I thought the loss at the parallel resonance frequency of the trap was not the issue. I thought it was the loss at the lower bands where the trap just acts as loading.... loading = lower radiation resistance = higher resistive losses. This applies more to trapped vertical antennas, not Yagis.
That's part of the confusion: if one antenna has less gain than another, it
is because it uses traps, it is shorter than full sized, or some other reason?
If you are discussing "lossy traps", then you have to compare an antenna
of similar size that uses some form of loading other than traps, in which
case the difference due to the antenna not being full sized doesn't enter
into the equation. So you need to be very clear whether you are comparing
traps to some other form of loading, or a trapped antenna to a monobander.
(Both are interesting comparisons, but this thread was specifically about
"how lossy are traps.")
A yagi designed for maximum gain often has a low radiation resistance, meaning
that current is higher than in a dipole. Thus trap losses can actually be higher
than in a trap vertical.
The voltage across the trap is highest at resonance, which is where the
losses will be highest due to high circulating currents. Designing a trap
antenna with the trap resonant just below the band where it needs to
act as a trap reduces losses, but it also complicates the design somewhat
because the outer sections still affect the tuning to some extent. The
further the trap is from resonance, the more current flows in the antenna
beyond the trap.
Many antennas that claim "NO LOSSY TRAPS" use instead some even lossier
substitute, such as self-resonant coils ("Iso-Res Inductors") that act like a
trap due to the parasitic capacitance of the coil rather than an intentional
capacitance added across it. Traps made using linear loading tend to have
slightly higher losses than those using standard coils.
The reason that W8JI's value of 1.6dB for coax traps is not typical of most
commercial offerings is that the loss is due to the poor Q of the coax
used as a capacitor. The traps in my TA-33jr use mostly air dielectric
(with some plastic spacers) and will be considerably more efficient.
(Unless the antenna comes down in an uncontrolled manner after Field
Day and breaks one of the connecting wires...)
True, there is some loss in performance due to a shorter element, but that
is the case whether one uses a trap or a loading coil. Actually, performance
is pretty reasonable down to about 60% of full size, after which the losses
accelerate as it gets shorter.
Because the traps are a combination of L and C, the bandwidth of a trapped
antenna will be less than that of one using just loading coils, but there
otherwise might not be much difference in performance.