Bandpass Filter Tutorial2

8/6/2019 Bandpass Filter Tutorial2

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Part II of this bandpass filter tutorial fea-tures several examples that illustrate the

general design procedure for bandpassfilters using resonators and coupling methodsof different types.

BANDPASS FILTER DESIGNThe general bandpass filter design proce-

dure utilizes the normalized, low pass ele-ments of the prototypefilter to determine therequired resonatorcoupling and couplingto the external circuit,that is, the source andload. In each case, the

external source andload are assumed to be50 , although the fil-ter could be matchedto other real imped-ances.

The general design procedure is listed inTable 1 . To illustrate the general bandpass fil-ter design procedure, several examples are of-fered. It should be mentioned that the cou-pling parameters, that is, the capacitor matrix,or even and odd mode impedances, for several

types of distributed resonators, may be deter-mined with the aid of an electromagnetic

(EM) simulator. This is an extremely valuabledesign tool because it eliminates the fabrica-tion of models in order to determine the cou-pling of symmetr ical, distributed resonators.

The illustrated examples include a lumpedelement, Chebishev, bandpass filter using -type resonators, a coaxial cavity bandpass filterusing /8 resonators with capacitive tuning(comb-line), a coaxial cavity bandpass filterusing /4 resonators (interdigital) and a half wavelength via-hole direct-coupled filter. Alsodescribed are a dielectric resonator, a band-pass filter using disk-shaped resonators, an in-ductively coupled filter in coplanar waveguide

and a stripline or microstrip, Chebishev, band-pass filter using /2, side-coupled resonators.

Lumped Element Bandpass FilterThe lumped element, -type resonator is

used in a five-section, 0.01 dB ripple, Chebi-shev filter. The low pass prototype elements(g-values) may be calculated using the equa-

A G ENERAL D ESIGNP ROCEDURE FOR BANDPASSFILTERS D ERIVED FROMLOW PASS P ROTOTYPEELEMENTS : P ART II

TUTORIAL

K.V. P UGLIA M/A-COM Inc. Lowell, MA

several examples that illustrate the general design procedure for bandpass filters

using resonators and coupling methods of different types.

Reprinted with pe rmission of MICROWAVE JOURNAL from the January 2001 issue.2001 Horizon House Publications, Inc.


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and the susceptance slope parameteris calculated as

= 1(2 f 0)C = 0.063662 mhosThe resonator coupling elements aredetermined using

and the input and output couplingare calculated as

and

The input and output coupling meth-ods need not be the same as the res-onator coupling. However, the inputand output coupling must satisfy therelationship

and

Table 2 lists the -type resonator,bandpass filter data.

A schematic for the five-section, -type resonator bandpass fi l ter is

QZ

J

g g f f e out

n n

n n=( )

=+

+ 01

21 0

,

QZ

J

g g f

f e

in

=( )

= 00 1

20 1 0

,

2 0 10 1 0

f C f f g g Zn n n n

, ++

=

2 0 0 10 0 1 0

f C f f g g Z,

=

2 0 1 1 f C k for

i i i i, ,+ +=i = 1 to i = n 1

tions within the appendix or may bedetermined from available tabulardata.

The filter parameters are

f 0 = 100 MHzf = 5 MHz

n = 5rdB = 0.01 dBg0 = g6 = 1.0000

g1 = 0.7563g2 = 1.3049g3 = 1.5773g4 = 1.3049g5 = 0.7563

The unloaded quality factor forthis type of resonator at this frequen-cy is Q u = 250. A schematic of theresonator is shown in Figure 1 .

BANDPASS FILTER DESIGNPROCEDURE

The bandpass filter design proce-dure is listed in Table 1. The values of

the inductance and capacitors may bedetermined using

where

and

The inductance formula provides agood estimate of a convenient valueof the resonator self-inductance fromwhich the resonator capacitance maybe calculated.

Next, the coupling values are cal-culated using

k f

f g gi i

i i,

,+

+=1

0 1

1

for i = 1 to i = n 1

Cf L

pF=( )

=22

50 66

02

.

Lf

nH =10 100 00

.

f LC

MH z01

22

100= =

TABLE IBANDPASSFILTER DESIGN PROCEDURE

Determine the Filter Parameters:

Center frequency, f 0 Bandwidth, f In-band ripple, r dB Number of resonators, nRejection requirements, R(f') Insertion loss, L(f)Resonator type: lumped element, comb-line, interdigital, coaxial cavity, dielectric Special conditions: MFTD, Bessel, Gaussian

Determine the Low Pass Prototype Elements:

Calculate elements Acquire from tabular data

Calculate Coupling Coefficients:

Determine Resonator Reactance or Su sceptance Slope Parameter:

or .

Determine Coupling Reactance or Susceptance:

Ki,j+1 or J i,i+1 for i = 1 to n1; K i,i+1 = k i,i+1 and J i,i+1 = k i,i+1.

Determine Input and Outp ut Coupling Parameters.

Determine Filter Elements (for lumped element resonators).

Determine Filter Dimensions (for distribut ed resonators).

Optional:

Computer simulationEstimate filter insertion lossEstimate filter group delay

k f

f 1

g gi,i 1

o i i 1+

+= for i = 1 to n1.

C C

L

w Fig. 1 Schemat ic of a -type resonator.

TABLE II-TYPE RESON ATOR BANDPASS

FILTER DATA

i g i C ,I,I + 1 C ia C ib

0 1.0000 16.4

1 0.7563 5.1 37.7 45.6

2 1.3049 3.5 45.6 47.1

3 1.5773 3.5 47.1 47.1

4 1.3049 5.1 47.1 47.1

5 0.7563 16.4 45.6 37.7

6 1.0000

TUTORIAL


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TUTORIALshown in Figure 2 . A computer sim-ulation was conducted on the five-resonator bandpass filter using onlythe inductors as variable or tuning el-ements. The results of the simulationare shown in Figure 3 . Note that thebandwidth is 5.12 MHz as comparedto the design bandwidth of 5.0 MHz,

and that the midband insertion loss isapproximately 2 dB. The midband in-sertion loss of a bandpass filter maybe estimated from the equation

The computer simulation of thetransmission group delay is also pre-sented in the results. The midbandgroup delay may be estimated fromthe formula

It should be mentioned that theonly fi l ter elements which weretuned in order to achieve the desiredpassband were the inductors of the -resonators.

COAXIAL CAVITY BANDPASSFILTER /8 RESON ATORS

The second bandpass filter designexample is the coaxial cavity type fil-ter using /8 resonators with capaci-tive tuning or comb-line filter, socalled because the resonators arefixed to ground on a single surface inmuch the same configuration of theteeth of a comb. This is a very popu-lar filter structure because a moder-ate value of unloaded resonator quali-ty factor may be achieved (and there-fore low loss), and because a widerejection band is indigenous to thestructure by virtue of the wide sepa-ration in resonant modes. The res-onator structure employed for the ex-ample filter is that depicted in Part I.Unlike the traditional comb-line fil-ter, which has no metallic obstaclebetween resonators, the filter exam-ple employs rectangular cavities withcoupling slots as shown in Figure 4 .

This structure yields a somewhathigher unloaded quality factor be-cause more of the field is enclosed.The coupling between resonators iscontrolled via the width of the slot, w.The coupling coefficient betweenresonators may be determined bymeasurements of symmetrical-cou-

d k k

n

f f g ns01

12 181( )= ==

IL f f

fQg dB

uk

k

n

00

1

4 3431 98( )= =

=. .

pled resonators as a function of theslot width or via analysis of the self and mutual capacitance using an EMsimulator. Both methods were em-ployed and resulted in acceptableagreement, that is, less than 5 per-cent over the slot widths used in thefilter, between the experimentally de-termined coefficients and the mea-sured values as shown in Figure 5 .

To illustrate the filter design pro-

cedure a PCS1900 transmit band fil-ter (19301990 MHz) is requiredwith minimum insertion loss (< 1.5dB) and volume as the principal de-sign specifications. A filter rejectionof 60 dB, minimum, in the PCS1900receive band (18501910 MHz) isalso required .

From the earlier data, an eight-res-onator filter is required to achieve therejection requirements. This may beverified from direct calculation using

where

L(f a) = the attenuation required atthe specific rejectionfrequency f a

rdb = the in-band ripple factorf n = the normalized bandwidth at

the rejection frequency,

nf

L f

r

n

a

dB

=( )

( )

cosh

cosh

1 10

10

1

10 1

10 1

that is

Because the reject band is close tothe passband, the passband was de-liberately narrowed to 55 MHz sothat coupling adjustment could be fa-cilitated in order to increase the finalfilter bandwidth to 60 MHz. The fil-

ter parameters aref 0 = 1960 MH zf = 55 MHz

n = 8rdB = 0.05 dB

Q u = 2250

Y v C mhosg0 01

60= =

0 4=

f f f

f na=

2 0

90 1 00 11 0

0

1 02 03 04 05 06 07 08 0

FREQUENCY ( 1 MHz/div)

8 00

7 00

6 00

5 00

4 00

3 00

2 00

1 00

0

S 1

1

( d B )

,

2

1

( d B )

w Fig. 3 Comp uter simulation results.

w

w Fig. 4 Coaxial cavities with slot coupling.

37.745 . 645 . 64 7. 14 7. 14 7. 1

INDUCTOR VALUESIN nHCA PACITOR VALUESI N pF

4 7. 145 . 645 . 637.7

1 6 . 4 1 00 1 00 1 00 1 005 .1 3. 5 3. 5 5 .1 1 6 . 41 00

v Fig. 2 Schematic of a five-section -type resonator bandpass filter.


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The LP prototype g-values areg0 = 1.0000g1 = 1.0437g2 = 1.4514g3 = 1.9899g4 = 1.6502g5 = 2.0457g6 = 1.6053g7 = 1.7992g8 = 0.8419

The coupling values are calculatedusing

The slot width may be determinedfrom the measured coupling data of symmetrical coupled resonators orfrom an EM simulator that providesthe capacitance matrix data for theparticular structure. For this exam-ple, both techniques are utilized.First, the measured coupling datafrom a pair of symmetrical coupledresonators was subjected to polyno-mial regression of degree three . Next,the coefficients of the polynomialwere used to generate an equationfor the coupling coefficient as a func-tion of the slot width. Finally, a plotof the coupling coefficient was used

Kf

f g gi i

i i, +

+= 1

0 1

1

to determine the slot width for eachcoupled section.

The measured coupling data is dis-played in Table 3 for three values of slot width for square cavities of 0.875inches and center conductor diame-ters of 0.375 inches. These dimen-sions produce a resonator characteris-

tic impedance of approximately 60 .Performing a polynomial regres-

sion produces an equation for thecoupling coefficient K c as a functionof the slot width, w such that

Kc(w) = 0.02717 + 0.10865w 0.03150w 2

The correlation coefficient R for thepolynomial regression was 1.00.

Alternatively, an EM simulatormay be utilized to determine the self-capacitance C g and the mutual capac-itance C m for various slot widths.Subsequent data may also be subjectto polynomial regression analysis todetermine the correct slot width foreach coupled resonator.The susceptance slope parameter iscalculated using

and the mutual coupling capacitors

= ( )+ ( )[ ]Y0 0 0 2 02 cot csc

becomes

The filter configuration is shownin Figure 6 . Note that all resonatorsare the same diameter and that cou-pling to the input and outpu t is via di-rect tap or contact to the first andeighth resonator at a low impedancepoint on the resonators. Alternatecoupling mechanisms are via capaci-tive probe at a high electric fieldpoint of the resonator or via trans-former coupling. Generally, the tap ispreferred because it eliminates theneed for another machined part, pro-vides a m ore compact fi lter, andmakes the filters input and output adirect short to ground at DC. The de-sign data for the comb-line filter islisted in Table 4 .

Filter SimulationIn order to conduct a simulation of

the filter characteristics, an equiva-lent circuit is required. A suitableequivalent circuit may be constructedwith the aid of the two-wire lineequivalent of the coupled line shownin Figure 7 .

Ck C

Ki ii i g

i i,,

,++

+= = +

1

1

012

12

0.030

0.0 26

0.0 22

0.0 18

0.0 1 4

0.0 1 00. 6 00. 5 60. 5 20. 4 8

SLOT WIDTH w (" )

SI MU LATE D MEA SU R E D

0. 440. 4 0

C O U P L I N G

K ( w )

v Fig. 5 Coupling coefficient for /8 linesvs. slot widt h.

TABLE IIIMEASURED COUPLING DATA

Slot Width (") Coupling Coefficient w k c

0.400 0.01125

0.500 0.01928

0.600 0.02668

0.375 Dia OD0. 228 Dia ID0.750 Long8 plcs . typ

0.750 Ref

0

Di m e nsion s in inch e s

4 4 0 t a p0. 2 5 D p . m im

1 8 plcs

0. 1 2 50. 1 8 75

0. 6 2 6

1 .1 2 5

1 .0 6 2 5

1 .1 8 75

1 . 6 2 5

2 .1 2 52 .0 6 2 5

3. 6 2 5

1 .000

0

04 . 2 50

. 6 2 5 2 . 6 2 50. 6 2 5

0. 2 00

0. 1 8 75

4 .1 2 52 .1 2 5 3. 1 2 51 .1 2 5

0. 1 2 5 R . typ 0. 1 2 5 R . typ0. 4 05

. 4 5 2 0. 4 5 2 0.5 4 7

0. 44 9

0.3 2 5

0.5 4 7

0. 1 2 5

2 . 2 50

0

w Fig. 6 Filter configuration.

TUTORIAL


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If the coupled line equivalence isapplied repeatedly, a complete filterequivalent circuit may be realized, asshown in Figure 8 , where the tuningcapacitance C t, resonator quality fac-tor Q u and external circuit couplinghas been included. The complete fil-ter was subjected to simulation and

optimization using only the tuning ca-pacitance and external coupling tapsas the variable. The simulation resultsare shown in Figure 9 .

Note that the actual bandwidth is52.8 MHz versus the design band-width of 55.0 MHz, and that the re-turn loss is consistent with the 0.05dB Chebishev response. The simulat-ed midband insertion loss and groupdelay are 0.85 dB and 37.1 ns, re-

TUTORIALpling to the input and output is ac-complished via contact at the low im-pedance point of the resonator.

The design procedure for interdig-ital bandpass filters is very similar tothe comb-line filter design proce-dure. In this case, the example illus-trates the design of a 500 MHz band-

width filter centered at 10 GHz.The filter parameters are

f 0 = 10 GHzf = 500 MHz

n = 5rdB = 0.1 dB

0 = /4Q u = 2500Zc = 70

g0 = 1.0000g1 = 1.1468g2 = 1.3712g3 = 1.9750

g4 = 1.3712g5 = 1.1468

The coupling values are calculatedusing

the susceptance slope parameter be-comes

and the mutual coupling capacitorsare determined using

The calculation of the resonatorcoupling dimensions must be preced-ed by selection of the resonatorground plane spacing. In order toproperly define a distributed res-onator and reduce evanescent modes,certain geometric and aspect ratiosmust be maintained. It was foundempirically that selection of groundplane spacing in accordance with

produced acceptable results.The formula results from a res-

onator aspect ratio (ratio of length todiameter) of 2 1. The approximateground plane spacing for a resonatorcharacteristic impedance of 60 islisted in Table 5 .

hZ

0 13832

100

CC k

i ig i i

,,

++=1

1

4

= Y04

k f

f g gi i

i i,

,+

+= 1

0 1

1

spectively. The midband insertionloss and group delay estimates are

and

INTERDIGITALBANDPASS FILTER ( /4-LINES)

The interdigital bandpass filter isanother popular type of microwavefilter implementation. They typicallyhave lower loss than comb-line struc-tures and are easier to tune. They re-quire resonators that are fixed to

ground at oppositesides of the sup-

porting housing asshown in F i g u r e10 . Therefore, theconstruction is notas suitable for man-ufacture as thecomb-line filter.

In most cases,the resonator lengthis slightly shorterthan /4 (typically,0. 9 /4), which al-lows the filter to betuned to the center

frequency with thetuning element s justbreaking the cavitywall. This facilitatesboth ease of tuningand maximum un-loaded quality fac-tor Q u of each res-onator. The cou-

d k k

n

f f

g ns01

12

35 9( )= == .

IL f f

fQg dB

uk

k

n

00

1

4 3430 85( )= =

=. .

TABLE IVCOMB-LINE FILTER DESIGN DATA

G Coupling Mutual Slot Index Values Coefficient Capacitance Width i g i k i,I +1 C i,I +1 W i,I +1

1 1.04370.02280 0.18402 0.547

2 1.45140.01651 0.13327 0.465

3 1.98990.01549 0.12498 0.452

4 1.65020.01527 0.12326 0.449

5 2.0457 0.01549 0.12498 0.452

6 1.60530.01651 0.13327 0.465

7 1.79920.02280 0.18402 0.547

8 0.8419

PORT1

PORT1

PORT2

PORT2

Yse = V o C m

Y se = V o C g

0

0 0

0

v Fig. 7 Coupled line equivalent circuit.


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For the present example, a groundplane spacing of 0.275" has been se-lected, which requires a resonator di-ameter of 0.128" to obtain a resonatorcharacteristic of 60 . This value iscalculated from

Cristal 2 has given the closed-formexpressions for the even and oddmode capacitance per unit length forthis line configuration, from whichthe self and mutual capacitance may

be calculated (see Appendix A ). Thegraph of the mutual capacitance ver-sus resonator center-to-center spac-ing is shown in Figure 11 .

The design data for the interdigitalfilter is listed in Table 6 .

Filter SimulationThe equivalent circuit shown in

Figure 12 is utilized to conduct acomputer simulation. As in the caseof the comb-line filter, a contact atthe low impedance end of the res-

Zhd v C

r g0

0

138 4 1=

=

log

onator serves as the input and outputcoupling to the filter.

The results of the computer simu-lation using only the end capacitanceand tap points as variables are shownin Figure 13 . Note that the actualbandwidth is 467 MHz versus the de-sign bandwidth of 500 MHz, and thatthe return loss is consistent with the0.1 dB Chebishev response. The sim-

ulated midband insertion loss andgroup delay are 0.30 dB and 2.3 ns,respectively. The midband insertionloss and group delay estimates are

and

d k k

n

f f

g ns01

12

2 2( )= == .

IL f f

fQg dB

uk

k

n

00

1

4 3430 30( )= =

=. .

TUTORIAL

Z 1 , 2

= 2 0 4 5

1 2

INPUT

3 4 6 7 8

Z 2 , 3

= 2 0 2

7

Z3 , 4

= 3 0 1

3

Z4 , 5

= 3 0 5 5

Z5 , 6

=

3 0 1 3

Z6 , 7

= 2

8 2 7

Z7 , 8

= 2

0 4 5

=

Z c = 6 0 0 = 45

0

4

Z 0 Z

5

6 0

Z 0

5

0 =

5

55

O UTPUT

v Fig. 8 Filter equivalent circuit.

0

1 0

3 0

4 05 06 0

2 0 3 51 88 5

FREQUENCY ( 1 5 MHz/div)

1 5 0

1 2 5

1 00

7 5

5 0

2 5

0

S 1

1

( d B )

S 2

1

( d B )

v Fig. 9 Simu lation results.

/4

v Fig. 10 Int erdigital filter construction.

TABLE VGROUND PLANE SPACING

Filter Frequency Ground Plane f 0 (GHz) Spacing h (" )

1 3.000

2 1.500

4 0.750

8 0.375

10 0.300

12 0.250

15 0.215

18 0.175

0.50

0.40

0.30

0.20

0.10

00.500.450.40

0.3 880.3 6 4

0.35

CENTER-TO- CENTER SPACING (")

0.300.25 N O R M A L I Z E D M

U T U A L

C A P A C I T A N

C E

0.1 9 66

0.14 9 8

v Fig. 11 Mut ual capacitance vs. spacing.

TABLE VIINTERDIGITAL FILTER DESIGN DATA

Index G Values Coupling Coefficient Mutual Capacitance Center Spacing

i g i k i,I +1 C i,I +1 S i,I +11 1.1468

0.03987 0.1966 0.364

2 1.37120.03038 0.1498 0.388

3 1.97500.03038 0.1498 0.388

4 1.37120.03987 0.1966 0.364

5 1.1468


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TUTORIAL

APPENDIX A

NO RMALIZED SELF AND MUTUAL CAPACITANCEOF ROUND RODSBETWEEN PARALLEL GROUND PLANES

Upon completion of specific elements of the design procedure andthe calculation of the normalized self and mut ual capacitance pe r unitlength, rod diameter and center-to-center spacing may be calculated.First, the filter ground plane spacing h must be selected. The selectionof a suitable ground plane spacing is bounded by the out-of-band spu-

rious response, passband frequency and insertion loss. Certainly, theground plane dimension should be less than one quarter wavelengthand no smaller than that required to achieve an unloaded Q u consis-tent with the insertion loss requirements. The maximum ground planespacing may be estimated in accordance with

This formula provides the approximate values for ground plane spacinglisted in Table A1 :

Cristal 2 has given the closed-form expressions for the even and oddmode capacitance per unit length from which the self and mutual ca-pacitance may be calculated from

and

For reasonable accuracy, the parameter m may be limited to 100. Theself and mutual capacitance is calculated using 1

C g(c) = C e(c)

and

Cm(c) = 0.25[C 0(c)C e(c)]

The e quations have be en programmed using Mathcad for a groundplane spacing of 0.275 inches and a rod diameter of 0.128 inches, thatis, Z o = 60 . The data are shown in Figures A1 and A2 .

C c

db

db

dbc

b

m cb

e

m

( )=

+

+

=

1

24

12

12

12

224

4

1ln

ln ln tanh

C c

db

db

dbc

b

m cb

m

m

0

4

4

1

12

4

12

12

12

2 12

( )=

+ ( ) =

ln

ln ln tanh

hZ

0 13832

100

TABLE AIAPPROXIMATE VALUES

FOR GROUND PLANE SPACING

Filter Frequency Ground Plane f 0 (GHz) Spacing h (" )

1 3.000

2 1.500

4 0.750

8 0.375

10 0.300

12 0.250

15 0.215

18 0.175

0.80.70.60.50.40.30.20.1

0500450400350

CENTER-TO- CENTER SPACING (mil)

300250 N O R M A L I Z E D M U T U A L

C A P A C I T A N C E

v Fig. A1 Mut ual capacitanve of coupled lines for h = 0.275 and d = 0.128".

7.0

6.5

6.0

5.5

5.0

4.5

4.05004504003 50

CENTER-TO- CENTER SPACING (mil)

3 002 50 N O R M A L I Z E D C A P A C I T A N C E

T O

G R O U N D

v Fig. A2 Norm alized self-capacitanceto ground for h = 0.275 and d = 0.128.

NORMALIZED SELF AND MUTUAL CAPACITANCE OF ROUND RODS BETWEEN PARALLEL GROUND PLANES


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TUTORIAL

APPENDIX B

ALTERNATE FILTER IMPLEMENTATIONSIn addition to the examples within Part II

of this tutorial, there are several alternative fil-ter implementations that lend themselves tothe general design procedure and should becited. These alternative filter implementationsutilize resonators not fully exploited in recent

literature and for which recent CAD toolshave permitted extensive analysis and under-standing. Two specific types of resonators aresuggested for special applications: cylindricaldielectric resonators and helical resonators.

DIELECTRIC RESON ATOR FILTERFigure B1 shows the electrical and me-

chanical schematic of a three-section band-pass filter using cylindrical dielectric res-onators. Resonators of this type are not typicalof conventional lumped or distributed ele-ment structures due to the existence of multi-

ple resonant frequencies or modes. This res-onator type permits the design of narrowband,low loss filters due to the high unloaded quali-ty factor (Q u > 10,000) in the principal ordominant resonant mode.

A note of caution is in order with respectto the multiple resonator modes and the envi-ronment necessary to suppress excitation of these m odes and th ereby eliminate loss spikesand spurious responses in the filter transferfunction. There are two techniques suitable

for such a determination. The first techniquerequires experimental characterization of theresonator modes and mode coupling via themethods described in Part I. The second, anduntil recently more difficult analysis, involvesanalytical determination of the modes andmode coupling through the utilization of athree-dimensional e lectromagnetic simulationtool. Some sophisticated filter designers havemade use of auxiliary modes to design so-called dual-mode or multi-mode filters thatutilize two or more of the resonant modes toobtain very compact, low loss filters with ex-cellent rejection band characteristics. Thegeneral design procedure is not suitable forthis task.

The input, output and inter-resonator cou-

pling is accomplished via the magnetic fieldwhich is orthogonal to the circular plane of the cylindrical resonator for the dominantTE 01 mode. The equivalent circuit of the di-electric resonator filter represents the electri-cal behavior in the principal mode only. It hasacceptable accuracy if the resonator environ-ment and mounting arrangement has demon-strated elimination of the auxiliary modes.

To obtain the highest unloaded quality fac-tor available from the cylindrical dielectricresonator, a low loss dielectric support struc-ture is required to separate the resonator fromthe electrical ground boundary.

HELICAL RESONATOR FILTERThe helical resonator filter is another filter

type for which the general design procedur e isapplicable. Helical resonator filters are partic-ularly useful within the VHF and UHF bandsfor low loss, narrowband applications, andwhere the greater volume of a distributed res-onator filter is prohibitive. The helical res-onator is at least partially distributed due tothe combination of self-inductance and theelectrical length of the coil structure. The he-lical resonator is tuned via the distributed ca-pacitance of the tuning screw at the high elec-tric field point of the resonator. A direct tap atthe low electric field point of the resonator ac-complishes input and output coupling. Theresonator spacing and coupling slot at the highmagnetic field point of the helical structurefacilitates inter-resonator coupling.

Figure B2 shows the mechanical andelectrical schematic of a typical five-sectionhelical resonator filter. Once again, resonatorparameters and coupling coefficients may bedetermined experimentally or analytically bythe use of EM simulation tools. Usually, a lowloss dielectric form that facilitates uniformity,placement and structure supports the helicalresonator.

DIELECTRICRE SON A TO R


C O UP LI N GSLO T

C O UP LI N GSLO T


O U TPU TC O UP LI N GLOO PTU N ER

H-F IELD LI N ESO F TE 01 M O DE LO W DIELECTRIC SUPP O RT

TU N ER T U N ER

O U TPU TC O UP LI N G

LOO P

DR 3DR 2DR 1

v Fig. B1 Dielectric resonator filter.

SLOT SLOT

TUNER TUNER TUNER TUNER TUNER

SLOTSLOT

v Fig. B2 Helical resonator filter.

Bandpass Filter Tutorial2

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