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How to shorten a Dipole Antenna

       
   

            
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
   

            
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
  

Half Wave  = 180 degrees

   

Quarter Wave = 90 degrees

         
                
  

Section B is  the antenna section to be shortened by using an inductor.

             
  

The -j X1 and -jX2 represent capacitance for the section being shortened.   In order to do this an inductor is made which cancels the capacitance for the section B.

             
                
  

Two formulas are used for determining the inductor value:

             
  

 

             
   

X = -jZo Co-tangent(Beta)

  

or

x= -j*Zo*cot(Beta)

        
                
   

Zo = 138 * log(4*h/d)

  

h is the height of the antenna above ground in meters.

         
      

d is the wire diameter used to make the inductor in millimeters.

         
                
   

-JX1= -j*Zo(Cot(X1 in degrees))

            
                
   

-JX2= -j*Zo(Cot(X2 in degrees))

            
                
   

 XL= -JX2 -(-JX1)

 

=>

XL = jX1 - JX2

         
                
      

X1 = -j*Zo*(Cot(X1 in degrees))

         
      

X2= -j*Zo*(Cot(X2 in degrees))

         
                
      

X1 is greater than X2

         
                
  

Calulations:

             
                
  

Resonance_Freq

 

7.07

Mhz

          
                
  

Wire_Length

 

21.2164073550212

Meters

69.5898161244696

Ft

0.110508628005658

Resistance

12 Gauge Wire

0.001588

Ohms/ft

   
                
  

Height of Antenna

 

34.7949080622348

in Feet

1/2 wave length at feedpoint

         
                
  

Wire Diameter

 

2

millimeter

          
                
  

Zo

 

597.065369926047

Ohms

          
                
  

X1 angle

 

30

Degrees

 

n length

3.53606789250354

in meters

 

0.005615275813296

Resistance

   
  

X2 delta angle

 

30

Degrees

 

m length

3.53606789250354

in meters

 

0.005615275813296

Resistance

   
                
       

Inductor Calculations

        
  

-JX1

 

1034.14755615182

Ohms

 

a

2

Form Diameter in inches

      
  

-jX2

 

344.715852050607

Ohms

 

b

4

Form length in inches

      
       

n

27

Number of Turns

      
  

jXL

 

689.431704101214

Ohms

  

339.292006587698

wire length

 

1.07759141292253

    
           

1.08882196454912

    
  

Coil Inductance

 

15.5200090002796

uH

 

Inductor

14.8775510204082

uH

 

Antenna Length

14.1442715700141

meters

  
  

Center Spacing in ~ 3 inches between the two elements

        

Rr

50

 

Radiation resistance

 
           

Rf

1.08882196454912

Ohms

Equivalence Resitance of all losses

 
           

n

97.8687667425476

%

Antenna system  efficiency