Maybe not. The analysis presented in this article:

http://fermi.la.asu.edu/w9cf/articles/balun/

leads to the conclusion that locating the choke balun at the input of
the tuner, and floating the tuner,  offers an advantage only for
balanced tuner designs (and good balance in the load). The stress on
the balun in a high SWR situation is unchanged by moving it to the
input. In short "An unbalanced tuner trades the large differential
mode impedance for a large unbalanced impedance making the balun's job
unchanged."

W8JI also addresses the issue in this article:

http://www.w8ji.com/tuner_baluns.htm

and comes to the same conclusion, with emphasis on the need for good
load balance in the case of a balanced tuner with choke balun at the
input. He ends with: "The irony is, moving the balun to the input
mostly works only when the balun is not needed!".

Food for thought.

I use a floating balanced-L tuner with choke balun at the input, but
try to keep decent balance in the antenna system for this reason.

Bob NW8L

>There may be no difference in efficiency between putting the balun at the input
>or the output of the tuner if you are operating into a nice 50ohm resistive
>dummy load, but the situation changes if you are operating into an antenna fed
>with ladder line on which there is a high SWR. In this case, the high SWR can
>cause high currents that saturate the ferrite core in the balun, and causing
>non-linearity and producing heat losses. This is why it may be preferable to
>locate the balun at the input of the tuner, where the SWR on the transmission
>line is low, and "float" the whole tuner. However, as Don mentioned, this can
>present difficulties if the tuner is not a balanced design.
>
>73, Matt VK2ACL
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