parallel dipole impedance question

[KB3CEB]

I want to get a good match for 15m on my 40m dipole. I have seen several sources that recommend using capacitance "hats" at ~11 ft from the feed point e.g.:
https://www.na6o.com/amateur_radio/ewExternalFiles/40_and_15m_dipole_NA6O.pdf
I have also seen one recommendation to add parallel 15m wires:
The 40 and 15 Meter Dipole - a Myth Exposed
But, other sources say this should not be done because the input impedance will become too low; the argument is that since the 40m wires are close to resonant on 15, if you add 15m wires, you will have two ~50Ω antennas in parallel and the transmitter would see 25Ω.
However, when I analyzed my 40m dipole, resonant at 7.058 MHz, with a RigExpert I find that |Z| at the resonant freq. is 59Ω, while |Z| at 14.058 is 29Ω. Yet nobody would object to adding 20m wires in parallel to a 40m dipole!
Obviously I am missing something... am I misreading the RigExpert? Do we need to consider the complex impedance and not just the absolute value of Z? Can someone explain how impedance really works in dipoles fed from the same coax? And if adding 15m wires is a reasonable option or not?
Thanks!
(PS. I am not asking for antenna recommendations, or suggestions to use a tuner. I am asking for help understanding how the parallel dipole configuration works vis-a-vis impedance... THX)

 

[prcguy]

I would not add a 15m dipole in parallel, your 40m is already a reasonable 15m antenna. I have seen very good VSWR on 15m with a 40m dipole and I suspect maybe yours is very close to the ground which will lower the impedance on 40 and 15m. How high is your dipole? Worst case you can use a tuner to operate 15m with a good match and the radiation pattern will be predictable as you can look that up.

If the 40m dipole is in free space the impedance would be in the 70+ ohm range on 40m and probably similar on 15m. If the dipole is 10ft off the ground the impedance could be sub 30 ohms on 40m and quite low on 15m also. 1/2 wave increments above ground will give higher impedance readings than 1/4 wave odd multiples or lower than 1/4 wave above ground.

 

[KB3CEB]

prcguy, tnx for the quick reply, i hear your practical experience - you are correct that my dipole is low, at ~26'. It is usable on 15 with an SWR of 2.5, which my rig seems to handle at lower power; and a tuner works great of course. But I must repeat: "I am not asking for antenna recommendations, or suggestions to use a tuner". My question is: given one antenna that is resonant on some frequency f + ε, and then adding in parallel a second antenna that is resonant on exactly f, what is the formula for the new impedance as seen by the rig and where will the power go? And to understand this, is it adequate to express impedance as |Z| (absolute value of the impedance, iiuc, which is not certain, lol) or do we need to know Z = R ±jΧ in each case, and then what is the formula?

 

[G7RUX]

prcguy, tnx for the quick reply, i hear your practical experience - you are correct that my dipole is low, at ~26'. It is usable on 15 with an SWR of 2.5, which my rig seems to handle at lower power; and a tuner works great of course. But I must repeat: "I am not asking for antenna recommendations, or suggestions to use a tuner". My question is: given one antenna that is resonant on some frequency f + ε, and then adding in parallel a second antenna that is resonant on exactly f, what is the formula for the new impedance as seen by the rig and where will the power go? And to understand this, is it adequate to express impedance as |Z| (absolute value of the impedance, iiuc, which is not certain, lol) or do we need to know Z = R ±jΧ in each case, and then what is the formula?

When you say "adding a second in parallel" do you mean electrically connecting it to the feed point, fan dipole style or do you mean setting it up as a parasitic element?

Both will affect the feedpoint impedance but the former more than the latter.