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Shiawassee Amateur Radio Association [SARA]

Established: January, 1958 an ARRL Affiliated Club since 1961

"Whiskey 8 Quack Quack Quack"

Meets at: James P. Capitan Center, Lower Level; 149 E. Corunna Ave.; Corunna, MI 48817 Monthly: 2nd Tuesday @ 7:00 PM

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SARA Coaxial Cable & Stubs

Coaxial Cable Design

The radio amateur operator has many uses for coaxial cable in his installation. Every (almost) station setup has a transmission line length which is usually a coaxial cable. The usage expands when they are used as part of an antenna or a matching network. Understanding the characteristics of different cable types becomes increasingly important as a ham's usage increases. The following is meant to be a quick information reference to assist our members. The data and information comes from many internet web sites and "The ARRL HANDBOOK for Radio Amateurs" (plus a few books I have stashed in my library). In the current interner status, I always check our friends at Wikipedia {https://en.wikipedia.org/wiki/Coaxial_cable}.

General Characteristics for some 'popular' coax cable types:

The following loss table assumes the cable is terminated on each end with the correct matched impedance value (1:1 SWR). The losses go up if either end deviates from this. Bascially, these are 'best case' conditions and in the real world the losses can be much higher. Be advised for efficent power transfer you MUST pay attention to both the generator and the terminating end of any transmission line.

One online technical source that I use is: Axon Coaxial Cable Technical Paper. It has a large amount of data on coaxial cables in a nice and concise format.

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Popular Coax Characteristics

 Type (or RG#)   Nom. Imp Zo   Outer Dia. (mm)   Nom loss (dB/100m) @ 
50 MHz
Attenuation (dB/100m)  Vel. Factor 
   %
 Cap. pF/m   Voltage Rating {Vrms} 
 100 MHz   200 MHz   400 MHz   1 GHz  
RG - 6/U 75 7.0 6.1 8.8 12.7 18.5 30.7 82 66.5 2700
RG - 6A/U 75 7.0 4.37 6.37 8.89 13.1 26.0 82 53.1 2700
RG - 8/U 50 7.0 8.4 6.4 9.3 13.7 23.2 66 97.1 2700
RG - 8X/U 50 10.3 8.4 12.0 17.4 25.3 42.3 66 101.0 600
RG - 9/U 51 10.67 5.2 7.2 17.4 25.3 42.3 66 101.0 600
RG - 11/U 75 10.29 4.5 6.4 9.3 13.7 23.2 66 67.3 1500
RG - 58/U 53.5 4.95 10.5 15.0 21.4 30.8 50.2 66 94.4 1500
RG - 58A/U 50 4.95 10.8 16.1 23.9 37.7 70.5 66 101 1900
RG - 58C/U 50 4.95 10.8 16.1 23.9 37.7 70.5 66 101 1900
RG - 58
Cellfoam
(9001)
50 4.95 9.6 12.7 18.9 27.4 51.1 76 101 1900
RG - 58
Cellfoam
(9006)
50 5.1 6.6 9.5 14.1 19.3 34.9 80 101 1900
RG - 59/U 73 6.15 7.9 11.2 16.1 23.3 39.423.2 66 69.2 2300
RG - 59B/U 73 6.15 7.9 11.2 16.1 23.3 39.4 66 67.2 2300
RG - 62/U 93 6.04 6.2 8.9 12.5 17.7 28.5 84 44.3 700
RG - 62B/U 93 6.15 6.6 9.5 13.8 20.0 36.1 84 44.3 700
RG - 122/U 50 4.06 14.8 23.0 32.8 49.9 87.0 66 101 1900
RG - 141A/U 50 4.83 6.9 10.5 15.4 22.6 42.7 69.5 95.1 1900
RG - 142/U 50 4.06 8.7 12.5 17.9 25.7 42.1 69 96.6
RG - 174/U 50 2.56 21.7 29.2 39.4 57.4 98.4 66 101 1500
RG - 178B/U 50 1.83 34.4 45.9 62.3 91.9 150.9 69.5 95.1 1000
RG - 179B/U 75 2.54 27.9 32.8 41.0 52.5 78.7 69.5 64 1200
RG - 180B/U 95 3.56 15.1 18.7 24.9 35.1 55.8 69.51 49.2 1500
RG - 187A/U 75 2.66 27.9 32.8 41.0 52.5 78.7 69.5 64 1200
RG - 188A/U 50 2.59 31.5 37.4 46.6 54.8 101.7 69.5 95.2 1200
RG - 196A/U 50 1.93 34.4 45.9 62.3 91.6 150.9 69.5 95.2 1200
RG - 213/U 50 10.29 5.2 7.2 10.5 15.4 29.2 66 101 5000
RG - 214/U 50 10.8 5.2 7.2 10.5 15.4 29.2 66 101 5000
RG - 223/U 50 5.38 10.1 14.8 21.0 30.2 53.5 66 101 1900
RG - 303/U 50 4.31 6.9 10.5 15.4 22.6 42.7 69.5 95.2 1900
RG - 316/U 50 2.49 30.8 34.1 43.3 54.1 101.7 69.5 95.2 1200
CNT - 400 50 10.29 3.18 4.3 5.5 8.0 12.7 85 78.4 2500
LMR - 300 50 4.06 4.5 6.4 9.1 13.0 21.0 85 78.4 600
LMR - 400 50 4.06 2.9 4.1 5.8 8.4 13.5 85 78.4 600
LMR - 500 50 2.3 2.9 3.3 4.7 6.7 10.9 86 77.5 2500
LMR - 600 50 2.3 1.8 2.6 3.7 5.3 8.7 87 76.5 2500
 LMR - 1200-DB  50 2.3 0.9 1.3 1.8 2.7 4.4 88 75.8 2500

 

Coax that connects things! topic divider

 

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Coaxial Cable Factors

As you look at coaxial cable information notice that the 'quoted' values from various sources have both English and metric values, that is really a 'conversion factor' issue only, do not let it confuse you. Also, be advised that loss values can vary widely from manufacturer to manufacturer - table values should only be considered as 'SWAG' [Some Wild A__ Guess] ~ consider the 'A' as "approximate" {Note: SWAG is a valid engineering term based on 35 years of practice}. One important item if you have log-log graph paper and two "frequency-dB loss points" for a given cable, graph two points on the paper and draw a straight line betweem them {put frequency on the horizontal and dB loss on the vertical axis}. Now you can pick any frequency of interest from the graph. The 'straight line' is an accurate SWAG for most frequency/loss point values. Note: The 'Graph Paper draw a line' method only requires two frequency calculations from a online calculator for '100 foot' length (or convert from "dB/100 meter" value by using [(dB/100 m) * (1/3.2808)], will provide two points that you can use! You may now act like the local expert for transmission lines and losses!

You will find "dB/100 foot" and "dB/100 meter" and sometimes other types of 'loss units' in various tables - so a little care on your part is required. This will allow you to determine the losses at various frequencies. Watch for "cutoff" frequencies as above those frequencies, all bets on actual loss for the line are off. Note: "the table values and graphs ALL assume perfectly matched line impedances {both ends}"... loss values can vary widely if impedances are not matched. The RF Cafe has information on cable. Look at the 'Related Pages' near the end of the page for additional links.

One great link for a coaxial cable calculator is the Times Microwave Coaxial Cable Calculator. This allows you get coaxial cable calculated values for many various cables. Note: That Graph Paper item mentioned above and two frequency calculations from this calculator for '100 foot' length, yields two points and you are setup. Note: that the calculator gives loss using both dB/100ft and dB/100m values - doing your conversion.

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Coaxial Cable Equations

Terms used to classify coaxial cables [See Equations Below]:

Coaxial Cable Capacitance View

 

   a = outside radius of inner conductor (inches)
   b = inside radius of outer conductor (not spacing = (inches)
   c = speed of light in a vacuum = 299,792 km/s = 186,282 mi/s
   ε = dielectric constant = ε0 * εr
   ε0 = permittivity of free space = 8.85419x10-12 F/m
   εr = relative dielectric constant
   μr = relative permeability 

See See SARA's Electrical Reference Page with properties for εr & μr. Use Page Navigation for 'Dielectric'.

The construction of coaxial cable considers an inner conductor, centered in a dielectric material of circular cross section, surrounded by an outer conductor (shied). The dimension for the Outer Radius [OR] and Inner Radius [IR] of the conductor and shield (or you can use diameter values; OD, ID) generate terms, 'a', and 'b'. These are only used to form a ratio of 'b/a' in the impedance equations, thus the radius vs diameter issue disappears inside the ratio calculation. The terms 'a' and 'b' are not used independently (except for cutoff frequency), only the ratio b/a is required for most calculations. Different references use both radius and diameter, I think just to confuse people, as they typically never explain that only the 'ratio' is the important characteristic. This means if units measurments are in the same units system, both radius or diameter ratios are equivalent and no metric/English conversions necessary.

The length of the cable, sometimes seen as or is required to process the equations. Various numerical constants are used to provide the correct units for the results in the various equations.

The dielectric material has two important characteristics to consider. The dielectric constant and the magnetic permeability. The inner material's dielectric constant, ε, which comes from the material type chosen, is just a product of εr and εo, or ε = εr * εo. Where εr is the relative dielectric constant (for the material) and εo is the permittiviity of free space (vacuum) which is 8.85419 x 10^12 F/m [Farads per meter].

The 'magnetic permeability', μ. Like with dielectric constant, μ = μr * μo. In almost all cases for transmission lines it's value will equal 1.000.

The values most sought transmission line calculation values are: Z0 = Line Impedance (requires C and L first), C = Capacitance per length , L = Inductance per length, and fcutoff = cutoff frequency.

Capacitance C

Coaxial Cable Capacitance

 

 

 

 

 

 

The value for ε and εr can be found at SARA's Electrical Reference page. Thus calculating the "b/a" ratio will get you the capacitance value quickly. Note Capacitance / unit length for popular coax types are in the spreadsheet data.

Inductance L

Coaxial Cable Inductance Equation

 

  Units must be as shown (metric).

 

 

 

 

Impedance Zo

Coaxial Cable Impedance Equation

 

  C must be in Farads and L must be in Henries.

 

 

 

 

Cutoff Frequency Fcutoff

Coaxial Cable Cutoff Frequency Equation

 

  Here a and b must match "radius" units in the equation !  Note number in Numerator change.

 

 

 

 

Coax that connects things! topic divider

 

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Coaxial Cable & Stubs

A stub (or resonant stub) is a length of transmission line that is connected at one end only. The 'free end' of the stub is either left open-circuit or short-circuited. Neglecting transmission line losses, the input impedance of the stub is purely reactive; either capacitive or inductive, depending on the electrical length of the stub, and on whether it is open or short circuit. Stubs may thus function as capacitors or inductors or resonant circuits at radio frequencies. [Repeating that: Stubs are like capacitors, inductors or a combination of both.] Thus stubs can be used as tuning devices and/or filters. A stub will only achieve the desired characteristic at a single frequency, so a series of stubs may be used to 'wideband' the effects. It has dramatic effects at various harmonics of the the 'desired' frequency and can be very effective as harmonic reduction filters. Where in the system the stubs are inserted does make a difference in performance, so some care is required with there use.

SARA's Transmission Line Calculation Spreadsheet

A Microsoft Excel spreadsheet can make many simple transmission line calculations easy. The following worksheet assumes lossless transmission lines and operation at low SWR conditions. Results will depart from these calculations as you leave these assumptions. Use at your own risk and make sure results apply to your situation. The sheet can easily be modified to your exact needs. Input areas are 'shaded blue' and you can freely change values to fit your needs. It can replace many Smith Chart for included calculations.

SARA's Transmission Line Calculations {click to download the worksheet} is divided into functional areas (see list below). Inputs will be on the left side of the sheet and results for that function will be to the right. It is best to stay away from any 'Computational Information Area' section, as they contain various calculation formulas for steps along the way to the final results. Enter some values and see results change, it is how you can start to understand what can be done.

List of Calculations available:
Tab # One ~ Resonance & Stubs
  • Resonating Inductance or Capacitance or Reactance (X) & Calculate 'Balancing Resonanting Component' Values
  • Convert Frequency, Wavelength (feet,meters,degrees) --> Line Length Calculations - need the Line Velocity Factor and Frequency (MHz)
  • Series and Parallel Equivalent Values --> Needs Resistive and Reactive Component Input Values
  • Reactance values for Transmission Line Stubs
  • Antenna load converted to reactance along a line's length. Yields SWR at Antenna and allows you to modify step size in table values.
  • Impedance Value Transform of a line starting with Antenna Load Reactance and moving towards 'Input Point' (assumes lossless line).
Tab # Two ~ Coaxial Physical Values

Many popular coaxial cable types listed with physical values -- look for those velocity factor values needed in the 'Resonance & Stubs' tab. It is the same data as presented above on this page, but has the 'English Units' calculated out for those that desire them.

A quick view of the YouTube video, "AmateurLogic.TV #126" (at the 33:00 minute mark) will show a 'quarterwave stub' will show you a simple sample of how coaxial stubs work (watch it through the frequency analyzer portion). Also, search Wikipedia using "Stub_(electronics)" as the topic with the equations needed for applying stubs. Any recent copy of the Radio Amateur ARRL Handbook is a great source for further details. Searching the internet for 'quarter wave stubs' will bring up additional examples for you to view. Then search the internet for some coaxial stub calculators... wow! is there a large amount of items or what? The amount of hits may indicate how important the topic can be. Stubs are amazing circuit devices and can be used for many purposes, once you get the concepts understood. Properly installed they can shield a station from nearby stations (like a 80M / 40M / 20M Field Day setup). Study coax a little and you can make a station system more frequency efficient and provide some great tuning and filtering capabilities for the cost of a few connectors and some coax line.

Links to some other transmission line sites:

Stubs need to be installed at the correct point in the system to achieve good results. See "Coax-Stubs.pdf" by Jim Brown, K9YC for some excellent information. It should be noted that you may need some testing to get proper operation. Velocity Factors vary with frequency in almost all real world cases, thus calculated stub lengths are only a starting value. You need to verify by testing to obtain good performance.

An additional source is Ward Silver's, N0AX, 'Hands on Radio' series in QST. He published some nice articles on stubs: See Nov 2004; Oct & Nov 2007; and Jan 2008 {ARRL members can do this 'online'}.

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