Feeding and matching a 1/4 lambda circumference loop antenna.
Wrong and correct loop calculations.
pa0nhc  20170611

Magnetic loop calculation software presumes that the RF-current has a constant value everywhere around the radiator.
This assumption gives useable results for very small loop antennas, with a circumference smaller than 1/20 lambda.

What if the circumference is 1/8 lambda to 1/4 lambda?

        Example : A tuned 1/4 lambda circumference loop antenna.
- 7.1 MHz
- 100Wrms
- Circumference 10m
- Radiator 80mm (!!) thick:

        Calculation example using 66pacific calculations :
- The "Radiation resistance" is only 0,566 Ohm.
- The "Resonant circulating current" is up to 9,2A
        The with R=P/I2 calculated feedpoint impedance is only 1,2 Ohm.
- The loop bandwidth on 7.1 MHz should only be 16 kHz => Q=444 !!
- The voltage at the tuning capacitor should be up to 5kVrms (equals 7kVpeak).

These calculations are wrong.

Transmitting loop with transfromer feed
connected at the tuning capacitor.

Low capacitance 7MHz transformer for 10m circumference loop. 
FT185-61  B (4C65-36mm). Sec : pri = 6t : 91.
FT240-61  sec : pri = 8t : 12t  (Lpri = 13uH).
Sec. wound over 1mm teflon tape. 

Transformer set mounted beside the splitstator tuning capacitor. 

By research, G0CWT found that the current around the circumference of a 1/4 lambda loop is NOT constant, but varies largely.

This has large consequences for practical (real) loop properties.

        Calculation example using practical impedance measurements by G0CWT.
    The loop current recalculated :
n the current maximum of a resonant 1/4 lambda loop G0CWT measured a feed point impedance of 5.5 Ohms.
                    Nearly five times larger than calculated from data of 66pacific.

From this and the 100W transmitter power we can calculate ( I2 = P / R) the loop current as 4.26A.
  Half the value calculated by 66pacific.

G0CWT measured a feedpoint impedance of 22.5 Ohms at the tuning capacitor.
The current at the tuning capacitor can be calculated as 2.13A.
Nearly 5x smaller than calculated by 66pacific.

        The capacitor voltage re-calculated.
The 63pF tuning capacitor shows at 7.1MHz a reactance Xc=365 Ohms.
With a loop current of 2.13A,
the voltage over the capacitor is (365 Ohm x 2,13 A) = 777 Vrms or only 1100Vp.
Nearly 5x smaller than calculated by 66pacific.

In practice my loop has on 40m an "VSWR < 1.5 bandwidth" of 85kHz.
More than 5x better.

Still not convinced ? Compare these results with calculations after DL4CKJ.


    Matching a 1/4 lambda circumference loop antenna.
G0CWT uses a broadband ferrite core transformer to match the 50 Ohms coax feeder to the loop. Coupling between his primary and secondary windings is mechanically tight, with the drawback of also capacitive coupling.

A suitable transformer can be inserted in any point into the loop :
- in the current maximum or
- in the current minimum or
- in-between.

Connecting the matching transformer to the tuning capacitor has a big advantage : 
the transformer can be installed inside the same housing as the tuning capacitor.

For these three cases, the transforming ratios will differ, as the feed point impedances will differ. G0CWT measured an impedance of 22.5 Ohms near the tuning capacitor.

Zpri : Zsec = 50 : 22.5 = 2.25 : 1 => turns = 1.5 : 1

According to my experience, capacitive coupling must be absolutely minimal, to prevent E-field radiation and reception, TVI / BCI and man-made-noise reception. 

To avoid capacitive coupling and capacitive unbalance to the loop, i constructed a transformer with very low coupling capacitance between the primary and secondary windings.


After experiments with several transformers i found :
- To small winding inductance has negative influences to the tuning behavior, selectivity and performance of the loop.
- A to high secondary winding inductance introduces, in parallel with the total tuning capacitance of the loop, a blocking parallel resonance.

An FT240-61 ring core with sec. 8t and pri. 12t 
an FT185-61B (Philips 4C65 - 36mm) 
are working well on 7 MHz.

#61 material is chosen for its low losses, and flat frequency- and temperature responses.

        Matching on 80m.
On 80m the circumference of the loop is only 1/8 lambda. Its feed point impedance drops by a factor 9.

By adding an auto- transformer with a transformation ratio of pri : sec = 3 : 1 good match is achieved again. This is done by winding a transformer on a FT240-61 or FT185-61B ringcore, wound with 15 turns, and a tap on 5 turns from the ground connection..