The null depth will depend also on the relative gain of the two antennas.
Forward, in the desired direction - assuming one is 45 degrees out, the *field*
will be 0.707 (cos(0) + cos(45)) = 1.707*.707 = 1.21 = 1.6 dB. Versus ideal
3 dB.
(field is voltage, so dB = 20*log10())
(the 0.707 is because the power is divided between the two antennas, so the
voltage is 0.707 = sqrt(1/2))
Null, though, would be 0.707 (cos(0)-cos(45)) = .707 * 0.293 = -13 dB (against
your +1.6 dB forward)
Of course, really, you might think in terms of the peak off to the side where
it's more 22.5 degrees off for each (cos(22.5)+cos(22.5)) = 0.707*(0.924+0.924)
- so on the "nose" of the skewed pattern, it's 2.3 dB
And the null, in the skewed direction will be "infinite" (assuming perfect
cancellation).
But if one of the antennas is 3 dB different gain, the null won't be as deep.
On Thu, 12 Mar 2026 12:42:24 -0400, "Joe Subich, W4TV" <lists@subich.com> wrote:
That is the case ... at least for horizontal antennas over ground.
I was playing with thoughts of vertical beam steering - primarily
for VHF use - but with antennas less than four or five wavelengths
above ground (e.g., HF + 6M), phase differences even approaching
90 degrees had very little effect on the take off angle.
Things got messy around 90 degrees difference but fairly quickly
jumped to the "out of phase" condition. As I recall (it's been a
few years), the loss of forward gain for even 45 degrees of phase
difference was less than 1 dB with no significant null fill.
73,
... Joe, W4TV
On 2026-03-12 11:44 AM, john@kk9a.com wrote:
> Regarding your " The last question is a real use case" I believe that Yagi
> phasing is not super critical. Your phasing between two dissimilar Yagis
> may be off but close enough for the stack to still work. This should be
> easy to model.
>
> John KK9A
>
>
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