# How to find the front-to-back ratio given an antenna radiation pattern diagram?

I know that the front-to-back ratio is 18dB in the below antenna radiation pattern diagram, but I don't know how to read the diagram to obtain this result. How does one read and understand such diagrams?

The diagram is a polar plot where 0 degrees (the 0 on the right-hand edge) corresponds to the front of the antenna and 180 degrees corresponds to the back.

Within the diagram, a logarithmic scale is utilized to represent radiation strength. This is in addition to the fact that the Decibel is a logarithmic unit. (The diagram really should explicitly list its units, but for the application of antenna radition, the unit is typically dB.) You can tell that a logarithmic scale is in use by observing that the distance between the $-6$ and $-12$ lines is the same as that between the $-12$ and $-24$ lines, so it's obviously not a linear scaling.

For the front-back ratio, we look at the values indicated on the plot for 0 and 180 degrees. In this particular instance, the value at 0 degrees is $0$, and the value at 180 degrees is approximately $-18$.

Since logarithmic scales transform division into subtraction, we calculate the ratio front to back by subtracting the logarithmic back value from that of the front.

Since $0 - (-18) = 18$, the answer is 18dB.

• Excellent answer, I would upvote but the system won't allow me to.
– Dan
Oct 23 '13 at 21:52
• If the scale is non-linear in decibels, wouldn't that make it a log-of-log scale (however you actually call that)? A log scale marked in decibels should have evenly spaced numbers, no? Oct 23 '13 at 22:00
• @KevinReid You're right that the overall representation is actually a log-log scale once you factor in that dB are already logarithmic. However, the scale of the plot is relative to its units, so the plot is merely logarithmic, while the overall representation is log-log. Oct 23 '13 at 23:04
• The scale looks anti-log to me. That is, if we move 5mm away from the origin, maybe the value changes by X. If we move another 5mm away, the value changes by less than it did the first time. This is the opposite of a log scale. This serves to cancel the logarithm of the decibel, meaning this is actually a linear plot. A F:B ratio of 2:1 would mean the back is twice as far away from the origin as the front, as measured by a ruler. Oct 29 '13 at 22:00