Design and Realization of 5th Order

Asymmetric Cross Coupled Coaxial Resonator

Filter

By Muhammad Latif

Manager

Satellite Research and Development

Center SUPARCO Lahore

1. Filter Synthesis Process

2. Filter Realization by Full-wave Simulation

3. Low-pass Prototype Filter design

4. Low-pass to Bandpass Filter transformation

5. Filter Topology

6. Electrical Circuit of multiple Coupled Resonators

7. coupling matrix Synthesis and Reconfiguration

8. Verification of Coupling matrix with Ansoft Designer

9. Coaxial Resonator Design

10. HFSS structure for Input and output Design

11. HFSS structure for Inter-resonator Iris Design

12. HFSS structure for Inter-resonator Loop Design

13. HFSS structure of complete Filter

14. Initial Results of Filter

15. Tolerance Analysis of Coupling Matrix

16. Final Results of Filter

17. Comparison of Initial Design and Optimized Design

18. Conclusion

Contents

Filter Specifications Selection of Filter Technology Type

Select Filter Topology

Polynomial Generation

Rejection Lobe Optimization

Group Delay Equalization

Synthesis of Coupling Matrix

Reconfiguration of Coupling Matrix

Conform Specifications

3

Coupling Matrix Resonator Design Input Coupling

Design

Inter-resonator Couplings Design

Resonator Loading Integration of Sub-

structures

Fine tuning of full structure

Manufacturing Post-manufacturing

Tuning

4

Specification Value

Center Frequency 2.04GHz

Bandwidth 50MHz

Insertion Loss ≤1dB

Return Loss ≥20dB

Out of band rejection ≥80dB @(2.19-2.240)GHz

Filter Design Specifications

TZ1= 1.7j; TZ2= 2.7j; TZ3=5.8j; TZ4=∞; TZ5=∞

Ps = 1.0000i*S^3+ 10.2000*S^2 -30.1100i*S -26.6220

Fs = 1.0000*S^5 - 0.6041i*S^4+ 1.1051*S^3 - 0.5865i*S^2+ 0.2049*S - 0.0668i

Es = 1.0000*S^5+ (2.2480 - 0.6041i) *S^4+ (3.6319 - 1.4792i) *S^3+

(3.3579 - 2.3855i) *S^2+( 1.7621 - 2.1248i) *S+(0.2747 - 0.8660i)

Low-pass Prototype Filter design

-4 -2 0 2 4 6 8-180

-160

-140

-120

-100

-80

-60

-40

-20

0Frequency Response of prototype Chebyshev Filter

Frequency (rad/s)

Retu

rn/I

nsert

ion L

oss

num2str(RL)dB

ReturnLoss

InsertionLoss

Return Loss line

Low-pass Prototype Filter design-continued

1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5-120

-100

-80

-60

-40

-20

0

Frequency (GHz)

Retlos&

Inslo

s (

dB

)

Insertion Loss and Return loss of a filter

X: 2.04

Y: -0.522

X: 2.18

Y: -89.61

X: 2.25

Y: -81.5

Retlos

Inslos

Low-pass to Bandpass Filter

transformation Qu=2000; IL=0.52dB; RL=22dB; rejection (82-89)dB

Load

5

4

3 2

1

Source

3 2

4

5

1

(c)

(b) (a)

(d)

Filter Topology

Electrical Circuit of multiple Coupled

Resonators

Coupling Matrix Generation

(a)

(b)

coupling matrix Reconfiguration to the

desired topology

0 0 0 0 0

Port1

Port2

c1

L4

04

c1

C4

05Q

u

R4

06 Q

u

R4

07 C

2

C4

08 C

2

L4

09

Qu

R4

10 C

3

C4

11 C

3

L4

12

Qu

R4

13 C

4

C4

14 C

4

L4

15

JIN

V

JINV

JINV

JINV JINV

JINV

Qu

R4

38 C

5

C4

39 C

5

L4

40

JINV

JINV

JINV

1.90 1.95 2.00 2.05 2.10 2.15 2.20 2.25 2.30F [GHz]

-120.00

-100.00

-80.00

-60.00

-40.00

-20.00

0.00

Y1

Ansoft LLC FilterAnalysisXY Plot 1 ANSOFT

m1 m2m3

m4

m5

Curve Info

dB(S(Port1,Port1))LinearFrequency

dB(S(Port1,Port2))LinearFrequency

Name X Y

m1 2.0150 -0.6272

m2 2.0400 -0.5239

m3 2.0650 -1.4977

m4 2.1900 -96.3931

m5 2.2400 -82.5586

(a)

(b) (c)

Verification of Coupling matrix with Circuit

Simulator

(a) (b)

Coaxial Resonator Design

Electrical length=63.28deg

Physical length=25.85mm

Box size=30*30*31.85mm

Unloaded Q=3750(Aluminum)

================== Number of Passes Completed : 20 Maximum : 20 Minimum : 1 ================== Criterion : Max Delta Freq. % Target : 0.01 Current : 0.022749 Target Consecutive Passes : 1 Current Consecutive Passes : 0 Converged : No ================== Pass Number|Total Tetrahedra|Max Delta Freq. %| 1| 1036| N/A| 2| 1183| 1.1723| 3| 1373| 0.52748| 4| 1560| 0.38407| 5| 1794| 0.29837| 6| 2164| 0.8101| 7| 2322| 0.077498| 8| 2825| 0.6717| 9| 3450| 0.23441| 10| 3758| 0.096755| 11| 4111| 0.043633| 12| 4570| 0.11315| 13| 5005| 0.056083| 14| 5485| 0.038865| 15| 5945| 0.049899| 16| 6567| 0.036722| 17| 7163| 0.03336| 18| 7932| 0.032606| 19| 8695| 0.026919| 20| 9710| 0.022749| Frequency= 2.03700011347 + 0.000271174147375 j GHz Q=3755

Coaxial Resonator Design-continued

2.000 2.020 2.040 2.060 2.080 2.100Freq [GHz]

2.00

4.00

6.00

8.00

10.00

12.00

Gro

up

De

lay(

1,1

)*1

e9

Ansoft LLC IOCouplingXY Plot 2

m1Curve Info max XAtYMax

GroupDelay(1,1)*1e9Setup1 : Sw eep1

11.6330 2.0570

Name X Y

m1 2.0570 11.6330

(a)

(b) (c)

Input and output Coupling Design

Design Values Physical

Dimensions

Simulation

Results

Design

Requirement

F0(GHz)

Connector

Displacement

5.25mm 11.32 ns 11.335ns 2.082

Coupling Mij Coupling Bandwidth

(MHz)

M12 45.070

M23 21.4200

M34 25.1050

M45 45.7500

M14 7.3400

M24 20.92

M15 0.7

Design Values Physical Dimensions Simulation Results F0(GHz)

a_m12 16.95mm 45.107 MHz 2.0097

a_m23 11.85mm 21.45MHz 2.023

a_m34 12.73 mm 25.25 MHz 2.021

a_m45 17.1 mm 45.8500 MHz 2.010

a_m14 W=9.1

h(depth)=15mm

7.37 2.032

(a)

(b)

Inter-resonator Coupling Iris Design

(a) (b)

1.950 1.975 2.000 2.025 2.050Freq [GHz]

-87.50

-75.00

-62.50

-50.00

-37.50

-25.00

-12.50

0.00

Y1

Ansoft LLC M24XY Plot 2

m1

m2

Curve Info

dB(S(1,1))Setup1 : Sw eep2

dB(S(2,1))Setup1 : Sw eep2

Name X Y

m1 1.9975 -16.7557

m2 2.0230 -6.7911

Name Delta(X) Delta(Y) Slope(Y) InvSlope(Y)

d(m1,m2) 0.0255 9.9646 390.7682 0.0026

(c)

Inter-resonator Loop Design

Design

Values

Physical Dimensions Simulation

Coupling

bandwidth

(MHz)

Design

Coupling

bandwidth

(MHz)

F0(GHz)

M24 Probe length=18.6mm

Diameter=2.5mm

Depth from top=14.77mm

Aperture depth=20mm, width=5.88

20.92 21. 2.025

M15 Aperture depth=5mm

width=6mm

length=8.6mm

Probe length=13.5mm

Diameter=1.5mm

Depth from top=14.2mm

0.8MHz 0.7MHz 2.02

Inter-resonator Loop Design-continued

Required Resonator

frequency (MHz)

Tuning screw

penetration.(mm)

M11=0.0547 ;F11=2.0386 5.89

M22=-0.0613;F22=2.0415 4.85

M33=-0.7117 ;F33=2.0579 4.99

M44=0.0746 ;F44=2.0381 4.82

M55=0.0525 ;F55=2.0387 5.9

(a)

Resonator Tuning for given Frequency

Complete Filter structure Simulation

Large Computational problem; almost 450,000 tetrahedral elements;45minutes for

one simulation on HPC

Filter Size Length=100mm, width =68mm, height=48(Assumptions: wall

thickness=3mm, screw-bed =2mm, screw height on top=4mm

wi=(-mii*w0*BWF+sqrt((mii*w0*BWF)^2+4*w0^2))/2;

1.90 2.00 2.10 2.20 2.30 2.40 2.50 2.60Freq [GHz]

-100.00

-80.00

-60.00

-40.00

-20.00

0.00

Y1

Ansoft LLC CompleteFilterV5XY Plot 2

m1

m4

m5Curve Info

dB(S(1,1))Setup1 : Sw eep2

dB(S(2,1))Setup1 : Sw eep2

Name X Y

m1 2.0800 -32.6629

m2 2.6150 -92.7610

m3 2.8100 -99.0697

m4 2.0500 -6.2307

m5 2.0450 -0.8075

(a)

(b)

Initial Results of Filter

-6 -4 -2 0 2 4 6-160

-140

-120

-100

-80

-60

-40

-20

0

Frequency (GHz)

Retlos&

Inslo

s (

dB

)

Insertion Loss and Return loss of a filter

Retlos

Inslos

(a )Analysis of M14 at .1468,.155,.16

-6 -4 -2 0 2 4 6-160

-140

-120

-100

-80

-60

-40

-20

0

Frequency (GHz)

Retlos&

Inslo

s (

dB

)

Insertion Loss and Return loss of a filter

Retlos

Inslos

(b)Analysis of M15 at .014,.01,.005

-6 -4 -2 0 2 4 6-160

-140

-120

-100

-80

-60

-40

-20

0

Frequency (GHz)

Ret

los&

Insl

os (

dB)

Insertion Loss and Return loss of a filter

Retlos

Inslos

(c)Analysis of M24 at .422,.48,.55

Tolerance Analysis of Coupling Matrix

1.95 2.00 2.05 2.10 2.15 2.20 2.25 2.30 2.35Freq [GHz]

-140.00

-120.00

-100.00

-80.00

-60.00

-40.00

-20.00

0.00

Y1

Ansoft LLC CompleteFilterV7XY Plot 2 ANSOFTm1 m2

m3

m6

m7

m8

m5m4

Curve Info

dB(S(1,1))Setup1 : Sw eep2

dB(S(2,1))Setup1 : Sw eep2

Name X Y

m1 2.0150 -0.1992

m2 2.0650 -0.0461

m3 2.0150 -13.8186

m4 2.0650 -20.1650

m5 2.0260 -17.0211

m6 2.0970 -48.3485

m7 2.1900 -97.1355

m8 2.2400 -86.2095

Final Results of Filter

Conclusion

1. Filter was synthesized as per specifications

2. Filter was realized utilizing full-wave EM Simulator

3. Now filter is on the course of manufacturing and post-

manufacturing tuning will be performed soon.