Everybody has seen the short antennae with the couple turns of a coil half-way up (like on a police car). I know this extends the electrical length of the antenna. Does anybody have, or know where to get the formula for calculating this? I've searched the ARRL Antenna Handbook but I couldn't find the reference.

 

The formula for the inductance of an air-coil inductor is what you want. It should also be in the handbook.

http://www.daycounter.com/Calculators/Air-Core-Inductor-Calculator.phtml

 

The link below considers the total picture with respect to the inductively loaded dipole antenna design.

http://eweb.chemeng.ed.ac.uk/jack/radio/software/loading.html

 

Thank you for the links. I will look at both of them in-depth.

 

There are those which work as a dual band 2m / 0.7m mobile antenna with a coil about a quarter of the way up from the base.
I define mobile in the understanding that the vehicle body becomes part of the antenna system.
I'd be grateful for a rounded description of this kind of operation.

 

so the coil can be 1/4, 1/2 or 3/4 up the antenna? Is the electrical length the same or does the positioning of the coil affect the SWR?

 

so the coil can be 1/4, 1/2 or 3/4 up the antenna? Is the electrical length the same or does the positioning of the coil affect the SWR?

In a nutshell - It's not simple.

Perhaps some numbers might prove helpful.

I use an antenna simulation application called MMANA.

I start with a bottom fed vertical dipole of 2.53 metres height above a 'real' ground. If this is a quarter wave dipole then the nominal operating frequency would be about 30MHz. Using MMANA I obtain a minimum VSWR [50 Ω] of 1.38 for this arrangement at 28.73MHz. The antenna impedance is 36.7+j3.3 Ω

For interest, I now interpose a 2uH loading inductance at three different locations along the antenna.

The three different locations I tried were 1/4, 1/2 & 3/4 the total length from the feed-point. For each situation I 'optimized' the VSWR by sweeping the frequency to find lowest VSWR and obtained the following results:

Coil (2uH) at 1/4 the antenna length from feed-point:
frequency=19.6 MHz and VSWR[50 Ω] = 2.9 [with antenna Z=17.4+j4 Ω]

Coil (2uH) at 1/2 the antenna length from feed-point:
frequency=21.8 MHz and VSWR[50 Ω] = 2 [with antenna Z=25.3+j4.25 Ω]

Coil (2uH) at 3/4 the antenna length from feed-point:
frequency=25.5 MHz and VSWR[50 Ω] = 1.5 [with antenna Z=33.7+j3.7 Ω]

If I cross check these results with the loading software at the link I posted earlier [#3] I have the following results

Since the applet uses imperial I first convert the 2.53 meters to 8.3 feet.

• A midpoint coil of ~zero inductance with the frequency at 28.193 MHZ - for reference only.
• A quarter way coil of 1.94uH at 19.6MHz [as obtained with MMANA above]
• A half way (mid-point) coil of 1.82uH at 21.8 MHz [as obtained with MMANA above]
• A three quarter way coil of 1.5uH at 25.5MHz [as obtained with MMANA above]

So the applet suggests inductance values somewhat different but there is no indication in the applet as to what is actually optimized for those values [e.g. match / VSWR ..???].

One important observation would be that the inclusion of the loading coil allows one to have a shorter antenna but without any subsequent matching techniques applied, the achievable VSWR suffers.

I also noticed in the simulations that the inductively loaded antenna has a lower gain than its unloaded counterpart at 'optimized' VSWR at some frequency - 1dB say for the center loaded case.