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## Yagi Front-to-Back Ratio

Aug 4th 2011, 13:51

#### N7TWL

Joined: Jun 5th 2011, 13:02
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I am studying for my Extra Class license, and the following question (E9B06) seems to be counter intuitive: "What usually occurs if a Yagi antenna is designed solely for maximum forward gain?" The correct answer is that the front-to-back ratio decreases. I would think that the ratio increases. That is, the difference between the numerator and denominator of the ratio is getting larger. If we define the ratio to be that of signal strength transmitted in a forward direction to that transmitted in a backward direction, then surely as the forward gain increases (and presumably signal strength), the backward signal strength has to be decreasing.

Clearly, I am not understanding something in the way antenna gain works. Some insight here would be greatly appreciated.

Thanks.
Todd
KF7QFN
Aug 4th 2011, 14:35

Joined: Jul 25th 2011, 14:25
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The balloon analogy is probably the best to use to explain antenna gain.

Imagine a baloon that is essentially round. This is an isotropic radiator, radiating equally in all directions, The distance across the balloon represents the "gain" of the antenna with a pattern shaped like the balloon.

Now, squeeze the balloon in the middle with your fingers in a small circcle. The ends bulge out. This forms a dipole antenna, and it has a wider dimension, so it has gain, but in two directions, at the expense of the lack of gain in other directions.

Now, grab the balloon towards one end. The ballon bulges out more in one direction than the other,. This is a Yagi antenna. There is a point you can grab that will give the maximum bulge in the "forward direction." This is the point that would give the most forward gain. There is still a small bulge towards the back, though, and the difference between the front and back bulges in the balloon is the front-to-back ratio.

However, if you grab the balloon farther back towards the small bulge, in an attempt to improve the ront-to-back ratio, the forward bulge tends to become more rounded, so it's maximum bulge is a little bit smaller, and a bit more energy goes to the sides and upward and downward angles. The point of maximum gain is not the point of best front to back ratio.

You'd have to run through the math, but the reason that improving the front-to-back ratio won't make much difference in forward gain is that there is very little energy going to the back in any case, so the difference in forward gain is pretty small. Any improvement in front-to-back ratio puts more energy into the forward bulge, but that energy is not always directed toward making the maximum dimension larger; it sometimes make the bulge more round and the actual maximum dimension can decrease slightly.

So the bottom line is that if you improve the front-to-back ratio, you will usually decrease the forward gain by making the forward bulge more round.

73,
Ed Hare, W1RFI
ARRL Lab
Technical forums moderator
Aug 7th 2011, 15:52

#### N7TWL

Joined: Jun 5th 2011, 13:02
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Ed, what a great answer! I can now easily visualize the principle. Thank you for your excellent reply.

73,
~todd, KF7QFN
Jan 24th 2017, 03:29

#### K4AGO

Joined: Oct 27th 2016, 22:36
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I am well on my way to my Extra Class ticket too. This answer helped me a great deal in understanding and visualizing the concept of front to back ratio. Outstanding job Ed.
73
John K4AGO
Apr 7th 2017, 19:53

#### k1kjr

Joined: Jun 23rd 2016, 01:23
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+1. Am studying for extra also. This is a fantastic explanation. THANKS!
Jun 12th 2018, 09:14

#### NE1EE

Joined: Apr 4th 1998, 00:00
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Total Posts: 0
I just passed my Extra Class, and this is one of the best tips I recalled on the exam. It is so great when someone understands the material so well that they can put it so clearly. Props, Ed. Still a great explanation in 2018!