Contents

The following Help Topics are available:

Coaxial Resonator Design (Resonator):

Resonant Frequency

Coaxial Resonator Parameters

Coaxial Resonator Part Number

Coaxial Resonator Design (Inductor):

Using Coaxial Elements as Inductors

Specifying Coaxial Inductors

Center Frequency

Inductance/Impedance Entry

Coaxial Inductor Parameters

Coaxial Resonator Part Number

General Information:

Changing Units

Element Profile

Dielectric Material

About Trans-Tech:

About Trans-Tech

Other Trans-Tech Products

Sales Offices

References and Application Notes

About COAX:

About Coaxial Resonator Design

For Help on Help, Press F1


Coaxial Resonator Part Number

The current coaxial resonator part number is displayed below the calculated results.

The part number can be decoded as follows:

Example:  SR 8800 LP Q 1300 B Y

SR	Product Code: SR - coaxial resonator SI - coaxial inductor.

8800	Type of material:  1000, 2000, 8800 or 9000.

LP	Resonator Profile:  HP, SP, LS, LP, MP, or SM.

Q	Type:  Q for λ/4 shorted resonator, H for λ/2 open resonator.

1300	Resonant Frequency (SR) or Frequency of use (SI) in MHz.

B	(SR only) Frequency Tolerance:  A = +/- 0.5%, B = +/- 1.0%

Y	Tab:  Y = Yes, N = No.

6.3	(SI only) Inductance:  Inductance desired at frequency of use (pF).


Coaxial Resonator Parameters

Coaxial Resonator Length (L):

The length of the resonator determines the resonant frequency in a particular material.  A quarter wavelength with a short or a half wavelength with an open results in the functionality of a parallel resonant circuit.

Coaxial Resonator Q:

The Q or Quality Factor of the resonator is the ratio of the dissipated energy to the stored energy in the resonator.  A high Q designates low losses and narrow frequency band performance.  A low Q signifies higher losses and wider frequency band performance.  Most of the loss associated with the resonator is due to metallization losses.


Changing Units

Length Units (inches/mm):

To change the length unit, select either the Inches or Millimeters menu pick under the Units menu.  Choosing either inches or mm will convert all length displays to the new length unit.  A check mark next to the length unit shows the length unit currently in use.


About Trans-Tech
Trans-Tech

A Subsidiary of Alpha Industries

Introduction:

An established world leader in the technical ceramic industry, Trans-Tech's ceramic materials include GPS patch antennas, microwave ferrites, microwave garnets, and microwave dielectrics, as well as dielectric and coaxial resonator materials and filters.  Additional materials and services include technical ceramic powders and thick- and thin-film metallization.

Trans-Tech can provide large-scale, automated processing as well as custom work;  the Adamstown, Maryland facility can handle production runs from 10 pieces to 10 million with a state-of-the-art electronics measurements laboratory for rigorous quality assurance testing.

Trans-Tech's experience in microwave ceramics has led to an increasing number of requests for custom research and development services.  To accommodate these requests, as well as provide internal, in-process quality control, Trans-Tech offers a fully equipped engineering R&D lab.

Cornerstones of Our Success:  Process Control

Trans-Tech believes that the best way to assure consistency and reproducibility is to thoroughly understand and control the entire ceramic process.  From formulating and blending raw materials, through firing and finishing the final product, Trans-Tech controls quality by controlling the entire manufacturing process, including designing and building its own dies and kilns.

The manufacturing process includes:

Qualifying --> Blending --> Forming --> Firing --> Finishing --> Quality

Excellent Technology and Customer Service

Trans-Tech is a manufacturing company built on outstanding ceramic technology tailored to satisfy customer requirements.  Our materials have established a reputation for quality, reproducibility and unsurpassed performance.  Our experienced applications engineers and sales staff team work with customers to provide the highest quality solutions for the best value.

•	Diverse, highly-trained technical staff, including electrical engineers, physicists, chemists, and ceramists.

•	Advanced forming and firing techniques based on proprietary processes and equipment.

•	Control of the entire ceramic process.

•	Our Commitment:  100% Customer Satisfaction.

•	Timely delivery of quality products.

•	Partnerships in product development.

•	Largest selection of RF/Microwave materials in the industry.

•	World-wide sales network for direct customer contact.

Continuous Quality Improvement

•	TQM -- Total Quality Management is an on going effort with each employee accepting responsibility to continuously improve our products, processes, and procedures.

•	Training -- Trans-Tech continually invests in its people with on going training.

•	Active Quality Assurance Group that oversees the analyzing and resolving of manufacturing problems.

•	The industry's most demanding customers, among them Motorola, Ericsson, Allen Telecom, and Lucent Technologies, have found Trans-Tech's Quality Systems satisfy their high standards. They have included our products in their select vendor status and ship-to-stock programs.

Alpha/Trans-Tech -- Your Single Source

In 1981, Trans-Tech became a wholly owned subsidiary of Alpha Industries.  Based in Woburn, Massachusetts, Alpha produces an extensive selection of RF GaAs integrated Circuits; amplifiers, attenuators, mixers, directional couplers, and power dividers, and Semiconductor Discretes; chip capacitors, FET fixed pad attenuators, receiving diodes, and varactors.  Our combined world-wide sales network enables Trans-Tech to service customers worldwide.  As a team, we can provide a variety of solutions to the design engineer.

Total Product Solution

Antennas

Ceramic

Patch Array

GPS

Ceramic

Ceramic Filters

GaAs MMIC Components

Attenuators

Amplifiers

Switches

Millimeterwave Products

FET Based DRO's

Gunn Oscillators

MMW GaAs MMIC's

Modules

Passive Components

Couplers

Directional Couplers

Mixers

Modulators

Power Dividers

Quadrature

Hybrids

Resonators

Coaxial

Dielectric

Semiconductor Discretes

Chip Capacitors

FET Transistors

Fixed Pad Attenuators

PIN Diodes

Receiving Diodes

Schottky Diodes

Varactors

Space

Die

Discrete Semiconductors

Hybrid Devices

MMIC

Packaged

Trans-Tech

A Subsidiary of Alpha Industries


Qualifying

Raw materials are carefully analyzed for purity, particle size and distribution, reactivity, density, chemical analysis, and microstructure, to ensure the quality of the incoming powders.


Blending

Raw materials are blended, presintered, milled, spray-dried, and screened to create an optimal particle size.


Forming

After adding a binder, pressure or heat is applied to form material into required shapes.


Firing

The kilns are microprocessor controlled to assure consistency of the finished product.


Finishing

The fired ceramic is diamond ground, polished or lapped according to customer specifications to guarantee precise dimensions and close tolerances.


Quality

On-line Inspection and Continuous Statistical Review enables Trans-Tech to identify and resolve problems at the source, thereby minimizing rework, controlling costs, and maintaining our commitment to superior quality.


Other Trans-Tech Products

In addition to Coaxial Resonators, Trans-Tech offers the following products:

(Click on name to see more information.)

Ceramic Bandpass Filters

Trans-Tech offers ceramic bandpass filters in the frequency range of 200 MHz to 2.5 GHz.  They exhibit definite advantages in comparison to other filter technologies -- Cavity, Discrete Component, Helical, Microstrip, and SAW.

Microwave Ferrites

Microwave Garnets

Microwave Dielectrics

Non-Microwave Ferrites

Technical Ceramic Powders

Advanced Technical Ceramics (ATC) consists of a multi-faceted production line ranging from abrasion-resistant and thermal barrier materials to new applications and new product development.  Trans-Tech is a strong research, development, and manufacturing company with a proven ability for scale-up production of new products.

Each powder can be synthesized in a number of modifications, either by conventional synthesis and processing or by state-of-the-art chemical precursor techniques.  Powders are available as fully reacted, flowable materials suitable for thermal spray processing.  They can also be custom prepared in sinterable form or as submicron particulates  for fabrication of monolithic ceramics and composites.  Specialized chemistries and purity, phase and particle surface area can be obtained depending on the specific application.

These powders are useful for a variety of specialized techniques and applications ranging from custom powders for research to high quality materials for thermal spraying, E-Beam deposition, and processing of semiconductor or dielectric composites.


Sales Offices

Click on area of interest for contact information:

United States 	Australia

Europe 	Brazil

Asia	Canada

Israel

Mexico

New Zealand

South Africa

Turkey


Advanced Technology Marketing

Serving Maine, Massachusetts, New Hampshire, Rhode Island, and Vermont :

Chelmsford, MA 01824

Telephone:  (978) 458-0200

FAX:  (978) 458-7990

E-Mail: atm@atmink.com


EM-TECH

Serving Upstate New York:

East Syracuse, NY 13057

Telephone:  (315) 437-6410

FAX:  (315) 437-6374

E-Mail: emtkassoc@aol.com


Trionic Associates

Serving Fairfield County Connecticut, New York City, Long Island and Northern New Jersey:

Great Neck, Long Island, NY 11021

Telephone:  (516) 466-2300

FAX:  (516) 466-2319


Beacon Electronics Associates

Serving Alabama, Northern Florida, Mississippi, and Western Tennessee:

Huntsville, AL

Telephone:  (205) 881-5031

FAX: (205) 883-9516

Serving Georgia and Eastern Tennessee:

Atlanta, GA

Telephone:  (404) 256-9640

FAX: (404) 256-1938

Serving Central and Southern Florida and Puerto Rico:

Longwood, FL

Telephone:  (407) 788-1155

FAX: (407) 788-1176

Serving North and South Carolina:

Raleigh, NC

Telephone:  (919) 787-0330

FAX: (919) 781-8431


Koebert Associates

Serving Delaware, Eastern Pennsylvania and Southern New Jersey:

Glenside, PA  19038

Telephone:  (215) 887-2310

FAX:  (215) 576-1329

Email: kobert@cyberix.com

Serving Northern Virginia, West Virginia and Western Maryland:

Jefferson, MD  21755

Telephone:  (301) 371-8578

FAX:  (301) 371-6915

Southern Virginia:

Carrboro, NC  27510

Telephone:  (919) 932-5366

FAX:  (919) 932-5856


Chas Group

Serving Indiana, Kentucky, Ohio,

Michigan, and Western Pennsylvania:

Fort Wayne, IN  46804

Telephone:  (219) 459-1971

FAX:  (219) 459-1972


Cain-Forlaw

Serving Illinois, and Wisconsin:

Palatine, IL 60067

Telephone:  (847) 202-9898

FAX: (847) 202-9896

E-mail: cainforlaw@aol.com

Serving Minnesota; North Dakota; South Dakota

Burnsville, MN 55337

Telephone:  (612) 882-4090

FAX: (612) 882-4088

Serving Kansas; Nebraska; Missouri; Iowa

Merriam, KS 66202

Telephone:  (913) 789-9896

FAX: (913) 789-9897

E-mail: cainforkc@aol.com


Phase Com

Serving Texas except El Paso (97543), Arkansas, and Oklahoma

Ft. Worth, TX 76126

Telephone:  (972) 664-0442

FAX:  (817) 249-4421


Y & O Associates

Serving Arizona and New Mexico; El Paso, TX

Phoenix, AZ  85044

Telephone:  (800) 515-1554

FAX:  (800) 515-1574


Cain-Pollock, Inc.

Serving Colorado and Utah:

Parker, CO  80134

Telephone:  (303) 805-2515

FAX: (303) 805-2514

Email: S.M.Pollock@worldnet.ATT.net


Sea-Port Technical Sales

Serving Oregon and Washington:

Redmond, WA  98053

Telephone:  (425) 391-6714

FAX:  (425) 391-6715


Y & O Associates

Serving Southern California:

Tustin, CA  92680

Telephone:  (714) 838-5114

FAX:  (714) 838-5321

E-Mail: contactus@yando.com


Cain-Sweet, Co.

USA Office for Cain-Sweet, Co.:

Bellevue, CA  98004

Telephone:  (425) 462-2118

FAX:  (425) 451-9418

Serving British Columbia:

Burnaby, B.C.  V3J 1R6

Telephone:  (604) 420-6511

FAX:  (604) 420-6511

Serving Alberta, Saskatchewan and Manitoba:

Calgary, Alberta  T2E 6K9

Telephone:  (403) 250-7288

FAX:  (403) 250-7289

Serving Winnepeg and Ontario:

Ottawa, Ontario  K2B 1A5

Telephone:  (613) 820-2606

FAX:  (613) 820-2709

Serving Quebec, New Brunswick, Nova Scotia and Newfoundland:

Dollards Des Ormeaux, QC  H9B 2N4

Telephone:  (514) 421-0848

FAX:  (514) 421-1324


Disman Bakner

Serving Northern California and Nevada:

Mountain View, CA 94043

Telephone: 650-969-3010

FAX: 650-969-5620

Website: www.dbsales.com


Microwave Ferrites

Magnesium Ferrites with Saturation Magnetization (4πMs) from 750 to 3000 Gauss.

Nickel Ferrites with Saturation Magnetization (4πMs) from 500 to 5000 Gauss.

Lithium Ferrites with Saturation Magnetization (4πMs) from 600 to 4800 Gauss.

Millimeter Wave Ferrites

Nickel-Aluminum Ferrites

Nickel-Zinc Ferrites

Magnesium-Aluminum Ferrites

Magnesium-Zinc Ferrites


Microwave Garnets

Yttrium-Iron Garnets

Yttrium-Aluminum-Iron Garnets

Yttrium-Gadolinium-Iron Garnets

Yttrium-Gadolinium-Aluminum-Iron Garnets

Calcium Vanadium


Microwave Dielectrics

Cordierite (εr=4.5)

Fosterite (εr=6.3)

Alumina (εr=9.5)

Magnesium Titanate (εr=13 to 16)

Barium Tetratitanate (εr=38, 50)

Titania (εr=100)

Nickel Aluminum Titanates (SMAT Series εr=9 to 14)

Magnesium Calcium Titanates (MCT Series εr=18 to 140)

Spinel Material (εr=71, 78, 98, & 110)


Non-Microwave Ferrites

Lithium-Zinc and Nickel-Colbalt Ferrites for non-microwave latching applications.

Pressure-sintered Manganese-Zinc and Nickel-Zinc Ferrites for record head applications.

Manganese-Zinc high permeability ferrites for shielding applications


Technical Ceramic Powders

Lanthanide Chromites and Ferrites

Yttrium oxide

Zirconia Materials

Conductive Spinels

Magnesium Aluminate Spinel

Alumina-Chromia

Ferrite 50 (For Radiation Absorption)


Tech-Briefs and Application Notes

For further information, call your Alpha/Trans-Tech sales representative for any of the following:

(Click name for more information)

Coaxial Line Elements

Voltage Controlled Oscillator (VCO)

DR Coupling

Dielectric Resonator Oscillator

DR Q-Factor

Filters

General/Miscellaneous


About Coaxial Resonator Design

Coaxial Resonator Design was developed for Trans-Tech by:

ScillaSoft Consulting

102 Holiday Court

Mount Laurel, NJ  08054

Phone/FAX: (609) 222-1279

E-mail: scillasoft@aol.com


Coaxial Inductor Parameters

Coaxial Inductor Length (L):

The length of the resonator determines the resonant frequency in a particular material.  A quarter wavelength with a short or a half wavelength with an open results in the functionality of a parallel resonant circuit.  Below the resonant frequency of the coaxial resonator, the impedance is inductive.

Coaxial Inductor Q:

The Q or Quality Factor of the resonator is the ratio of the dissipated energy to the stored energy in the resonator.  A high Q designates low losses and narrow frequency band performance.  A low Q signifies higher losses and wider frequency band performance.  Most of the loss associated with the inductor is due to metallization losses.

Coaxial Inductor Self-Resonant Frequency (SRF):

The self-resonant frequency is the frequency where the input impedance of the inductor is entirely real.  An inductor should be chosen with the highest possible SRF to minimize the inductance/impedance change over frequency.  Trans-Tech measures SRF (and Q) under critically-coupled conditions.  For a description of the technique, see Publication No. 50030170, "Coaxial Transmission Line Elements."

Coaxial Inductor Characteristic Impedance (Zo):

The characteristic impedance (Zo) of the inductor is a function of the profile dimensions and the dielectric constant of the material.  Zo is reduced over its air line value by the square root of the dielectric constant of the material.


Ceramic Bandpass Filters

Two Pole Filters:

Cellular/NMT900/E-AMPS

Frequencies (MHz):  836.5, 881.5, 902.5,947.5

Cordless Telephone

Frequencies (MHz):  886.0, 914.5, 931.0

Spread Spectrum

Frequencies (MHz):  915.0, 922.0, 926.5

GPS

Frequencies (MHz):  1227.0, 1575.0

Three Pole Filters:

Cellular/NMT900/E-AMPS

Frequencies (MHz):  836.5, 881.5, 902.5,947.5

Cordless Telephone

Frequencies (MHz):  886.0, 914.5, 931.0

Spread Spectrum

Frequencies (MHz):  915.0, 922.0, 926.5

GPS

Frequencies (MHz):  1227.0, 1575.0


Center Frequency (Inductor)

The center frequency of the coaxial inductor determines the frequency at which the inductance/impedance desired is exact.  COAX displays either inductance vs frequency or impedance vs frequency to show the variation about the center frequency.  Choosing the profile with the highest self-resonant frequency (SRF) will give the inductor with the least inductance/impedance variation over frequency.


Resonant Frequency

The resonant frequency of the coaxial resonator determines the frequency at which the highest impedance occurs.  At resonance, the impedance is real and equal to R of the parallel equivalent circuit.  Below resonance the coaxial resonator is inductive and above resonance it is capacitive.  Trans-Tech measures SRF (and Q) under critically-coupled conditions.  For a description of the technique, see Publication No. 50030170, "Coaxial Transmission Line Elements."


Inductance/Impedance Entry

The designer enters the desired inductance or impedance of the coaxial inductor for the specified center frequency.  The inductance/impedance will be exact at the center frequency, with lower inductance/impedance below center frequency and higher inductance/impedance above center frequency.  COAX displays either inductance vs frequency or impedance vs frequency to show the variation about the center frequency.


Dielectric Material

Coaxial Resonators/Inductors may be selected from four types of dielectric material:

Parameter	1000 Series	2000 Series

Color	White	Gray

Dielectric Constant	10.3 +/- .5	20.5+/- 1

Temperature Coefficient of 	0 +/- 10	0 +/- 10

Resonant Frequency (Tf) (ppm/°C)

Parameter	8800 Series	9000 Series

Color	Tan	Dark Gray

Dielectric Constant	39 +/- 1.5	90 +/- 3

Temperature Coefficient of 	4 +/- 2	0 +/- 10

Resonant Frequency (Tf) (ppm/°C)


Element Profile

Designer can select from six Coaxial Resonators/Inductors profiles:

Profile	Size

HP	12 mm sq (0.476 in)

SP	6 mm sq (0.237 in)

LS	4 mm sq (0.155 in)

LP	4 mm sq (0.155 in)

MP	3 mm sq (0.119 in)

SM	2 mm sq (0.080 in)

The current dimensioned drawing for the profile selected is displayed in the lower right of the screen at all times.


Trans-Tech, Inc.

Serving Alaska, Hawaii, Idaho, Montana and Wyoming:

Adamstown, MD

Telephone:  (301) 695-9400

FAX:  (301) 695-7065


Electronic Development Sales Pty., Ltd

Serving Australia:

Australia

Telephone:  011-61-2-9418-6999

FAX:  011-61-2-9418-6550

E-Mail: esaus@ozemail.com.au


Tech Partner A/S

Serving Denmark:

Denmark

Telephone:  011-45-874-61600

FAX:  011-45-874-61616


Alpha Industries Ltd.

Serving England, Ireland, Scotland, and Wales:

England

Telephone:  011-44-1628-475562

FAX:  011-44-1628-474078


Millimondes

Serving France and Belgium:

France

Telephone:  011-33-1-45-37-12-30

FAX:  011-33-1-46-32-81-06

E-Mail:  millimondes@wanadoo.fr


Integrated Electronics Oy Ab

Serving Finland and Russia:

Finland

Telephone:  011-358-9-586-1770

FAX:  011-358-586-1771

E-Mail: info@ieoy.fi


Alpha Industries GmbH
Municom

Serving Germany, Austria, Yugoslavia, Switzerland, and Eastern Europe:

Germany

Telephone:  011-49-8641-9585-0

FAX:  011-49-8641-3039

E-Mail: municom@dcinet.de


Kostas Karayannis S.A.

Serving Greece:

Greece

Telephone:  011-301-68-00-4601

FAX:  011-301-68-53-522


Semi Dice International BV

Serving The Netherlands, Luxembourg and Vlamish Belgium:

The Netherlands

Telephone:  011-31-075-6476968

FAX:  011-31-075-6408795


Aarjay International Pvt Ltd.

Serving India:

India

Telephone:  (91) 80-5262874

FAX: (91) 80-5274616

Elkay International, Inc.

Serving USA India:

Succasunna, NJ  07876

Telephone:  (973) 927-8647

FAX:  (973) 927-5370


Ormic Components, Inc.

Serving Israel:

Israel

Telephone:  011-972-3-649118

FAX:  011-972-3-6471942


Microelit S.P.A.

Serving Italy:

Milan, Italy

Telephone:  011-39-2-481-7900

FAX:  011-39-2-481-3594

E-Mail: microeli@mbox.vol.it

Rome, Italy

Telephone:  011-39-6-86894323

FAX:  011-39-6-8275270

E-Mail:  microeli@mbox.vol.it


M-RF Co., Ltd.

Serving Japan:

Tokyo, Japan

Telephone:  011-81-3-5821-3623

FAX:  011-81-3-5821-3625

E-Mail:  mrftokyo@2.mbn.or.jp

Osaka, Japan

Telephone:  011-81-6-313-7180

FAX:  011-81-6-313-7182

E-Mail:  mrfosaka@az.mbn.or.jp


S-Tec International Co. Ltd.

Serving Korea:

Korea

Telephone:  011-82-2-784-9898

FAX:  011-82-2-784-8600

E-Mail:  stec@kotis.net


DATA MATIK A/S

Serving Norway:

Norway

Telephone:  011-47-22-301730

FAX:  011-47-22-300273

E-mail: datamatik@sn.no


Vermont Representatives Commercial S/C Ltda

Serving Brazil:

Brazil

Telephone:  011-55-11-846-7372

FAX:  011-55-11-846-0308

E-Mail:  vermont@sanet.com.br


Iberica de Componentes, S.A.

Serving Spain:

Spain

Telephone:  011-34-919-2970

FAX:  011-34-1-6531019

E-Mail:  ibercom2@mad.servicom.es


Compomill AB
Nordimar

Serving Sweden:

Sweden

Telephone:  011-46-8-753-3760

FAX:  011-46-8-622-6304


Ameleks Corp.

Serving Taiwan:

Taiwan

Telephone:  011-886-2-2758-6958

FAX:  011-886-2-2758-6987

E-Mail: ameleks@ms9.hinet.net


Pangaea (HK) Limited

Serving Hong Kong and People's Republic of China:

Hong Kong

Telephone:  011-852-2836-3301

FAX:  011-852-2834-7340

email: panagaea@wlink.net


Pangaea Corporation Philippines
Pangaea Corporation

Serving Philippines:

Philippines

Telephone:  011-632-810-5809

Fax: 011-632-818-0603

E-Mail: pangaea@compass.com.ph

USA Office for Pangaea:

Littleton, MA  01460

Telephone:  (508) 486-0942

FAX:  (508) 486-4647

E-Mail:  pangaeaus@internetMCI.com

S&T Enterprises

Serving Singapore:

Singapore

Telephone: 011-65-745-8910

FAX: 011-65-741-8200


Eltronik Incorporated

Serving Turkey:

North Bergen, NJ  07047

Telephone: (201) 453-0401

FAX: (201) 453-0959

Eltronik Elektronik Sanayli Ve Ticaret Ltd. Sti

Serving Turkey:

Turkey

Telephone:  011-90-312-467-9952

FAX:  011-90-312-467-9828


Components & Instruments, Ltd.

Serving New Zealand:

Telephone:  011-644-237-5632

FAX:  011-644-237-8392


Simm Electronics

Serving South Africa:

South Africa

Telephone:  011-27-11-802-7808

FAX:  011-27-11-802-7875

E-Mail:  pengel@cis.co.za


Mexitek, S.A.

Serving Mexico:

Mexico

Telephone:  011-525-575-0269

FAX:  011-525-575-9981

E-mail: 74173.757@compuserve.com


US Sales Offices

Click on the area of interest in the United States for contact information:


European Sales Offices

Click on the area of interest in Europe for contact information:


Asian and Australian Sales Offices

Click on the area of interest in Asia for contact information:


Using Coax Elements as Inductors

Coaxial (or coax) line elements can be used below resonance to simulate high-Q, temperature-stable, compact inductors.  More precisely, shorted coax lines will exhibit an inductive reactance when used below quarter-wave resonance, and will approximate the behavior of an ideal inductance or "coil" over a limited frequency range.  Similarly, open coax lines will exhibit an inductive reactance when used below half-wave resonance.  As the operating frequency approaches the self-resonant frequency (SRF) of the coax line element, the approximation will be less valid.  An exact equivalent circuit is complex and would include parasitic elements resulting from a transition from the printed wiring board to the interior of the coax line.  In this program, a first-order model includes only the ceramic coax line and an estimate of the inductance due to the physical length of the center conductor tab.  The tab inductance will appear in series with the coax line's input impedance.  An ideal, lossless transmission line is assumed to simplify the calculations.  Minor corrections to part length may be evident from prototype circuit performance.

When used in VCO circuits, for example, the coaxial line element will exhibit an inductive reactance below SRF which can be resonated and tuned with a varactor.  Designers typically choose SRF to be 10% to 15% above the center frequency of the VCO, or even higher.


Specifying Coaxial Inductors

COAX determines a Trans-Tech part number derived from the self-resonant frequency (SRF) of the coaxial line, which is then equivalent to specifying a coaxial resonator.  Trans-Tech measures SRF under critically-coupled conditions, with either 1% or 0.5% SRF frequency tolerance available on most parts.  For most applications, the accuracy of the equivalent inductance is sufficient.  Part-to-part variation in SRF, dielectric constant, and part dimensions will result in a window tolerance on the equivalent inductance.  Consult Trans-Tech for an application note to assist in evaluating these effects.

For more demanding applications, the tolerance on the equivalent inductance can be improved by specifying not SRF, but the part equivalent inductance (or reactance) at a specified frequency, which is usually the center frequency of circuit operation.  Trans-tech can measure the value required at the specified frequency, rather than the SRF of the coaxial element.


Coaxial Line Elements

Trans-Tech Application Notes:

1009	Computer Simulation of Coaxial Resonators

1010	Frequency Tuning Coaxial Resonators

1014	The Characteristic Impedance of Coaxial Resonators

1015	Measuring SRF and Q of Coaxial Resonators

Selected Articles and Books:

T. Moreno, "Microwave Transmission Design Data," ARTECH House, ISBN 089-006-346-X

G. Matthaei, L. Young, and E. Jones, "Microwave Filters, Impedance-Matching Networks, and Coupling Structures, "ARTECH House, ISBN 089-006-099-1.

K. Hano and K. Sawamoto, "A Bandpass Filter Using Direct-Coupled Quarter-Wavelength Coaxial Dielectric Resonators," Microwave Journal, November 1987, pp. 141-160.


Voltage Controlled Oscillator (VCO) References

Trans-Tech Application Notes:

1008	Coaxial Resonators for VCO Applications

1017	The Influence of Coaxial Inductors on VCO Tuning Bandwidth

1021	Empirically Determining the VCO Inductor

Selected Articles and Books:

D. Rosemarin, "Design improves linearity of PLL synthesizers, "Microwaves & RF, December 1991. [includes VCO calculations for tuning range]

B. Kelly, N. Evans, and B. Burns, "1.8 Ghz direct frequency VCO with ACD assessment, " RF Design, February 1993, pp.29-38.

U. Rhode, "Oscillator design for lowest phase noise, " Microwave Engineering Europe, May 1994, pp. 31-40. [900 Mhz example]

U. Rhode and S. Joshi, "Compact PLLs cut current in portable systems, " Microwaves & RF, July 1995, pp. 115-120.

D. Polidi, "Design method for a coaxial-resonator oscillator," RF Design, October 1995, pp. 66-68. [2.3 Ghz example]

U. Rhode, "Digital PLL frequency synthesizers - theory and design, " Prentice-Hall, Englewood Cliffs, NJ, 1983.

W. Hayward, "Introduction to radio frequency design, " ARRL, 1994, ISBN 0-87259-492-0.

R. Rhea, "Oscillator design and computer simulation, " Noble Publishing, 1995, ISBN 1-884932-30-4.

"A comparison of microstrip & coaxial resonator voltage controlled oscillator design approaches, " Synergy Microwave Corporation (Paterson, NJ) 1996 Supplementary Catalog.


DR Coupling References

Selected Articles and Books:

R. Boneti, A. Atia, "Analysis of Microstrip Circuits Coupled to Dielectric Resonators, " IEEE Trans. Microwave Theory Tech., Vol. MTT-29, No. 12, December 1981, pp. 1333-1337. [single curved microstrip line]

J. Brand and J. Ronnau, "Practical Determination of Dielectric Resonator Coupling Coefficients, " Microwave Journal, November 1986, pp. 141-144.  [Empirical image technique for finding coupling coefficients]

P. Champagne, "Better Coupling Model of DR to Microstrip Insures Repeatability,"Microwaves & RF, September 1987, pp. 113-118. [coupling to single line]


Dielectric Resonator Oscillator Reference

Trans-Tech Application Notes:

1030	Optimize DRO's for Low Phase Noise

Selected Articles and Books:

J. Walworth, "Theory of operation of the DRO," RF Design, January 1985, pp. 26-31.[coupling to one or two lines, equivalent circuits, empirical determination of coupling]

K. Agarwal, "Applications of GaAs Heterojunction Bipolar Transistor in Microwave Dielectric Resonator Oscillators, " Microwave Journal, November 1986, pp. 177-182. [phase noise comparison]

U. Rhode, "Designing a Low Noise Oscillator Using CAD Tools, " Microwave Journal, December 1986, pp. 140-144. [Noise reduction by locking 13 Ghz DRO. Example of author's CAD program]

R. Jaques, "Paving the way for stabilized DR oscillators," Microwaves & RF, September 1987, pp.103-108. [temperature drift analysis]

A. Murphy and P. Murphy, "Computer Program Aids Dielectric Resonator Feedback Oscillator Design," Microwave Journal, September 1988, pp.131-148. [FORTRAN, feedback configuration]

A.P.S. Khanna, "A Highly-Stable 36 Ghz GaAs FET DRO with Phase-Lock Capability,"Microwave Journal, July 1989, pp.117-122.

A.P.S. Khanna, "Understand DRO design methods and operation," Microwaves & RF, April 1992, pp.120-124. [Fundamentals, operating principles, dielectric material choices]

A.P.S. Khanna, "Picking devices for optimum DRO performance,"Microwaves & RF, May 1992, pp.179-182. [Active devices and various circuit topologies]

H. Ashoka, "Directly-modulated DRO drives S-band video links,"Microwaves & RF, June 1992, pp.89-90. [Varactor coupled to DR, 20 Mhz tuning at 3.45 GHz]

A.P.S. Khanna, "Design a wide range of quiet DRO circuits,"Microwaves & RF, July 1992, pp.95-98. [Various circuit configurations]

J. Floch, "Technique allows simple design of microwave DROs,"Microwaves & RF, March 1995, pp.107-112. [Series feedback example near 10 GHz]


DR Q-Factor Reference

Selected Articles and Books:

A. Podcameni et al, "Unloaded quality factor measurement for MIC dielectric resonator applications,"Electronic Letters, 3rd September 1981, Vol. 17, No. 18, pp. 656-657. [network analyzer measurement of DR's coupled to 50-ohm microstrip]

A.P.S. Khanna, "Q Measurement of microstrip-coupled dielectric resonators,"Microwaves & RF, January 1984, pp. 81-86. [equivalent circuit, network analyzer measurement of DR's coupled to 50-ohm microstrip]


Filter References

Trans-Tech Application Notes:

1012	A Notch Filter Using A Coaxial Resonator

1013	A Bandpass Filter Using A Coaxial Resonator

1016	A Ceramic Waveguide Highpass Filter

Selected Articles and Books:

S. Cohn, "Microwave Bandpass Filters Containing High-Q Dielectric Resonators, " IEEE Trans. Microwave Theory Tech., Vol. MTT-16, No. 4 April 1968, pp. 218-227. [experimental coupling coefficents and simplified formula for DR's in waveguide]

A. Podcameni et al, "Design of microwave oscillators and filters using transmission-mode dielectric resonators coupled to microstrip lines, " IEEE Trans. Microwave Theory Tech., Vol. MTT-33, No. 12, December 1985, pp. 1329-1332. [equivalent circuit for transmission-mode, coupling to two lines]


General/Miscellaneous References

Selected Articles and Books:

Courtney, W.E., "Analysis and evaluation of a method of measuring the complex permittivity and permeability of microwave insulators, " IEEE Trans. Microwave Theory Tech., Vol. MTT-18, pp. 476-485, August 1970. [descriptiion of the Courtney test fixture for εr measurement]

T. Higashi and T. Makino, "Resonant frequency stability of the dielectric resonator on a dielectric resonator on a dielectric substrate," IEEE Trans. Microwave Theory Tech., Vol. MTT-29, pp. 1048-1052, October 1981. [approximate formulas, temperature stability on substrate]

D. Kajfez, P. Guillon, "Dielectric Resonators,"ARTECH House 1986, ISBN 0-89006-201-3

D. Kajfez, "PC Program evaluates higher-order modes in shielded dielectric resonators," Microwave Journal, May 1988, pp. 345-355. [Introduction to FOAM program]

R. Mongia, "Easy resonant frequency computations for ring resonators," Microwave Journal, November 1992, pp. 105-108. [effects of center axial hole on frequency].

N. Klein et al, "Properties and applications of HTS-shielded dielectric resonators: state-of-the-art report," IEEE Trans. Microwave Theory Tech., Vol. MTT-44, No. 7, July 1996, pp. 1369-1373. [results of superconducting experiments]