© 2007 DAS Engineering This presentation belongs to DAS Engineering Unauthorized reproduction and/or distribution of this article is prohibited

Compact Hairpin BPF design

David A. Straight

© 2007 DAS Engineering This presentation belongs to DAS Engineering Unauthorized reproduction and/or distribution of this article is prohibited

Calculation of coupling coefficients and Qe

External (or loaded) Q and coupling coefficients between resonators are calculated using low pass filter prototype values. This is a well known procedure found in many text books [2], [3].

© 2007 DAS Engineering This presentation belongs to DAS Engineering Unauthorized reproduction and/or distribution of this article is prohibited

Calculation of coupling coefficients and Qe

A procedure for relating coupling coefficient and loaded Q to physical structures using EM wave simulators is outlined in [1].

Graphs of coupling coefficients verses physical distance of specific resonators configurations are generated by an EM wave solver (HFSS in this case)

Similarly the loaded Q of the end resonators are solved for using HFSS

© 2007 DAS Engineering This presentation belongs to DAS Engineering Unauthorized reproduction and/or distribution of this article is prohibited

Loaded Q

HFSS was used to calculated loaded Q. In the picture below we see a single resonator connected to a 50 Ω resistor. Because the resonator is ½ λ an electric field node is located at the center of the resonator; the unloaded Q will degrade as the tap moves away from this center point.

The eigenmode solver of HFSS was used to find the tap point that gives a loaded Q of 14.5 while maintaining a resonance of 7.59GHz

© 2007 DAS Engineering This presentation belongs to DAS Engineering Unauthorized reproduction and/or distribution of this article is prohibited

Magnetic Coupling Example

A coupling coefficient for a specific spacing of a resonator can be solved for using an EM wave simulator such as HFSS.

In HFSS several simulations were performed using the parametric sweep to generate several points for several spacing.

The coupling coefficient can be calculated by knowing the frequency separation of the two modes (tighter coupling will separate the frequencies further).

© 2007 DAS Engineering This presentation belongs to DAS Engineering Unauthorized reproduction and/or distribution of this article is prohibited

Mixed Coupling - (relating coupling to physical separation of resonators)

Coupling vs. Resonator Spacing (M23)

-0.010

0.010.020.030.040.050.060.070.08

0 20 40 60 80

distance (mil)

Cou

plin

g C

oeffi

cien

t (M

23) HFSS

Interpolated

Only four HFSS points were used for this calculation

© 2007 DAS Engineering This presentation belongs to DAS Engineering Unauthorized reproduction and/or distribution of this article is prohibited

Electric Coupling - (relating coupling to physical separation of resonators)

Coupling vs. Resonator Spacing (M12)

0

0.02

0.04

0.06

0.08

0.1

0.12

0 20 40 60 80

distance (mil)

Cou

plin

g Co

effic

ient

(M

12) HFSS

Interpolated

© 2007 DAS Engineering This presentation belongs to DAS Engineering Unauthorized reproduction and/or distribution of this article is prohibited

First Pass Results – No Optimization or Tuning

© 2007 DAS Engineering This presentation belongs to DAS Engineering Unauthorized reproduction and/or distribution of this article is prohibited

First optimization

The graph below is valid between 7 to 8 GHz (i.e. HFSS solved for these frequencies only – ignore data below 7GHz)

© 2007 DAS Engineering This presentation belongs to DAS Engineering Unauthorized reproduction and/or distribution of this article is prohibited

PCB implementation

© 2007 DAS Engineering This presentation belongs to DAS Engineering Unauthorized reproduction and/or distribution of this article is prohibited

References

[1] J.S. Hong and M.J. Lancaster, "Microstrip Filters for RF/Microwave Applications," Wiley & Sons, Inc. 2001

[2] G. Matthaei , E.M.T. Jones , L. Young, “Microwave Filters, Impedance-Matching Networks, and Coupling Structures”

[3] Anatol I. Zverev, “Handbook of Filter Synthesis”

[4] Hong, J. S. and M. J. Lancaster, "Couplings of microstrip square open-Loop resonators for cross-coupled planar microwave filters," IEEE Trans. Microwave Theory Tech., Vol. MTT-44, 2099-2109, Dec., 1996.