# Calculate small transmitting loop gain from bandwidth measurement

***EXPERIMENTAL***

This calculator allows calculation of the efficiency and and gain of a small simple single turn transmitting loop in free space from VSWR bandwidth, matched frequency, loop radius and conductor radius or resonating capacitance.

A Small Transmitting Loop is one where the perimeter is less than about 0.1λ. The calculator will work for perimeter up to 0.3λ but radiation resistance estimates are poor above 0.1λ.

 Inputs: Frequency for min VSWR (<1.5) (MHz) Loop type Circle Square Hexagon Octagon Loop perimeter (m) Conductor diameter (mm) Min VSWR RR0 VSWR Bandwidth @ VSWR (kHz) Rr/Rrfs (pu) Directivity (dB) Results: Perimeter (λ) -3dB BW (kHz) Q Chu min Q limit Loop inductance (µH) X (Ω) Cs (pF) Rtotal (Ω) Rradiation (Ω) Efficiency (%) Efficiency (dB) Gain (dBi)

* loop perimeter >0.1λ.

The loop conductor must be a round conductor.

If Min VSWR is greater than 1, it matters whether R is less than or greater than R0, select as appropriate.

Rr/Rrfs allows multiplying the value of free space radiation resistance to obtain the radiation resistance used in the calculation.

Rtotal and Rradiation are referred to the main loop.

The calculator depends on an assumption that the current is uniform around the loop. It is most accurate for small loop perimeter, accuracy suffers for perimeter>0.1λ.

The calculator assumes a free space value for radiation resistance. Total resistance which includes radiation resistance, conductor and other losses, is calculated from Q and loop reactance.

Cs is estimated for a circular loop of the same perimeter. There will be some small error for other loop geometries.

The calculator does not do a lot of error checking, if you enter nonsense, it will produce nonsense.

VSWR should be significantly larger than Min VSWR. For best accuracy, min VSWR should be near to 1, and VSWR at which the bandwidth is measured should be near to 2.6 (which is the half power bandwidth for a matched antenna).

If the calculator reports "check inputs", the scenario is not possible, or not capable of accurate calculation.

The free space gain of an ideal loop is 1.76dBi.

The calculator is based on a free space model and will tend to overestimate overall efficiency (total radiated power in the far field / power input) when used with measurements of an antenna near ground.

## Effect of real ground

The calculator uses an estimate of loop inductive or capacitive reactance and an estimate of free space radiation resistance to determine free space radiation efficiency from Q calculated from measured VSWR bandwidth.

The radiation resistance of a loop over real ground may be different to its free space value due to the changed gain pattern resulting from the real ground reflecting downwards waves (with some loss and phase change). This will lead to error in calculated efficiency.