[Elecraft] Efficiency of MFJ remotely-tuned loop antennas

[Alan Bloom]

Well let's see...

Radiation resistance of a small loop is 31,171 * (Area / wavelength^2)^2

For a loop with a 91cm diameter at 14 MHz, I believe that comes out to 
0.064 ohms.

Assuming the loss is due to the RF resistance of the loop:

 From the internet I get the volume resistivity and skin depth for 6063 
aluminum is 0.03 microohms-meter and 23.3 micrometers respectively, so 
the surface resistivity is 0.03/23.3 = 0.0013 ohms per square.  The 
outside circumference of the tubing is PI * 1.05" = 3.3" and the loop 
length is PI * 36" = 113" so the loss resistance is .0013 * 113/3.3 = 
0.045 ohms.

So I calculate an efficiency of 0.064 / (0.064 + 0.045) = 59%

So worse than AEA claimed, but in the ballpark.

Alan N1AL




On 1/18/2021 3:39 PM, Wayne Burdick wrote:
> Hi Alan,
>
> 72% sounds a bit high. Is this number based on loop size alone ("in theory")? Or are they taking conductor geometry and other losses into account?
>
> Wayne
> N6KR
>
>
>> On Jan 18, 2021, at 2:05 PM, Alan Bloom <n1al at sonic.net> wrote:
>>
>> MFJ makes a pair of small, remotely-tuned loop antennas, the MFJ-1786 that covers 10-30 MHz and the MFJ-1788 that covers 7 to 21+ MHz.  As far as I can tell, the two antennas are identical except for the size of the tuning capacitor.  Each consists of a 3 foot (91 cm) diameter loop made of aluminum tubing and a plastic housing that contains the tuning capacitor, motor, and coupling loop.  No control cable is required since the control voltage is sent from the control box in the shack to the motor in the antenna via the coaxial cable.
>>
>> Before I purchase one of these I wanted to get an idea of the efficiency of such a small loop.  MFJ is silent on the subject so I did my own calculations.  The calculations and results are on a 1-page document that I uploaded to Dropbox and can be downloaded here:
>>
>> https://www.dropbox.com/s/l8mv67cjrck2ssn/MFJ-1786-1788.pdf?dl=0
>>
>> My calculations are based on the assumption that the efficiency of the MFJ antennas is similar to the (no longer manufactured) AEA Isoloop (my reasoning for that is in the document) and that AEA's specification of 72% efficiency at 14 MHz is correct.  From that number I can calculate the efficiency and gain on all the other bands.
>>
>> If you don't want to download the document, here is a summary of the results:
>>
>> Freq	Eff	Gain with respect to a half-wave dipole
>> MHz	dB	dBd
>> 7.0	-7.3	-7.7
>> 10.1	-3.5	-3.9
>> 14.0	-1.4	-1.8
>> 18.068	-0.6	-1.0
>> 21.0	-0.4	-0.8
>> 24.89	-0.2	-0.6
>> 28.0	-0.15	-0.5
>>
>> I'd be interested in any comments people may have on the accuracy of
>> my assumptions and calculations in the document.
>>
>> Alan N1AL
>> ______________________________________________________________
>> Elecraft mailing list
>> Home: http://mailman.qth.net/mailman/listinfo/elecraft
>> Help: http://mailman.qth.net/mmfaq.htm
>> Post: mailto:Elecraft at mailman.qth.net
>>
>> This list hosted by: http://www.qsl.net
>> Please help support this email list: http://www.qsl.net/donate.html
>> Message delivered to n6kr at elecraft.com
>