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Yes Exactly,

 20db front to back ratio.  F/B. not  signal to noise ratio.


 12 dbd reduction on the sides I.E. 45 degree angles from front of yagi and from back of yagi. Picture a clover leaf pattern for the nulls for the sides of the yagi.


 12dbd gain from the front of the yagi, correct for discussion purposes that is ALSO a 12 dbd gain in receive from the front of the yagi, so no matter what direction you point the yagi the receive will be stronger than a three element that has maybe 5.9dbd gain which is one S unit at 6db per S unit.


 The more elements  spaced correctly the more F/B ratio the yagi will have.


Yagi is a compromise antenna, power is not created it is redirected at the expense of losing some radiated power in other areas. Thus the side rejections and F/B. I.E. nulls per say.


 By creating those nulls and redirecting the signal it increases  the ERP of the signal.


 The best thing about a yagi is you can turn the yagi to NULL out offending QRM, this may be what you are referring to as being quieter??


  Of course you already understand this as you have mentioned you have built some yagi's before. Nothing new.