sr05TiO3thin-film slow-wave

structurerdquo International Journal of Microwave Science andTechnology vol 2011 Article ID 468074 9 pages 2011

[7] Y Chiou and G M Rebeiz ldquoTunable 155ndash21 GHz 4-poleelliptic bandpass filter with bandwidth control and gt50 dBrejection for wireless systemsrdquo IEEE Transactions onMicrowaveTheory and Techniques vol 61 no 1 pp 117ndash124 2013

[8] R Mao X Tang and F Xiao ldquoMiniaturized dual-mode ringbandpass filters with patterned ground planerdquo IEEE Transac-tions on Microwave Theory and Techniques vol 55 no 7 pp1539ndash1546 2007

[9] A Miller and J-S Hong ldquoReconfigurable cascaded coupledline filter with four distinct bandwidth statesrdquo IET MicrowavesAntennas and Propagation vol 5 no 14 pp 1730ndash1737 2011

[10] H-WHsu C-H Lai and T-GMa ldquoAminiaturized dual-modering bandpass filterrdquo IEEEMicrowave andWireless ComponentsLetters vol 20 no 10 pp 542ndash544 2010

[11] MA El-Tanani andGMRebeiz ldquoA two-pole two-zero tunablefilter with improved linearityrdquo IEEE Transactions on MicrowaveTheory and Techniques vol 57 no 4 pp 830ndash839 2009

[12] H Ozaki and J Ishii ldquoSynthesis of a class of strip-line filtersrdquoIRE Transactions on Circuit Theory vol 5 no 2 pp 104ndash1091958

[13] Y Nemoto K Kobayashi and R Sato ldquoGraph transformationsof nonuniform coupled transmission line networks and theirapplicationrdquo IEEE Transactions on MicrowaveTheory and Tech-niques vol 33 no 11 pp 1257ndash1263 1985

[14] R Sato and E G Cristal ldquoSimplified analysis of cou-pled transmission-line networks and their application (Short

Paper)rdquo IEEE Transactions on Microwave Theory and Tech-niques vol 18 no 3 pp 122ndash132 1970

[15] Skyworks Solution Datasheet for SMV-1232 httpwwwsky-worksinccomfor SMV-1232

[16] N Zahirovic S Fouladi R R Mansour and M Yu ldquoTunablesuspended substrate stripline filters with constant bandwidthrdquoin Proceedings of the IEEE MTT-S International MicrowaveSymposium (IMS rsquo11) June 2011

International Journal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



Cr Cr

Cr

Cr

Zr

Zr

Zrlr

lr

lr

Zoe Zoo

(a)

Frequency (GHz)

Nominalresponse

Shifted response

0

minus10

minus20

minus30

minus40

minus50

S11S12

fominusx fo = 2GHz

S-pa

ram

eter

s (dB

)

(b)

Figure 1 Reconfigurable ring filter electrical length 119897119903 and four shunted capacitors designed at center frequency 119891

119900= 2GHz for 119885

119903= 85Ω

119885119900119890= 70Ω 119885

119900119900= 35Ω and 119862

119903= 1 pF (a) Topology and (b) frequency responses

The first method applies RF lumped capacitors as thetuning element This filter is designed at higher centerfrequency 119891

119900and by varying the value of the capacitor the

nominal center frequency can be shifted to a desired positionwhich is lower than the nominal center frequency at 119891

119900119903 The

advantage of this design is that the position of reconfiguredcenter frequency can be fixed to a desired position whilethe value of the capacitors and the odd-mode impedanceare calculated automatically using the synthesis Impedancematching can be achieved by adjusting the impedance valuesof the ring The filter is miniaturized up to 71 comparedto the ring filter designed directly at the same reconfiguredcenter frequency 119891

119900119903

To further explore the tuning aspect of the reconfigurablefilter varactor-diode with biasing circuit is introduced as thetuning element to electronically tune the center frequencyof the ring filter The advantage of this method is that evenwith a small capacitance values the circuit is capable of tun-ing continuously to create a frequency-agile characteristicFinally both designs are realized on microstrip substratessimulated and measured using EM solvers to demonstratethe idea

2 Design of Reconfigurable Ring Filter

A ring resonator is shunted with four capacitive elements119862119903

at the edges of the ring lines to vary the nominal electricallength 119897

119903 of the ring The variation of electrical length

depends on the variation values of 119862119903to reconfigure the

nominal center frequency to a new position As shown inFigure 1(a) the ring is reconfigured with a set of chosenimpedances as follows ring impedance 119885

119903= 85Ω even-

mode impedance 119885119900119890= 70Ω and odd-mode impedance

119885119900119900= 35Ω while the tuning element known as reconfigured

capacitor 119862119903 is chosen to be equal to 1 pF Figure 1(b) illus-

trates the frequency responses between the reconfigured ringand the nominal ring without the four reactive elements Asobserved the nominal center frequency 119891

119900 is reconfigured

to the left at 119891119900-119909 due to the changes in electrical length of the

ring lines

21 Equivalent Circuit and Synthesis Applying the definitionsand parameters of a 3-port coupled-line section given by[12ndash14] a simplified circuit diagram of the reconfigured ringresonator is constructed as shown in Figure 2(a)

The definitions of transformer 119879 the unit element 119884ueand the coupling capacitor 119884

119888are given in (1) to (5) to

represent the 3-port coupled-line section while the 3119885119903and

reconfigured capacitor 119862119903represent the ring lines and the

tuning elements respectively Running a circuit simulation ofthe diagram in Figure 2(a) with the same value of impedancesgiven earlier in Figure 1(a) where 119891

119900= 2GHz 119885

119903= 85Ω

119885119900119890= 70Ω 119885

119900119900= 35Ω and 119862

119903= 1 pF will give the same

results as shown in Figure 2(b)

119884ue = 11988411 minus11988412

2

11988411

(1)

119884119888= 119895 tan

120587119891tz2119891119900

11988411 (2)

11988411=(1119885119900119900+ 1119885

119900119890)

2 (3)

11988412=(1119885119900119900minus 1119885

119900119890)

2 (4)

119879 =11988411

11988412

(5)

Next the reconfigured equivalent circuit in Figure 2(a) issimplified forming a quadripole admittancematrix119884

119877 of the

closed-loop while transformer 119879 and admittance 119884119888 at the

outer section are as depicted in Figure 3At this stage we need to determine the controlling

parameters that influence the position of transmission zeros


1

Input

32 1 Output

Cr Cr

CrCr

Zr

Zr Zr

1205824

1205824

1205824

1205824

Yc

Yue

T

(a)

Frequency (GHz)


0

1


05

S11

S12

fo = 2GHz

minus10

minus20

minus30

minus40

frequency for

S-pa

ram

eter

s (dB

)

zero ftzr

(b)



119884 = [11988411

11988412

11988412

11988411

]

11988411=(4 cos (120579)2 minus 3 + 4119884ue119885119903 cos (120579)

2

minus 119884ue119885119903) cos 120579

119895119885119903sin 120579 (4 cos (120579)2 minus 1)

11988412= minus

1 + 4119861119884ue119885119903cos (120579)3


119903sin 120579

(6)


119861 =(tan (120579)2 + 1)

radic1 + tan (120579)2 (7)


12= 0 resulting in

1 + 4119862119884ue119885119903cos (120579)3

minus 119862119884ue119885119903 cos 120579 = 0 (8)



) (9)


120579tz =120587119891tz2119891119900

(10)

1

Input

32

1 OutputTYC

YR


119877


119884ue = minus1

(minus1 + 4 cos ((12) (120587119891tz119891119900))2

)119885119903

(11)


119885119900119900= 119885119900119890(2119885119900119890minus 119884ue

119884ue) (12)



119885119903and 119885

119900119890 while 119885






119877 of


119884119877= [

11988411119903

11988412119903

11988412119903

11988411119903

] (13)



0

minus20

minus40

minus60

minus80884MHz

922MHz955MHz


Cr = 243pF

S-pa

ram

eter

s-S 1

2(d

B)

(a)


0

1209

minus20

minus40


1132GHz 629dB

1178GHz 703dB

1220GHz 772dB

S-pa

ram

eter

s-S 1

1(d

B)

(b)



11


by 119885119903= 85Ω 119885

119900119890= 70Ω and 119885

119900119900= 35Ω




100 243 0955 12200900 270 0922 11780800 304 0884 1132



by equating 11988412119903

= 0

11988412119903

= 4119885119903

2

1205872

119891tz1199032

119862119903

2

119876minus1

(1 minus cos (120579)2)

minus 119875 cos (120579) + 119876minus1 (4119885119903

2

1205872

119891tz1199032

119862119903

2

+ 1)

+ 44119885119903

2

1205872

119891tz1199032

119862119903

2(12) sin (120579)2 cos (120579)2 = 0

(14)



119862119903= minus


119876119885119903

2

1205872119891tz1199032 sin (120579)2

(15)


119875 = radic1 + tan (120579)2

119876 = minus1

minus1 + 4 cos ((12) (120587119891tz1198910))2

(16)




119885119900119900



= 85Ω and 119885119900119890

= 70Ω and given by (12) 119885119900119900












119900119890= 75Ω while 119885


35066Ω


119900119903



0

1209 14 16


minus20

minus40

minus60

minus80


S-pa

ram

eter

s-S 1

1(d

B)


11




119903and 119885









frequency

BWS-pa

ram

eter

s (dB

)

BWr





RBW =BW119891119900

=2 (119891119900minus 119891tz)

119891119900

(17)



follows

RBW119903=BW119903

119891119900119903

= 2(119891119900119903minus 119891tz119903119891119900119903

) (18)







119900Therefore the



119903asymp RBW



119900

(119891119900minus 119891tz)

119891119900

asymp 2119891119900119903(119891119900119903minus 119891tz119903119891119900119903

)

(19)


03 10

0

0705Frequency (GHz)

x = 1 Cr = 3527pF

x = 0805 Cr = 3328pF

minus20

minus40

minus60

minus80

S-pa

ram

eter

s (dB

)




119891119900119903asymp2119891tz119903119891119900119891tz

(20)



119900119903has to


119891119900119903asymp 2(

119891tz119903119891119900119891tz

)119909 (21)




119900119903


as follows

119877119900119888=119891119900119903

119891119900

(22)




119903= 85Ω and 119885

119900119890= 70Ω and given by (12)

119885119900119900






119891tz = 083GHz and 119877oc = 070

Parameter 119909 100 0805119885119903 119885119900119900(Ω) 8500 3500 7500 3462

119885119900119890(Ω) 70 70


119900119903(GHz) 0668 0700

Calculated 119862119903(pF) 353 3328


119909 = 1 119909 = 13

Simulated 119891119900119903

0871 GHz 0984GHz119885119903 119885119900119890 119885119900119900(Ω) 85 70 35 99 92 32


252 pF 275 pF







119900= 2GHz with




119900119890=

70Ω and 119885119900119900





119900119888 is found at





119900119890is

equal to 92Ω and 119885119900119900


119903is given by




119903is used


0


minus20

minus40

minus60

minus80

S 12-p

aram

eter

s (dB

)

x = 1 Cr = 252pF

x = 13 Cr = 275pF

fo = 10

(a)

Frequency (GHz)

0

07 12

S 11-p

aram

eter

s (dB

)

x = 1 Cr = 252pF

x = 13 Cr = 275pF

minus20

minus40fo = 10

(b)


119900119888= 05

Ground Ground

Ground

Ground

RF inRF out

L1

L2

Wr

Wc s

(a) (b)










Length1198711

(mm)

Length1198712(mm)




2400 1895 227 190 040





08 12

0

Frequency (GHz)

minus10

minus20

minus30

minus40

minus50

minus60

S 12-p

aram

eter

s (dB

)

(a)

Frequency (GHz)

0

08 12

minus10

minus20

minus30

minus40

minus50

S 11-p

aram

eter

s (dB

)


(b)


measured 11987812

(a) (b)











119869) =



RF inRF out

Varactor

Via hole

VaractorVia hole

Varactor

Via hole

Varactor

Via hole

Vdc

Vdc

Vdc

Rdc

Rdc

Rdc Rdc

Cdc

Cdc

Cdc Cdc

Wr

Lr

Lr1

Wcs

+minus

+minus

+minus

(a) (b)


119900119890= 75Ω and 119885



Length 119871119903(mm) Length 119871




2250 2020 230 140 024 2000 100




119878) = 08 nH




119903= 80Ω

119885119900119890= 75Ω and 119885



119903= 45 ℎ = 163mm







12

0


minus20

minus40


26 volts30 volts

S-pa

ram

eter

s (dB

) (S 1

2)

(a)

12

0


minus20

minus40

10 volts

14 volts

18 volts

22 volts26 volts

30 volts

S-pa

ram

eter

s (dB

) (S 1

1)

(b)


11

10Frequency (GHz)

0

1812 14 1608

10 volts14 volts


S-pa

ram

eter

s (dB

) (S 1

2) minus10

minus20

minus30

minus40

minus50

(a)

Frequency (GHz)

0

1810 12 14 16

10 volts14 volts


30 volts

minus20

minus40

S-pa

ram

eter

s (dB

) (S 1

1)

(b)


11


5 Conclusion






Acknowledgment


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










1

Input

32 1 Output

Cr Cr

CrCr

Zr

Zr Zr

1205824

1205824

1205824

1205824

Yc

Yue

T

(a)

Frequency (GHz)


0

1


05

S11

S12

fo = 2GHz

minus10

minus20

minus30

minus40

frequency for

S-pa

ram

eter

s (dB

)

zero ftzr

(b)



119884 = [11988411

11988412

11988412

11988411

]

11988411=(4 cos (120579)2 minus 3 + 4119884ue119885119903 cos (120579)

2

minus 119884ue119885119903) cos 120579

119895119885119903sin 120579 (4 cos (120579)2 minus 1)

11988412= minus

1 + 4119861119884ue119885119903cos (120579)3


119903sin 120579

(6)


119861 =(tan (120579)2 + 1)

radic1 + tan (120579)2 (7)


12= 0 resulting in

1 + 4119862119884ue119885119903cos (120579)3

minus 119862119884ue119885119903 cos 120579 = 0 (8)



) (9)


120579tz =120587119891tz2119891119900

(10)

1

Input

32

1 OutputTYC

YR


119877


119884ue = minus1

(minus1 + 4 cos ((12) (120587119891tz119891119900))2

)119885119903

(11)


119885119900119900= 119885119900119890(2119885119900119890minus 119884ue

119884ue) (12)



119885119903and 119885

119900119890 while 119885






119877 of


119884119877= [

11988411119903

11988412119903

11988412119903

11988411119903

] (13)



0

minus20

minus40

minus60

minus80884MHz

922MHz955MHz


Cr = 243pF

S-pa

ram

eter

s-S 1

2(d

B)

(a)


0

1209

minus20

minus40


1132GHz 629dB

1178GHz 703dB

1220GHz 772dB

S-pa

ram

eter

s-S 1

1(d

B)

(b)



11


by 119885119903= 85Ω 119885

119900119890= 70Ω and 119885

119900119900= 35Ω




100 243 0955 12200900 270 0922 11780800 304 0884 1132



by equating 11988412119903

= 0

11988412119903

= 4119885119903

2

1205872

119891tz1199032

119862119903

2

119876minus1

(1 minus cos (120579)2)

minus 119875 cos (120579) + 119876minus1 (4119885119903

2

1205872

119891tz1199032

119862119903

2

+ 1)

+ 44119885119903

2

1205872

119891tz1199032

119862119903

2(12) sin (120579)2 cos (120579)2 = 0

(14)



119862119903= minus


119876119885119903

2

1205872119891tz1199032 sin (120579)2

(15)


119875 = radic1 + tan (120579)2

119876 = minus1

minus1 + 4 cos ((12) (120587119891tz1198910))2

(16)




119885119900119900



= 85Ω and 119885119900119890

= 70Ω and given by (12) 119885119900119900












119900119890= 75Ω while 119885


35066Ω


119900119903



0

1209 14 16


minus20

minus40

minus60

minus80


S-pa

ram

eter

s-S 1

1(d

B)


11




119903and 119885









frequency

BWS-pa

ram

eter

s (dB

)

BWr





RBW =BW119891119900

=2 (119891119900minus 119891tz)

119891119900

(17)



follows

RBW119903=BW119903

119891119900119903

= 2(119891119900119903minus 119891tz119903119891119900119903

) (18)







119900Therefore the



119903asymp RBW



119900

(119891119900minus 119891tz)

119891119900

asymp 2119891119900119903(119891119900119903minus 119891tz119903119891119900119903

)

(19)


03 10

0

0705Frequency (GHz)

x = 1 Cr = 3527pF

x = 0805 Cr = 3328pF

minus20

minus40

minus60

minus80

S-pa

ram

eter

s (dB

)




119891119900119903asymp2119891tz119903119891119900119891tz

(20)



119900119903has to


119891119900119903asymp 2(

119891tz119903119891119900119891tz

)119909 (21)




119900119903


as follows

119877119900119888=119891119900119903

119891119900

(22)




119903= 85Ω and 119885

119900119890= 70Ω and given by (12)

119885119900119900






119891tz = 083GHz and 119877oc = 070

Parameter 119909 100 0805119885119903 119885119900119900(Ω) 8500 3500 7500 3462

119885119900119890(Ω) 70 70


119900119903(GHz) 0668 0700

Calculated 119862119903(pF) 353 3328


119909 = 1 119909 = 13

Simulated 119891119900119903

0871 GHz 0984GHz119885119903 119885119900119890 119885119900119900(Ω) 85 70 35 99 92 32


252 pF 275 pF







119900= 2GHz with




119900119890=

70Ω and 119885119900119900





119900119888 is found at





119900119890is

equal to 92Ω and 119885119900119900


119903is given by




119903is used


0


minus20

minus40

minus60

minus80

S 12-p

aram

eter

s (dB

)

x = 1 Cr = 252pF

x = 13 Cr = 275pF

fo = 10

(a)

Frequency (GHz)

0

07 12

S 11-p

aram

eter

s (dB

)

x = 1 Cr = 252pF

x = 13 Cr = 275pF

minus20

minus40fo = 10

(b)


119900119888= 05

Ground Ground

Ground

Ground

RF inRF out

L1

L2

Wr

Wc s

(a) (b)










Length1198711

(mm)

Length1198712(mm)




2400 1895 227 190 040





08 12

0

Frequency (GHz)

minus10

minus20

minus30

minus40

minus50

minus60

S 12-p

aram

eter

s (dB

)

(a)

Frequency (GHz)

0

08 12

minus10

minus20

minus30

minus40

minus50

S 11-p

aram

eter

s (dB

)


(b)


measured 11987812

(a) (b)











119869) =



RF inRF out

Varactor

Via hole

VaractorVia hole

Varactor

Via hole

Varactor

Via hole

Vdc

Vdc

Vdc

Rdc

Rdc

Rdc Rdc

Cdc

Cdc

Cdc Cdc

Wr

Lr

Lr1

Wcs

+minus

+minus

+minus

(a) (b)


119900119890= 75Ω and 119885



Length 119871119903(mm) Length 119871




2250 2020 230 140 024 2000 100




119878) = 08 nH




119903= 80Ω

119885119900119890= 75Ω and 119885



119903= 45 ℎ = 163mm







12

0


minus20

minus40


26 volts30 volts

S-pa

ram

eter

s (dB

) (S 1

2)

(a)

12

0


minus20

minus40

10 volts

14 volts

18 volts

22 volts26 volts

30 volts

S-pa

ram

eter

s (dB

) (S 1

1)

(b)


11

10Frequency (GHz)

0

1812 14 1608

10 volts14 volts


S-pa

ram

eter

s (dB

) (S 1

2) minus10

minus20

minus30

minus40

minus50

(a)

Frequency (GHz)

0

1810 12 14 16

10 volts14 volts


30 volts

minus20

minus40

S-pa

ram

eter

s (dB

) (S 1

1)

(b)


11


5 Conclusion






Acknowledgment


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











0

minus20

minus40

minus60

minus80884MHz

922MHz955MHz


Cr = 243pF

S-pa

ram

eter

s-S 1

2(d

B)

(a)


0

1209

minus20

minus40


1132GHz 629dB

1178GHz 703dB

1220GHz 772dB

S-pa

ram

eter

s-S 1

1(d

B)

(b)



11


by 119885119903= 85Ω 119885

119900119890= 70Ω and 119885

119900119900= 35Ω




100 243 0955 12200900 270 0922 11780800 304 0884 1132



by equating 11988412119903

= 0

11988412119903

= 4119885119903

2

1205872

119891tz1199032

119862119903

2

119876minus1

(1 minus cos (120579)2)

minus 119875 cos (120579) + 119876minus1 (4119885119903

2

1205872

119891tz1199032

119862119903

2

+ 1)

+ 44119885119903

2

1205872

119891tz1199032

119862119903

2(12) sin (120579)2 cos (120579)2 = 0

(14)



119862119903= minus


119876119885119903

2

1205872119891tz1199032 sin (120579)2

(15)


119875 = radic1 + tan (120579)2

119876 = minus1

minus1 + 4 cos ((12) (120587119891tz1198910))2

(16)




119885119900119900



= 85Ω and 119885119900119890

= 70Ω and given by (12) 119885119900119900












119900119890= 75Ω while 119885


35066Ω


119900119903



0

1209 14 16


minus20

minus40

minus60

minus80


S-pa

ram

eter

s-S 1

1(d

B)


11




119903and 119885









frequency

BWS-pa

ram

eter

s (dB

)

BWr





RBW =BW119891119900

=2 (119891119900minus 119891tz)

119891119900

(17)



follows

RBW119903=BW119903

119891119900119903

= 2(119891119900119903minus 119891tz119903119891119900119903

) (18)







119900Therefore the



119903asymp RBW



119900

(119891119900minus 119891tz)

119891119900

asymp 2119891119900119903(119891119900119903minus 119891tz119903119891119900119903

)

(19)


03 10

0

0705Frequency (GHz)

x = 1 Cr = 3527pF

x = 0805 Cr = 3328pF

minus20

minus40

minus60

minus80

S-pa

ram

eter

s (dB

)




119891119900119903asymp2119891tz119903119891119900119891tz

(20)



119900119903has to


119891119900119903asymp 2(

119891tz119903119891119900119891tz

)119909 (21)




119900119903


as follows

119877119900119888=119891119900119903

119891119900

(22)




119903= 85Ω and 119885

119900119890= 70Ω and given by (12)

119885119900119900






119891tz = 083GHz and 119877oc = 070

Parameter 119909 100 0805119885119903 119885119900119900(Ω) 8500 3500 7500 3462

119885119900119890(Ω) 70 70


119900119903(GHz) 0668 0700

Calculated 119862119903(pF) 353 3328


119909 = 1 119909 = 13

Simulated 119891119900119903

0871 GHz 0984GHz119885119903 119885119900119890 119885119900119900(Ω) 85 70 35 99 92 32


252 pF 275 pF







119900= 2GHz with




119900119890=

70Ω and 119885119900119900





119900119888 is found at





119900119890is

equal to 92Ω and 119885119900119900


119903is given by




119903is used


0


minus20

minus40

minus60

minus80

S 12-p

aram

eter

s (dB

)

x = 1 Cr = 252pF

x = 13 Cr = 275pF

fo = 10

(a)

Frequency (GHz)

0

07 12

S 11-p

aram

eter

s (dB

)

x = 1 Cr = 252pF

x = 13 Cr = 275pF

minus20

minus40fo = 10

(b)


119900119888= 05

Ground Ground

Ground

Ground

RF inRF out

L1

L2

Wr

Wc s

(a) (b)










Length1198711

(mm)

Length1198712(mm)




2400 1895 227 190 040





08 12

0

Frequency (GHz)

minus10

minus20

minus30

minus40

minus50

minus60

S 12-p

aram

eter

s (dB

)

(a)

Frequency (GHz)

0

08 12

minus10

minus20

minus30

minus40

minus50

S 11-p

aram

eter

s (dB

)


(b)


measured 11987812

(a) (b)











119869) =



RF inRF out

Varactor

Via hole

VaractorVia hole

Varactor

Via hole

Varactor

Via hole

Vdc

Vdc

Vdc

Rdc

Rdc

Rdc Rdc

Cdc

Cdc

Cdc Cdc

Wr

Lr

Lr1

Wcs

+minus

+minus

+minus

(a) (b)


119900119890= 75Ω and 119885



Length 119871119903(mm) Length 119871




2250 2020 230 140 024 2000 100




119878) = 08 nH




119903= 80Ω

119885119900119890= 75Ω and 119885



119903= 45 ℎ = 163mm







12

0


minus20

minus40


26 volts30 volts

S-pa

ram

eter

s (dB

) (S 1

2)

(a)

12

0


minus20

minus40

10 volts

14 volts

18 volts

22 volts26 volts

30 volts

S-pa

ram

eter

s (dB

) (S 1

1)

(b)


11

10Frequency (GHz)

0

1812 14 1608

10 volts14 volts


S-pa

ram

eter

s (dB

) (S 1

2) minus10

minus20

minus30

minus40

minus50

(a)

Frequency (GHz)

0

1810 12 14 16

10 volts14 volts


30 volts

minus20

minus40

S-pa

ram

eter

s (dB

) (S 1

1)

(b)


11


5 Conclusion






Acknowledgment


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119900119890= 75Ω while 119885


35066Ω


119900119903



0

1209 14 16


minus20

minus40

minus60

minus80


S-pa

ram

eter

s-S 1

1(d

B)


11




119903and 119885









frequency

BWS-pa

ram

eter

s (dB

)

BWr





RBW =BW119891119900

=2 (119891119900minus 119891tz)

119891119900

(17)



follows

RBW119903=BW119903

119891119900119903

= 2(119891119900119903minus 119891tz119903119891119900119903

) (18)







119900Therefore the



119903asymp RBW



119900

(119891119900minus 119891tz)

119891119900

asymp 2119891119900119903(119891119900119903minus 119891tz119903119891119900119903

)

(19)


03 10

0

0705Frequency (GHz)

x = 1 Cr = 3527pF

x = 0805 Cr = 3328pF

minus20

minus40

minus60

minus80

S-pa

ram

eter

s (dB

)




119891119900119903asymp2119891tz119903119891119900119891tz

(20)



119900119903has to


119891119900119903asymp 2(

119891tz119903119891119900119891tz

)119909 (21)




119900119903


as follows

119877119900119888=119891119900119903

119891119900

(22)




119903= 85Ω and 119885

119900119890= 70Ω and given by (12)

119885119900119900






119891tz = 083GHz and 119877oc = 070

Parameter 119909 100 0805119885119903 119885119900119900(Ω) 8500 3500 7500 3462

119885119900119890(Ω) 70 70


119900119903(GHz) 0668 0700

Calculated 119862119903(pF) 353 3328


119909 = 1 119909 = 13

Simulated 119891119900119903

0871 GHz 0984GHz119885119903 119885119900119890 119885119900119900(Ω) 85 70 35 99 92 32


252 pF 275 pF







119900= 2GHz with




119900119890=

70Ω and 119885119900119900





119900119888 is found at





119900119890is

equal to 92Ω and 119885119900119900


119903is given by




119903is used


0


minus20

minus40

minus60

minus80

S 12-p

aram

eter

s (dB

)

x = 1 Cr = 252pF

x = 13 Cr = 275pF

fo = 10

(a)

Frequency (GHz)

0

07 12

S 11-p

aram

eter

s (dB

)

x = 1 Cr = 252pF

x = 13 Cr = 275pF

minus20

minus40fo = 10

(b)


119900119888= 05

Ground Ground

Ground

Ground

RF inRF out

L1

L2

Wr

Wc s

(a) (b)










Length1198711

(mm)

Length1198712(mm)




2400 1895 227 190 040





08 12

0

Frequency (GHz)

minus10

minus20

minus30

minus40

minus50

minus60

S 12-p

aram

eter

s (dB

)

(a)

Frequency (GHz)

0

08 12

minus10

minus20

minus30

minus40

minus50

S 11-p

aram

eter

s (dB

)


(b)


measured 11987812

(a) (b)











119869) =



RF inRF out

Varactor

Via hole

VaractorVia hole

Varactor

Via hole

Varactor

Via hole

Vdc

Vdc

Vdc

Rdc

Rdc

Rdc Rdc

Cdc

Cdc

Cdc Cdc

Wr

Lr

Lr1

Wcs

+minus

+minus

+minus

(a) (b)


119900119890= 75Ω and 119885



Length 119871119903(mm) Length 119871




2250 2020 230 140 024 2000 100




119878) = 08 nH




119903= 80Ω

119885119900119890= 75Ω and 119885



119903= 45 ℎ = 163mm







12

0


minus20

minus40


26 volts30 volts

S-pa

ram

eter

s (dB

) (S 1

2)

(a)

12

0


minus20

minus40

10 volts

14 volts

18 volts

22 volts26 volts

30 volts

S-pa

ram

eter

s (dB

) (S 1

1)

(b)


11

10Frequency (GHz)

0

1812 14 1608

10 volts14 volts


S-pa

ram

eter

s (dB

) (S 1

2) minus10

minus20

minus30

minus40

minus50

(a)

Frequency (GHz)

0

1810 12 14 16

10 volts14 volts


30 volts

minus20

minus40

S-pa

ram

eter

s (dB

) (S 1

1)

(b)


11


5 Conclusion






Acknowledgment


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










03 10

0

0705Frequency (GHz)

x = 1 Cr = 3527pF

x = 0805 Cr = 3328pF

minus20

minus40

minus60

minus80

S-pa

ram

eter

s (dB

)




119891119900119903asymp2119891tz119903119891119900119891tz

(20)



119900119903has to


119891119900119903asymp 2(

119891tz119903119891119900119891tz

)119909 (21)




119900119903


as follows

119877119900119888=119891119900119903

119891119900

(22)




119903= 85Ω and 119885

119900119890= 70Ω and given by (12)

119885119900119900






119891tz = 083GHz and 119877oc = 070

Parameter 119909 100 0805119885119903 119885119900119900(Ω) 8500 3500 7500 3462

119885119900119890(Ω) 70 70


119900119903(GHz) 0668 0700

Calculated 119862119903(pF) 353 3328


119909 = 1 119909 = 13

Simulated 119891119900119903

0871 GHz 0984GHz119885119903 119885119900119890 119885119900119900(Ω) 85 70 35 99 92 32


252 pF 275 pF







119900= 2GHz with




119900119890=

70Ω and 119885119900119900





119900119888 is found at





119900119890is

equal to 92Ω and 119885119900119900


119903is given by




119903is used


0


minus20

minus40

minus60

minus80

S 12-p

aram

eter

s (dB

)

x = 1 Cr = 252pF

x = 13 Cr = 275pF

fo = 10

(a)

Frequency (GHz)

0

07 12

S 11-p

aram

eter

s (dB

)

x = 1 Cr = 252pF

x = 13 Cr = 275pF

minus20

minus40fo = 10

(b)


119900119888= 05

Ground Ground

Ground

Ground

RF inRF out

L1

L2

Wr

Wc s

(a) (b)










Length1198711

(mm)

Length1198712(mm)




2400 1895 227 190 040





08 12

0

Frequency (GHz)

minus10

minus20

minus30

minus40

minus50

minus60

S 12-p

aram

eter

s (dB

)

(a)

Frequency (GHz)

0

08 12

minus10

minus20

minus30

minus40

minus50

S 11-p

aram

eter

s (dB

)


(b)


measured 11987812

(a) (b)











119869) =



RF inRF out

Varactor

Via hole

VaractorVia hole

Varactor

Via hole

Varactor

Via hole

Vdc

Vdc

Vdc

Rdc

Rdc

Rdc Rdc

Cdc

Cdc

Cdc Cdc

Wr

Lr

Lr1

Wcs

+minus

+minus

+minus

(a) (b)


119900119890= 75Ω and 119885



Length 119871119903(mm) Length 119871




2250 2020 230 140 024 2000 100




119878) = 08 nH




119903= 80Ω

119885119900119890= 75Ω and 119885



119903= 45 ℎ = 163mm







12

0


minus20

minus40


26 volts30 volts

S-pa

ram

eter

s (dB

) (S 1

2)

(a)

12

0


minus20

minus40

10 volts

14 volts

18 volts

22 volts26 volts

30 volts

S-pa

ram

eter

s (dB

) (S 1

1)

(b)


11

10Frequency (GHz)

0

1812 14 1608

10 volts14 volts


S-pa

ram

eter

s (dB

) (S 1

2) minus10

minus20

minus30

minus40

minus50

(a)

Frequency (GHz)

0

1810 12 14 16

10 volts14 volts


30 volts

minus20

minus40

S-pa

ram

eter

s (dB

) (S 1

1)

(b)


11


5 Conclusion






Acknowledgment


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0


minus20

minus40

minus60

minus80

S 12-p

aram

eter

s (dB

)

x = 1 Cr = 252pF

x = 13 Cr = 275pF

fo = 10

(a)

Frequency (GHz)

0

07 12

S 11-p

aram

eter

s (dB

)

x = 1 Cr = 252pF

x = 13 Cr = 275pF

minus20

minus40fo = 10

(b)


119900119888= 05

Ground Ground

Ground

Ground

RF inRF out

L1

L2

Wr

Wc s

(a) (b)










Length1198711

(mm)

Length1198712(mm)




2400 1895 227 190 040





08 12

0

Frequency (GHz)

minus10

minus20

minus30

minus40

minus50

minus60

S 12-p

aram

eter

s (dB

)

(a)

Frequency (GHz)

0

08 12

minus10

minus20

minus30

minus40

minus50

S 11-p

aram

eter

s (dB

)


(b)


measured 11987812

(a) (b)











119869) =



RF inRF out

Varactor

Via hole

VaractorVia hole

Varactor

Via hole

Varactor

Via hole

Vdc

Vdc

Vdc

Rdc

Rdc

Rdc Rdc

Cdc

Cdc

Cdc Cdc

Wr

Lr

Lr1

Wcs

+minus

+minus

+minus

(a) (b)


119900119890= 75Ω and 119885



Length 119871119903(mm) Length 119871




2250 2020 230 140 024 2000 100




119878) = 08 nH




119903= 80Ω

119885119900119890= 75Ω and 119885



119903= 45 ℎ = 163mm







12

0


minus20

minus40


26 volts30 volts

S-pa

ram

eter

s (dB

) (S 1

2)

(a)

12

0


minus20

minus40

10 volts

14 volts

18 volts

22 volts26 volts

30 volts

S-pa

ram

eter

s (dB

) (S 1

1)

(b)


11

10Frequency (GHz)

0

1812 14 1608

10 volts14 volts


S-pa

ram

eter

s (dB

) (S 1

2) minus10

minus20

minus30

minus40

minus50

(a)

Frequency (GHz)

0

1810 12 14 16

10 volts14 volts


30 volts

minus20

minus40

S-pa

ram

eter

s (dB

) (S 1

1)

(b)


11


5 Conclusion






Acknowledgment


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











08 12

0

Frequency (GHz)

minus10

minus20

minus30

minus40

minus50

minus60

S 12-p

aram

eter

s (dB

)

(a)

Frequency (GHz)

0

08 12

minus10

minus20

minus30

minus40

minus50

S 11-p

aram

eter

s (dB

)


(b)


measured 11987812

(a) (b)











119869) =



RF inRF out

Varactor

Via hole

VaractorVia hole

Varactor

Via hole

Varactor

Via hole

Vdc

Vdc

Vdc

Rdc

Rdc

Rdc Rdc

Cdc

Cdc

Cdc Cdc

Wr

Lr

Lr1

Wcs

+minus

+minus

+minus

(a) (b)


119900119890= 75Ω and 119885



Length 119871119903(mm) Length 119871




2250 2020 230 140 024 2000 100




119878) = 08 nH




119903= 80Ω

119885119900119890= 75Ω and 119885



119903= 45 ℎ = 163mm







12

0


minus20

minus40


26 volts30 volts

S-pa

ram

eter

s (dB

) (S 1

2)

(a)

12

0


minus20

minus40

10 volts

14 volts

18 volts

22 volts26 volts

30 volts

S-pa

ram

eter

s (dB

) (S 1

1)

(b)


11

10Frequency (GHz)

0

1812 14 1608

10 volts14 volts


S-pa

ram

eter

s (dB

) (S 1

2) minus10

minus20

minus30

minus40

minus50

(a)

Frequency (GHz)

0

1810 12 14 16

10 volts14 volts


30 volts

minus20

minus40

S-pa

ram

eter

s (dB

) (S 1

1)

(b)


11


5 Conclusion






Acknowledgment


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










RF inRF out

Varactor

Via hole

VaractorVia hole

Varactor

Via hole

Varactor

Via hole

Vdc

Vdc

Vdc

Rdc

Rdc

Rdc Rdc

Cdc

Cdc

Cdc Cdc

Wr

Lr

Lr1

Wcs

+minus

+minus

+minus

(a) (b)


119900119890= 75Ω and 119885



Length 119871119903(mm) Length 119871




2250 2020 230 140 024 2000 100




119878) = 08 nH




119903= 80Ω

119885119900119890= 75Ω and 119885



119903= 45 ℎ = 163mm







12

0


minus20

minus40


26 volts30 volts

S-pa

ram

eter

s (dB

) (S 1

2)

(a)

12

0


minus20

minus40

10 volts

14 volts

18 volts

22 volts26 volts

30 volts

S-pa

ram

eter

s (dB

) (S 1

1)

(b)


11

10Frequency (GHz)

0

1812 14 1608

10 volts14 volts


S-pa

ram

eter

s (dB

) (S 1

2) minus10

minus20

minus30

minus40

minus50

(a)

Frequency (GHz)

0

1810 12 14 16

10 volts14 volts


30 volts

minus20

minus40

S-pa

ram

eter

s (dB

) (S 1

1)

(b)


11


5 Conclusion






Acknowledgment


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










12

0


minus20

minus40


26 volts30 volts

S-pa

ram

eter

s (dB

) (S 1

2)

(a)

12

0


minus20

minus40

10 volts

14 volts

18 volts

22 volts26 volts

30 volts

S-pa

ram

eter

s (dB

) (S 1

1)

(b)


11

10Frequency (GHz)

0

1812 14 1608

10 volts14 volts


S-pa

ram

eter

s (dB

) (S 1

2) minus10

minus20

minus30

minus40

minus50

(a)

Frequency (GHz)

0

1810 12 14 16

10 volts14 volts


30 volts

minus20

minus40

S-pa

ram

eter

s (dB

) (S 1

1)

(b)


11


5 Conclusion






Acknowledgment


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












Acknowledgment


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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