# Antenna gain calculator - three antenna method

This calculator is designed to solve the gain of three antennas where measurements are made of the path gain from a source to receiver using each of the three combinations of the three antennas.

The source and receiver could be a VNA, or it could be a signal generator and calibrated power meter, or a spectrum analyser and tracking generaor. In the latter case, the calculated dB path loss is entered for the s21dB fields of the form.

The first input field and the label fields are for documentation (eg if you screen capture the form).

The calculator assumes the measurements are in the far field, sufficient distance from the antenna to be true radiation propagation, and no multipath (eg ground reflection). Distance is between phase centres of the antennas. This method does not require the gain of any of the antennas be known.

By rearranging the Friis transmission equation, we can write $$G_a+G_b=G_{ab}-20 log(\frac{c_0}{4 \pi f r})$$ where all gain values G are in dB. WIth three antennas of unknown gain G1, G2 and G3, we can measure Gab for the various combinations (ie G12, G23, and G31) and write three simultaneous equations. The solution of those equations gives G1, G2 and G3. The measured G12, G23, and G31 are entered into the calculator as s21dB12, s21dB23, and s21dB31. The subscripts might imply an order, but s21dB32 is equivalent to s21dB23.

# Calculator

 Frequency (MHz) Distance (m) s21dB12 s21dB23 s21dB31 Label Gain Antenna 1 (dBi) Antenna 2 (dBi) Antenna 3 (dBi)

The calculator does not do a lot of error checking, if you enter nonsense, it will probably produce nonsense. NaN means not a number, check the input values. Make sure there are no embedded blanks in numeric values, "- 25.1" is evaluated as 0 due to the embedded blank.

# Changes

 Version Date Description 1.01 30/01/2022 Initial. 1.02 1.03 1.04 1.05