Search RFCafe.com                           
      More Than 17,000 Unique Pages
Please support me by ADVERTISING!
Serving a Pleasant Blend of Yesterday, Today, and Tomorrow™ Please Support My Advertisers!
   Formulas & Data
Electronics | RF
Mathematics
Mechanics | Physics
     AI-Generated
     Technical Data
Pioneers | Society
Companies | Parts
Principles | Assns


 About | Sitemap
Homepage Archive
        Resources
Articles, Forums Calculators, Radar
Magazines, Museum
Radio Service Data
Software, Videos
     Entertainment
Crosswords, Humor Cogitations, Podcast
Quotes, Quizzes
   Parts & Services
1000s of Listings
 Vintage Magazines
Electronics World
Popular Electronics
Radio & TV News
QST | Pop Science
Popular Mechanics
Radio-Craft
Radio-Electronics
Short Wave Craft
Electronics | OFA
Saturday Eve Post

Software: RF Cascade Workbook
RF Stencils Visio | RF Symbols Visio
RF Symbols Office | Cafe Press
Espresso Engineering Workbook

Aegis Power  |  Alliance Test
Centric RF  |  Empower RF
ISOTEC  |  Reactel  |  RFCT
San Fran Circuits

RF Electronics Shapes, Stencils for Office, Visio by RF Cafe

Anritsu Test Equipment - RF Cafe

LadyBug RF Power Sensors

Please Support RF Cafe by purchasing my  ridiculously low-priced products, all of which I created.

RF Cascade Workbook for Excel

RF & Electronics Symbols for Visio

RF & Electronics Symbols for Office

RF & Electronics Stencils for Visio

RF Workbench

T-Shirts, Mugs, Cups, Ball Caps, Mouse Pads

These Are Available for Free

Espresso Engineering Workbook™

Smith Chart™ for Excel

Advertise your products and services on RF Cafe

Quarter-Wave (λ/4-wave) Coaxial Resonators

Quarter-wave (λ/4-wave) coaxial resonators are constructed by shorting the center conductor of a coaxial cable to the shield at the far end of the circuit. The length of the cable is exactly λ/4 at the desired resonant frequency. A short circuit is transformed to an open circuit a quarter wavelength away, so when the λ/4-wave coaxial resonator is part of an oscillator circuit, it electrically is not even present (Z~∞); however, whenever the frequency of the oscillator attempts to go above or below the resonator's center frequency (due to load changes, temperature changes, etc.), the λ/4-wave section looks like a low impedance that works to attenuate other frequency components. It acts like a parallel tuned L/C tank circuit. The advantage of a λ/4-wave coaxial resonator over a tuned L/C tank circuit is the much higher quality factor, "Q."

Coaxial resonators are often made from sections of normal coaxial cable (both flexible and semi-rigid), but many form factors are available that are manufactured for specific frequencies and mount on printed circuit boards, or have coaxial connectors installed on both ends. Amateur radio hobbyists often use λ/4-wave resonators to filter (trap) interference outside the working band of the radio operation. The nice thing about λ/4-wave trap it that is can be connected inline with the antenna feed cable using a simple "T" adapter (remember, it is effectively not even there at the center frequency).

Quality factor of a λ/4-wave coaxial resonator is determined by the ratio of the center frequency to the 3 dB power bandwidth, as shown in the figure below. A set of equations is then presented for calculating the necessary λ/4-wave coaxial resonator parameters.

Measurement of Q from Frequency Response of a Coaxial Resonator - RF Cafe

Quality Factor (Q) of a λ/4-Wave Coaxial Resonator

Dimension Reference for Coaxial Resonator Equations - RF Cafe

Dimension Reference for λ/4-Wave Coaxial Resonator Equations

1/4-Wave Coaxial Resonator Equation (1) - RF Cafe

1/4-Wave Coaxial Resonator Equation (2) - RF Cafe

1/4-Wave Coaxial Resonator Equation (3) - RF Cafe

1/4-Wave Coaxial Resonator Equation (4) - RF Cafe

Zo coaxial cable equation - RF Cafe

Zopt coaxial cable equation  - RF Cafe

Qc

Qcc

Qd

Q

a

b

 f

μ

σ

εr

n

Z0

Zopt

 

= conductor contribution to unloaded Q

= conductor contribution to unloaded Q for copper

   conductors with optimum b/a ratio of 3.59112

= dielectric contribution to unloaded Q

= unloaded quality factor of a λ/4-wave resonator,

   including conductor and dielectric losses

= outside radius of inner conductor (m)

= inside radius of outer shield (m)

= resonant frequency (Hz)

= permeability of the conductor (H/m)

= conductivity of the conductor (mho/m)

= relative dielectric constant between a and b

= resonator mode (# of 1/4 wavelengths at resonance)

= characteristic impedance of coaxial structure (Ω)

= characteristic impedance that yields the highest

   theoretical value of Q (b/a = 3.59112) λ

Note: These are commonly available equations; my source was Vizmuller

Related Pages on RF Cafe

- Coaxial Cable Specifications

- Capacitor Dielectrics & Descriptions

- Dielectric Constant, Strength, & Loss Tangent

- Conductor Bulk Resistivity & Skin Depths

- Coaxial Cable Equations

- Coaxial Cable Specifications

- Coaxial Cable Vendors

- Coaxial Resonator

- Skin Depth Calculator

- Coaxial Connector Usage Chart

Advertise your products and services on RF Cafe
Cafe Press

Amplifier Solutions Corporation (ASC) - RF Cafe