Random Wire Revelations

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I was inspired to dig my old Hendricks PFR3 QRP rig out of the closet recently. I wanted a super lightweight rig with an easy to deploy, but efficient, antenna that I could grab and go without any advance planning.

VA3KOT’s Hendricks PFR3 QRP/CW radio

The antenna I chose was a random wire that would work on the three bands supported by the PFR3 (20m, 30m, 40m). To make this as simple as possible I decided a directly connected antenna and single ground radial would fit the bill.

I setup as a “Backyard On The Air” field station with my antenna oriented as a sloper supported by a convenient tree. A random wire antenna is not resonant on any band and requires a tuner. One of the great features of the PFR3 is that it has an internal Balanced Line Tuner (BLT). The BLT can also be used with unbalanced antennas by setting a switch on the back panel to ground one side of the tuner.

I tuned up on 40m with no problems and quickly made a contact with a Parks On The Air (POTA) station in Ohio. He gave me a 559 report – not bad for a 5 watt radio with a simple wire antenna.

Strange, Very Strange!

Next, I attempted to tune up on the other two bands, but no luck there. The first step in tuning is to listen for a peak in the noise as the two variable capacitors are adjusted. There was no noise peak. It was as if no antenna was connected. Strange, very strange.

Aha!

I reconnected the antenna and radial wire through a 9:1 unun with a short coax connection to the radio. Now all three bands tuned perfectly. Aha, a clue as to why 20m and 30m would not tune with the antenna directly connected – the impedance was too high for the BLT to match.

But why did the antenna present too high an impedance on 20m and 30m and yet it tuned perfectly on 40m? After much time spent in my reclining thinking chair, drawing diagrams on the back of my eyelids, I came up with a solution.

A random wire antenna should be longer than a quarter wavelength on the lowest band of interest. So let’s examine a full wavelength wire on each band to see if we can discover the problem.

We know that the conditions along a wire repeat every half wavelength. If the feedpoint impedance (Z) along a half wave wire varies linearly and assuming Z = 50 ohms at the quarter wave point and 2500 ohms at the half wave point (those numbers vary in practice), the impedances along a 41ft random wire for each band are shown below.

20m
__________16.5/50__________33/2500_____41____49.5/50__________66 feet/2500 ohms

Looking at just the quarter wave where the 41ft point lies: 33/2500______41____49.5/50

The impedance at 41ft is 8.5÷16.5×2450=1262 ohms and the impedance ratio the tuner has to tackle is 25:1

30m
__________23.2/50_______41__46.4/2500__________69.6/50__________92.8/2500 feet/ohms

Looking at just the quarter wave where the 41ft point lies: 23.2/50_______41____46.4/2500

The impedance at 41ft is 17.8÷23.2×2450=1879 ohms and the impedance ratio the tuner has to tackle is 38:1

40m
__________33.3/50___41______66.6/2500__________99.9/50__________133.2/2500 feet/ohms

Looking at just the quarter wave where the 41ft point lies: 33.3/50___41______66.6

The impedance at 41ft is 7.7÷33.3×2450=566 ohms and the impedance ratio the tuner has to tackle is only 11:1

Random wire antenna, radial and 9:1 unun on winder

Now, if we add a 9:1 unun, the impedance on all three bands becomes very easily manageable by the BLT
20m: 1262/9=140 ohms
30m: 1879/9=209 ohms
40m: 566/9=63 ohms

Conclusion
A directly connected random wire antenna can only work in conjunction with a wide range manual tuner for 20m and 30m bands, otherwise a 9:1 unun must be used to bring the feedpoint impedances down to manageable levels.

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