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Gain in dB scale of the transmitting antenna is:

$$G=10\cdot\log \frac{P_o}{P_i}$$

The input power will always be larger than the output power. However, I see a lot of radiation pattern graphs with positive gains in dB. How is that possible? Shouldn't the gain value ALWAYS be negative as the power ratio P_o\P_i will always be less than zero?

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  • \$\begingroup\$ The gain is always the ratio to a perfect omnidirectional antenna in that direction. \$\endgroup\$
    – PlasmaHH
    Sep 14 '18 at 9:42
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I suggest that you read the Wikipedia article about Antenna gain

Antenna gain is defined as the power radiated in a certain direction (so for a directional antenna, you would obviously choose the direction to which most power is radiated) relative to the power if the antenna was omnidirectional. Meaning: it radiates an equal amount of power in all directions.

So a high gain antenna will "focus" all power in one (or more) directions and that is defined as "gain".

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