Removing the Veil

Granted, during our advancement as Ham’s, we have done a lot of memorizing. Now that we are where we want to be, it would be great to try building our own antennas. We should work on understanding how to get it done.

When calculating wire lengths (L) for building half-wave antennas, where does the number 468 come from in the formula; L=468/cf ?

That 468 looks like magic until you unpack it. It’s actually just a bundle of physics + unit conversions + real-world antenna behavior.

The starting point: wavelength

A half-wave antenna is based on half the wavelength of the signal λ = c / f   

  • c = speed of light ≈ 299,792,458 m/s
  • f = frequency (Hz)

A half-wavelength is L =  λ / 2 = c / 2f

As this formula for calculating half-wavelength (L) sits, it is not very friendly. Hams like the formula in feet and MHz, not meters and Hz.

Step 1: Convert speed of light to feet/second: c =~983,571,056 ft/s 
Step 2: Convert Hz to MHz: f(Hz) = f(MHz) x 10k, where 10k = 1,000,000.
Now plug it all in:

L = 983,571,056 / 2 x f(MHz) x 10k. That simplifies to 983.571056 / 2 =~491.8, so

L = 491.8 / f(MHz)

Why 468 instead of 492? Because real antennas aren’t in free space. A wire antenna:

  • Has end effects
  • Has capacitance along the wire
  • Radiates in the near field of itself

All of that makes the antenna electrically longer than its physical length. So, we shorten it by about 5%:

491.8 x 0.95 =~ 468

Final practical formula:

                                            L(feet) = 468 / f(MHz)                                   

This gives a good starting length for a half-wave dipole. It usually tunes close to resonance for the frequency f(MHz). Remember f(MHz) is the frequency that you wish to use for your band center frequency. Now then, you need to trim the antenna to obtain the best S WR for that center frequency. Let’s define center frequency (f) as a frequency near the middle of the band you are building the antenna to transmit and receive with. For example, for a 40-meter band antenna, f may be selected as 7.2MHz.

Extra ham-radio nuggets:

  • Each dipole leg is simply half of L, or L/2 = 468 / 2f = 234/f
    Thicker wire → slightly shorter antenna

Insulated wire → slightly shorter

Height above ground also affects final tuning

That’s why old-school advice is still true: Cut it long and trim it down.

 

Comments

Post a Comment

Popular posts from this blog

Antenna Theory - What's Happening

  Antenna Theory – A small bit, anyway It is an early Sunday evening, and you have been in the shack for over an hour. You have been tuning the HF bands on your new Icom 7300 transceiver. Linked to the 40-meter half-wave dipole that stretches from the far yard tree to the house eave, you are experiencing noiseless, 1.2 SWR transmissions and picking up DX stations in South America and the Pacific rim. Your wife calling you to dinner quickly snaps you out of your Tuesday, after work nap. It's time to get up from the Lazy-Boy lounge chair. While at the dinner table, you reflect on the dream that you just had. It was all a fantasy; you get no such performance from your ham shack setup. You know it is not good, but you don’t know why.   It's time to dig into what may be happening. Radiation occurs when electric charges accelerate. Constant-velocity current does not radiate; time-varying current does. In a half-wave dipole, the RF source forces electrons to speed up, slow dow...
Read more

A Blog Site to share Ham Stuff

I am an experimenter, a builder of things, and I have been a teacher. I am a man of Maths and of Science; when curious, I will dwell until I have an understanding. As a Ham, I am probably a poor excuse. I enjoy scanning the bands. It is interesting to me to observe how well the reception may be on a given band, at a particular time.  But I find that my interest is not in long Ham visits, rather it is in seeing what and where I can detect.  Signal reception, of course, is governed by many, some often nasty factors. However, all else being fine, how well you will receive depends in a major way on your antenna setup. A primary purpose of this blog will be to share experiences with antenna construction. There seems to be no end of the technical stuff that a newer Ham has to become acquainted with. This site will present technical stuff, too. What I hope to achieve is to present the material in a down-to-earth understandable way.  When reading a particular post, if you see an ...
Read more