<< Wrong and correct calculations for matching a 1/4 lambda circumference loop antenna. pa0nhc  20181106 / 20181205 (C) The use, publication, copy and modification of all info on this site is only permitted for non-commercial purposes, and thereby explicitly mentioning my radio amateur call sign "PA0NHC", as the original writer / designer / photographer /publisher. (C)

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

But a maximal large 1/4 lambda circumference capacitive tuned loop has very different properties :

Example : A tuned 1/4 lambda circumference loop antenna.
- 7.1 MHz
- 100 Wrms
- Circumference 10 m
- Radiator 80 mm (!!) 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 (Z =  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).    G0CWT proved that these calculations are wrong.

The loop currents recalculated using practical impedance measurements by G0CWT : Testing/adjusting the transformer matching circuit.

Using an antenna analyser, G0CWT measured in the current maximum of a resonant 1/4 lambda loop a feed point impedance of  5.5 Ohms.

From this and the 100W transmitter power, we can calculate with ( I2 = P / R) the RFcurrent there as 4.26A.
=> This is half the value calculated by 66pacific.

Near the tuning capacitor, G0CWT measured a feed point impedance of 22.5 Ohms
From this the RFcurrent at the tuning capacitor can be calculated as 2.11A.
=> This is nearly 5x smaller than calculated by 66pacific.

The capacitor voltage recalculated.

The 63pF tuning capacitor shows at 7.1MHz a reactance Xc=365 Ohms.
With the above calculated 2.11 Arms RF current through the tuning capacitor, the voltage over the capacitor is (365 Ohm x 2,11 A) = 770 Vrms or only 1090 Vp. Transmitting loop, optimal  impedance  matched by a transformer.

=> This is nearly 5x lower than calculated by 66pacific.

=> Conclusion : a vacuum capacitor tuning is NOT needed, a transmitting air tuning capacitor could be used for 100W power.

Bandwidth.

In practice my loop has on 40m a "VSWR < 1.5 bandwidth" of 75 kHz. According to DL4KCJ this cannot be used to calculate the loop-Q.
But this practical bandwidth is
more than 3 times wider than calculated by 66pacific.

Important conclusions :
1. The value of the RF current near the tuning capacitor is half the value of the RF current in the top of the loop. RF currents therefore have NOT the same value around a 1/4 lambda loop circumference.

2.  The values of RF currents in a 1/4 lambda circumference loop are lower than in smaller sized loops.

Resulting in :
less losses,
lower Q,
larger useable bandwidth
smaller copper diameter needed
simpler tuning capacitor and its mechanical reduction is possible.

Still not convinced ? Compare these results with calculations after DL4CKJ. Installing the 40m + 80m matchbox at the top of my loop. Running down the wooden mast : 1)  RG58 coax feeder. 2)  3x 0.75mm2 band switch relay line and + 12V heather supply. At the bottom the tuning cabinet,  with split-stator tuning capacitor and DC tuning motor.

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.

A suitable transformer circuit can be inserted in any point around the loop circumference :
-  in the current maximum or
-  in the voltage maximum or
-  in-between.

For these three cases, the feed point impedances will differ.

 Connecting the matching transformer to the lowZ top of the loop, gave me in practice the best results. When now tuned to VSWR 1:1.0, the loop is also exactly tuned to maximal magnetic field strength.This new coupling circuit ensures a fully BALANCED excitation of the loop, resulting in no power unbalance, nor capacitive unbalance, and pure magnetic behavior.

My loop has 10m circumference, this equals 1/4 lambda for 40m

G0CWT measured at the current maximum of such a 1/4 wave circumference loop an impedance of 5.5 Ohms

Matching with a transformer :
Zpri : Zsec = 50 : 5.5 = 9.1 : 1 => Pri turns : sec turns = 9 : 3

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

By adding a tap on the secondary winding good match is possible om 3.65 MHz.

Zpri : Zsec = 50 : (5.5 / 9) = 81 : 1 => Pri turns : sec turns = 9 : 1 .

For a detailed description of the matching system : see designing the matching transformer.