Electromagnetic Simulation of Cavity

Filters and Dielectric Resonators

Mark Bedford Childmbedford@ieee.org

Part Time Lecturer in Engineering, School of Engineering, Design & Technology / Visiting Researcher, Mobile and Satellite Communications Research Centre / University of Bradford.

Presentation notes for the 4th CST European User Group Meeting, Darmstadt, March 17th 2009.

Overview.

• Résumé of BTS Filter Technology.– Complementary rôle for electromagnetic analysis in

filter synthesis/optimisation

– Rationale for compact triple mode.

• Development of basic filter response.– Broadband analysis/Model Order Reduction (MOR).

– Eigenmode searches.

– Performance analysis and tuning.

• Realisation.

• Discussion and Conclusions.

Requirements for EM-analysis.

Require:

– Fast and efficient

calculations.

– Equally valid in time

and frequency domain.

– Properly represent the

topology and geometry

of Maxwell’s

equations.

CST:

– Inbuild AR filtering in

TD, MOR.

– Leap-frog algorithm,

dual grid.

– Finite integration

technique (FIT)and

perfect boundary

approximation (PBA).

BTS Filter Technology.

• Standard filter technology is multi-conductor coaxial (combline), with some contribution from ceramics.

• Next generation BTS filtering for advanced 3G and early 4G systems demand volume and weight reductions.

• Need to produce filter technologies which are:– Smaller and lower cost.

– Similar or better Q than combline.

– Superior Qu/Vol.

• Single vs. multimode technologies.

• Expect several new technologies to become available:– Single Mode.– Dual Mode.

– Triple Mode.

Cavity Filter Technologies.

1. Multi-conductor coaxial / combline.

2. Dielectric combline.

3. Dual mode ceramic (metallised).

1

2

3

S-Plane Synthesis.

• Generalised Chebyshev approximation

• Symmetrical network analysis– Form the transmission coefficient, S21, in terms of even- and odd-mode

admittances• For a stable system, LHP poles of S21 are extracted using the alternating-

pole technique

– Form even- and odd-mode admittances, Ye and Yo , from the polynomial comprising the LHP poles

– Form ABCD matrix from Ye and Yo

• Extract the circuit element from the ABCD matrix– Finite frequency transmission zero is extracted in the form of a phase

shifter, a shunt inductor in series with frequency invariant reactance followed by another phase shifter

• Transform the synthesized network into a cross-coupled network

Coupling Paths and Alignment.

• Store reflected

phase across

passband and into

stopband.

• Tune coupling and

resonant

frequency of each

resonator to

approximate error

over stored band.

• Finite

Transmission

Zeros.RX path, 8

resonators,

3 cross

couplings

TX path, 7

resonators,

2 cross

couplings

M12

M23

M13

M34

M45

M56

M67

M78 M68

Dielectric Resonators.

• Standard definition:– an unmetallized piece of dielectric which functions as a resonant

cavity by means of reflections at the air-dielectric interface.

• High permittivity, low loss microwave ceramic materials.

• Single mode technologies:– Compact TE01

– Ceramic combline.

– Ceramic waveguide.

• Dual and triple mode technologies:– Dual mode: HE11

– Dual and triple mode: TE01

– Triple mode: TE01 & HE11

• Metallization.

The Spherical TE01 Resonator

• First spur is TM10

• Introduce central hole

• Open to 30% of sphere diameter

• Upwards frequency shift bounded below 1%, with maximum SPFF of 1.42. Implies 21% increase in spur free BW cf solid DR.

• Hollow spheres, not mechanically sound.

• Circulation of E with orthogonally varying H of TE01 v.similar to cubic structure.

Triple Mode DR – Dielectric Sphere.

JDMJDMAKS

1.41071.34811.34101.366SPFF

2.59652.47112.47112.52561st spur

1.84141.83391.8337

1.84011.83271.8327

1.84011.83261.83261.8485Triplet

Meshing 40 lines /

No -refinement in initial conditions

Calc.Mode

Hollow,

di/do=0.3

Sphere, ro=12.4mm, r=45, 60mm

cube

JDMJDMAKS

1.41071.34811.34101.366SPFF

2.59652.47112.47112.52561st spur

1.84141.83391.8337

1.84011.83271.8327

1.84011.83261.83261.8485Triplet

Meshing 40 lines /

No -refinement in initial conditions

Calc.Mode

Hollow,

di/do=0.3

Sphere, ro=12.4mm, r=45, 60mm

cube

The TE01 Resonator

• TE01 , HEM11 , HEM21 , TM01 – depends on dimensions and .

• When <1, the TE01dominates as the lowest order resonance.

• When >1, the HEM11dominates as the lowest order resonance.

• The indicates less than half a sine wave variation along the direction of propagation.

• For 35 approx. 95% of the stored electrical energy of the TE01 -mode is confined within the resonator. The corresponding figure for the magnetic energy is 60%.

• The remaining EM energy is distributed through the air in the neighbourhood of the dielectric surface, and rapidly decays with distance.

The TE01 Resonator

• Optimisation of , 0.4.

• Introduction of central hole perturbs E, shifts resonance and spurs having similar E-variation to higher frequencies.

• In fact any mode having its E-field concentrated near the axial line will be affected.

• The central hole can be opened up to 35% without significantly affecting the frequency.

• Effect of supporting structure. – Typically alumina, 9.5 – 9.9.

– Polystyrene, 2.2.

• Support has non trivial effect on TM – can become first spur.– The downward frequency shift

is due to its E field lying almost entirely on the outside flat surface of the dielectric.

– Sensitive to metal tuning discs.

– Possible strong coupling to inter-cavity irises.

• Multi-criteria optimisation, but constrained by synthesis requirement.

Compact TE01 .

• Application:– Full band filter.

– High Qu.

• Advantages:– Better SPFF than HE11

dual.

– Small cavity and single mode flexible layout.

• Disadvantage:– Low Qu/Vol=310cm-3.

– Minimum cavity size is Diam 35 mm x 25 mm deep height is a limiting factor for some applications.

Eigenvalue Search.

JDM solver, 25 lines per

wavelength.

1.269743SPFF

ratio

3.50E-122.59E-0082.6283704

1st spur

2.66E-135.8E-0072.0269023

HEM11

5.34E-0131.61E-0082.0232742

HEM11

9.45E-0141.50E-0092.0169961

TE01

div e2-normFreqMode

Solver errorModes

JDM solver, 25 lines per

wavelength.

1.269743SPFF

ratio

3.50E-122.59E-0082.6283704

1st spur

2.66E-135.8E-0072.0269023

HEM11

5.34E-0131.61E-0082.0232742

HEM11

9.45E-0141.50E-0092.0169961

TE01

div e2-normFreqMode

Solver errorModes

Chamfered Rectangular DR.

Mode 1: TE01 , e-field

Mode 2: HE11 , h-field.

Mode 3: HE11 , e-field

Mode 1: TE01

Mode 2: HE11

Mode 3: HE11dual

triple

Chamfer 6mm, cavity width 35.3mm

Field Distributions, Calculated Qu-factor.

• Electric and magnetic field monitors at 2GHz (XY-plane):

• Losses and unloaded Q-factor.

e-field h-field

Coupling Mechanism.

• The excitation probes are aligned along the dual modes (HE11 ) the M12 and M23 couplings controlled as a function of the coupling hole diameters (to and from the circular TE01 mode).

• Dual mode coupling M13 is controlled in practice by having tuning screws above the DR.

M12

1

3M23

h-field, 2GHz

Basic Filter

Response, N = 3.

1.9 2.32 2.05 2.1 2.15 2.2 GHz

-60

0

-55

-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

dB

S21

-50

0

-45.83

-41.67

-37.5

-33.33

-29.17

-25

-20.83

-16.67

-12.5

-8.333

-4.167

dB

S11

umts : Graph : S21 Mag dB / S11 Mag dB

1

1.9 2.31.96 2 2.04 2.09 2.14 2.19 2.24 GHz

-60

0

-55

-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

dB

S21

-50

0

-45.83

-41.67

-37.5

-33.33

-29.17

-25

-20.83

-16.67

-12.5

-8.333

-4.167

dB

S11

pcs_at_2 : Graph : S21 Mag dB / S11 Mag dB

1

UMTS

PCSCT-section

Tuned Output of EM-analysis.

Final Comparison, N = 3.

CH1 S22 LOG 5 dB/ REF 0 dB

Cor

PRm

CH2 S21 LOG 5 dB/ REF 0 dB

CENTER 2 000 . 000 000 MHz SPAN 500 . 000 000 MHz

Cor

PRm

15 Jul 2002 14:44:53

1

2

1 : -19 . 175 dB 1 937 . 000 000 MHz

CH1 Markers 2 : -18 . 359 dB 2 . 00900 GHz

1 2

3

4

5

5 : - . 16020 dB 1 975 . 700 000 MHz

CH2 Markers 1 : - . 16210 dB 1 . 93700 GHz

2 : - . 24330 dB 2 . 00900 GHz

3 : -48 . 886 dB 2 . 05710 GHz

4 : -8 . 3259 dB 1 . 83700 GHz

Next Step: N = 6.

• Internal Couplings approximately correct.

• Input/output probes to be increased.

• EM-geometry of probes to be optimised.

• Current Unloaded Qvalue 7000 9000.

CH1 S11 LOG 5 dB/ REF 0 dB

START 1 894 . 836 004 MHz STOP 2 144 . 836 004 MHz

Cor

PRm

CH2 S21 LOG 10 dB/ REF 0 dB

Cor

PRm

10 Sep 2002 10:01:17

1

2

3

4

4 : . 25370 dB 2 070 . 000 000 MHz

CH1 Markers 1 : -9 . 2733 dB 1 . 97500 GHz

2 : -16 . 391 dB 2 . 01161 GHz

3 : -19 . 698 dB 2 . 05000 GHz

1 2 3

4

4 : -53 . 609 dB

CH2 Markers 1 : - . 83090 dB 1 . 97500 GHz

2 : - . 14520 dB 2 . 01161 GHz

3 : - . 55090 dB 2 . 05000 GHz

CH1 S11 LOG 5 dB/ REF 0 dB

START 1 894 . 836 004 MHz STOP 3 000 . 000 000 MHz

PRm

CH2 S21 LOG 10 dB/ REF 0 dB

PRm

MARKER 5 2.66746807 GHz

10 Sep 2002 10:01:35

1

2 3

4

5

5 : -1 . 7323 dB 2 667 . 468 070 MHz

CH1 Markers 1 : -12 . 762 dB 1 . 97500 GHz

2 : -17 . 136 dB 2 . 01161 GHz

3 : -16 . 030 dB 2 . 05000 GHz

4 : -1 . 5829 dB 2 . 07000 GHz

1 2 3

4

5

5 : -35 . 030 dB

CH2 Markers 1 : -2 . 2911 dB 1 . 97500 GHz

2 : -1 . 7381 dB 2 . 01161 GHz

3 : -3 . 0676 dB 2 . 05000 GHz

4 : -56 . 046 dB 2 . 07000 GHz

Broadband

Eventual Goal.

• Diplexer unit.

• N = 6 RX and TX.

• Phased common junction,

physically using a simple

trough line construction.

• Integrated with LNA

package.

Discussion.

• Proof of principle is apparent for compact triple mode, but not yet sufficient for useful application.

• Practical implementation not clear, notably with respect to suspension of DR and also degree of external tuning.

• Full identification of coupling mechanism, redundancy, proper linkage to network model. Experiment with use of iris apertures. Space filling layout ?

• Dual mode operation may be more sensible interim goal.

• Eventual mixed dual and triple mode operation ?

• Selective use of partial metal deposition directly to ceramic.

References.[1] Liang and Blair, High Q TE01 mode DR filters for PCS base stations, IEEE Trans. MTT-46, 12, 2493,

1998.[2] Fiedziuszko et al, Dielectric materials, devices and circuits, IEEE Trans. MTT-50, 3, 706, 2002.[3] I.C.Hunter et al, Dual mode filters with conductor loaded dielectric resonators, IEEE Trans. MTT-47, 12,

2304, 1999.[4] I.C.Hunter et al, Triple mode hybrid reflection filters, IEE Proc. MAP-145, 4, 337. 1998.

[5] V.Walker and I.C.Hunter, Design of cross coupled dielectric loaded waveguide filters, IEE Proc. MAP-148, 2, 91, 2001.[6] P.J.B.Clarricoats, Propagation along unbounded and bounded dielectric rods – part 2, Proc. IEE 108C,

177, 1961.[7] J.D.Rhodes, General constraints on propagation characteristics of electromagnetic waves in uniform

inhomogeneous waveguides, Proc. IEE, 118, 7, 849, 1971.[8] T.Weiland, Eine methode zur losung der Maxwellschen Gleichungen fur sechs-komonentige Felder auf diskreter Basis, AEU, 31, 116, 1977.

[9] G.Deschamps, Differential Forms, in E.C.Roubine (ed), Mathematics applied to physics, Springer Verlag/UNESCO.

[10] T.Weiland, Finite integration and discrete electromagnetism, in C.Carstensen et al (eds), Lecture notes in comp. sci. and eng. Vol. 28, Springer Verlag.[11] I.Munteanu and F.Hirtenfelder, Convergence of the FIT on various mesh types, Proc. German Microwave

Conference (GeMic05), Ulm, April 2005.[12] P.D.Sleigh, Asymmetric filter design for satellite communication applications, IEE colloquium on

microwave filters, IEE colloquium digest 1982/4, 1982 (6 pages).[13] R.J.Cameron, Advanced coupling matrix synthesis for microwave filters, IEEE Trans. MTT-51, 1, 1, 2003.[14] A.G.Lamperez, et al, Effective electromagnetic optimization of microwave filters and multiplexers using

rational models, IEEE Trans. MTT-52, 2, 508, 2004.