Using the Moebius Transformation to Predict the Effect of Source Impedance on Insertion Loss

2018 ◽  
Vol 66 (2) ◽  
pp. 105-116 ◽  
Author(s):  
Yitian Zhang ◽  
Jinghao Liu ◽  
D. W. Herrin ◽  
Gayatri Kadlaskar ◽  
Jiawei Liu
2015 ◽  
Vol 137 (3) ◽  
Author(s):  
Y. Zhang ◽  
D. W. Herrin

The Moebius transformation maps straight lines or circles in one complex domain into straight lines or circles in another. It has been observed that the equations relating acoustic or mechanical impedance modifications to responses under harmonic excitation are in the form of the Moebius transformation. Using the properties of the Moebius transformation, the impedance modification that will minimize the response at a particular frequency can be predicted provided that the modification is between two positions. To prove the utility of this method for acoustic and mechanical systems, it is demonstrated that the equations for calculation of transmission and insertion loss of mufflers, insertion loss of enclosures, and insertion loss of mounts are in the form of the Moebius transformation for impedance modifications. The method is demonstrated for enclosure insertion loss by adding a short duct in a partition introduced to an enclosure. In a similar manner, it is shown that the length or area of a bypass duct in a muffler can be tuned to maximize the transmission loss. In the final example, the insertion loss of an isolator system is improved at a particular frequency by adding mass to one side of the isolator.


Author(s):  
D. W. Herrin ◽  
Y. Zhang ◽  
J. Liu

If a mechanical or acoustical impedance modification is introduced between two positions, the effect of that modification can be plotted in the complex plane at a given frequency. It has been shown that the mechanical or acoustical response will trace a circle in the complex plane for straight-line modifications to impedance in the complex plane. In that case, the equations relating the response to an impedance modification are in a form consistent with the Moebius transformation, which maps straight lines or circles in one complex domain into straight lines or circles in another complex plane. It is demonstrated that the equations for muffler transmission loss and mount insertion loss are in a form consistent with the Moebius transformation for certain design changes. Accordingly, the usefulness of this linear system property will be illustrated for both muffler and mount design.


2012 ◽  
Vol 132 (7) ◽  
pp. 727-735 ◽  
Author(s):  
Michio Tamate ◽  
Tamiko Sasaki ◽  
Akio Toba ◽  
Yasushi Matsumoto ◽  
Keiji Wada ◽  
...  

2002 ◽  
Vol 722 ◽  
Author(s):  
T. S. Sriram ◽  
B. Strauss ◽  
S. Pappas ◽  
A. Baliga ◽  
A. Jean ◽  
...  

AbstractThis paper describes the results of extensive performance and reliability characterization of a silicon-based surface micro-machined tunable optical filter. The device comprises a high-finesse Fabry-Perot etalon with one flat and one curved dielectric mirror. The curved mirror is mounted on an electrostatically actuated silicon nitride membrane tethered to the substrate using silicon nitride posts. A voltage applied to the membrane allows the device to be tuned by adjusting the length of the cavity. The device is coupled optically to an input and an output single mode fiber inside a hermetic package. Extensive performance characterization (over operating temperature range) was performed on the packaged device. Parameters characterized included tuning characteristics, insertion loss, filter line-width and side mode suppression ratio. Reliability testing was performed by subjecting the MEMS structure to a very large number of actuations at an elevated temperature both inside the package and on a test board. The MEMS structure was found to be extremely robust, running trillions of actuations without failures. Package level reliability testing conforming to Telcordia standards indicated that key device parameters including insertion loss, filter line-width and tuning characteristics did not change measurably over the duration of the test.


2020 ◽  
Vol 12 ◽  
Author(s):  
Pampa Debnath ◽  
Ujjwal Mondal ◽  
Arpan Deyasi

Aim:: Computation of loss factors for one-bit RF MEMS switch over Ku, K and Ka-band for two different insulating substrates. Objective:: Numerical investigation of return loss, insertion loss, isolation loss are computed under both actuated and unactuated states for two different insulating substrates of the 1-bit RF MEMS switch, and corresponding up and down-capacitances are obtained. Methods:: The unique characteristics of a 1-bit RF MEMS switch of providing higher return loss under both actuated and unactuated states and also of isolation loss with negligible insertion loss makes it as a prime candidate for phase shifter application. This is presented in this manuscript with a keen focus on improvement capability by changing transmission line width, and also of overlap area; where dielectric constant of the substrate also plays a vital role. Results:: The present work exhibits very low down-capacitance over the spectrum whereas considerable amount of up-capacitance. Also when overall performance in terms of all loss parameters are considered, switch provides very low insertion loss, good return loss under actuated state and standard isolation loss. Conclusion:: Reduction of transmission line width of about 33% improved the performance of the switch by increasing isolation loss. Isolation loss of -40 dB is obtained at actuated condition in higher microwave spectra for SiO 2 at higher overlap area. Down capacitance of ~ 1dB is obtained which is novel as compared with other published literature. Moreover, a better combination of both return loss, isolation loss and insertion loss are reported in this present work compared with all other published data so far.


Author(s):  
Kittipong Nithiporndecha ◽  
Chatrpol Pakasiri

Background: A compact complex impedance-transforming balun for UHF frequencies, which is based on a coupled-line structure that matched all ports and provided high output port isolation, was designed in this paper. Methods: A lumped component transformation was used to minimize circuit size. The implemented circuit operated at 433 MHz with the reflection coefficients less than -16 dB at all ports, 0.22 dB amplitude balance and 180° phase balance at the output ports. The signal coupling between the output ports was -16.8 dB. The circuit size is small at 0.032λ. Results: Complex impedance-transforming baluns were designed to operate at 433 MHz. The source impedance at port 1 was set at Zs = 12 - j12Ω and the load impedances at port 2 and 3 were set at ZL = 80 + j30Ω. Conclusion: A compact complex impedance-transforming balun at UHF frequency, with all ports matched and high isolations, was designed and illustrated in this paper.


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