A Transformer for Ground-Independent Receiving Antennas

The 4 rule

The reactance of the windings should be at least four times the impedance the winding is designed to look into.

exf1.jpg

where

Zi ... input impedance
Zw ... winding impedance

thus

exf2.jpg
where

Lw ... winding inductance
Zi ...
input impedance
f
... design frequency

To find the number of turns the formula is

exf3.jpg
where

N ... number of turns
Lw ... inductance in mH
A
L ... core constant (find in the catalog)

To find the number of turns on the secondary, use

exf4.jpg

where

Np =number of turns on the primary
NS= number of turns on the secondary
Zp
=impedance of primary
Zs = impedance of secondary

Example - a 1:9 transformer for a 450 ohm antenna:

Np/Ns = sqrt(Zp/Zs) or Np/Ns = sqrt(450/50) = 3, this is the ratio of primary to secondary turns. If you have a 450 impedance, 4 x 450=1800 ohms of reactance. Using 1.8 MHz as your minimum frequency, the inductance would need to be L = 1800 / 2 x pi x 1.8 MHz. So L= 0.000159 henrys or 0.159 mh. Thus N=1000(sqrt(.159/8500))= 5.24 turns on the primary. So NS = 5.24/3 = 1.75 turns on the secondary, a 6 turn primary and 2 turn secondary is ideal.
 
Instead of toroid cores, binoculars are widely recommended. Their advantage is in very low turn numbers to obtain the desired inductance, resulting in more bandwidth and lower capacitance between windings. Suitable cores shows Table 1.

Table 1. Binocular cores for transformers and the AL constant

Core AL
BN-43-202 2890
BN-43-2302 680
BN-43-2402 1277
BN-43-3312 5400
BN-43-7051 6000
BN-61-202 425
BN-61-2302 100
BN-61-2402 280
BN-61-1702 420
BN-61-1802 310
BN-73-202 8500
BN-73-2402 3750

You can also use the BN Calculator, available here.

The highest AL has the BN-73-202 which would be probably the preferred core. W7IUV successfully used such cores for his transformers used with rotatable Flag antenna.

Anyway, the 73 mix seems to be the best. Even higher AL can be obtained by stacking more binocular cores. W8JI uses 3 stacked BN-73-202 and also I tried to construct similar transformer. The only problem is the winding technique and the possibility to damage the enameled wire. Unfortunately, here is the teflon coated wire an 'unobtainium', so I put a length of soft silicone tubing into the holes. Anyway, you should work very carefully and a final check with inductance meter and impedance analyzer is a must.

A 1:9 transformer

My 1:9 transformer

Remember, that the winding of turns on a binocular core means: 1 turn is the wire passing through both holes (like a hairpin) as opposed to the convention for a toroid core where 1 turn is the wire passing through the core once.