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Just of curiosity...

Outside of kits/ham produced prototypes, Do you know about any commercially produced 6m handhelds?

Should be technically feasible despite the fact that it would be more cumbersome than VHF / UHF radios, But I recall that CB operators have 27 Mhz handhelds.

Do you know the historical/technical/marketing other reason for them not to exist?

Or maybe they do exist and I cannot find any positive info about them...

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The Yaesu VX-5R had/has 50-54 MHz FM, 5 watts. Nice compact little radio!
The VX-7 and VX-8 can also transmit 5 watts FM on 6 m, and 1 watt AM. None of the 3 will transmit SSB.

It had a little extension of the rubber duck to make it work at 50 MHz, though I doubt it was very efficient.

Antenna calculation:
The whip is about 25 cm long, so I'll consider a 0.5 m dipole. Radiation resistance the dipole is 1.4 $\Omega$. Reactance is about -1500 ohms, resonating this with a coil will introduce the rest of the 50 $\Omega$ resistance, probably giving a reasonable match. Efficiency is thus about -15 dB.

Further thoughts:
When talking to someone with a full-size dipole, like a repeater, the gain of the 6 m antenna will be partially compensated for by the reduced path loss. The path loss is 6 dB smaller at 6 m, compared to 2 m. Assuming the gain at 2 m is -3 dBi, and the gain at 6 m is -15 dBi, at 6 m the handheld will deliver only 6 dB less signal to the repeater.

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  • $\begingroup$ +1 but the term "resonate" is perhaps misplaced since I doubt the antenna system is anywhere near fully resistive (i.e. +j0). $\endgroup$
    – Glenn W9IQ
    Aug 22 '18 at 22:34
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    $\begingroup$ You never know! There might be a resistor in there ... remember, a dummy load has a fully resistive impedance ;) $\endgroup$
    – Scott Earle
    Aug 23 '18 at 1:01
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    $\begingroup$ Same with the VX-8DR - advertised as 4 bands in the US with 6m, 2m, 1.25m and 70cm. It's utterly useless without a real 6m antenna, which means it is no longer a handheld. $\endgroup$ Aug 23 '18 at 7:37
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    $\begingroup$ I've used the vx-8 once on 6m at a hamfest, because all the other bands were full. It was effective with the stock antenna at least short range. Don't forget that they make CB handhelds too, so if 11m can work, 6m can work. $\endgroup$
    – user10489
    Aug 24 '18 at 11:26
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    $\begingroup$ To say that the VX5R is useless without a longer antenna is not based on first hand knowledge. Indeed the factory provided antenna is less than optimal; however, a range of communication between two points, exceeding 20 km or more is not unusual. In addition, there are 6M repeaters all over the country that extend the communication range to over the horizon distances, sometimes better than 200 km, depending on location. Bear in mind that 50-54 MHz falls in the middle of the Military band (30-75 MHz). Military radios are not any better than our ham equipment and the HT military radios use short $\endgroup$ Aug 26 '18 at 5:44
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Also the Cherokee AH-50, which is the 6m big brother to the AH-27 (CB variant). They were produced from about 1995 to the early/mid 2000s. FM-only and able to use with repeaters. Very basic radio but back then, choices were limited to this radio for a 6m ht/handheld.

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    $\begingroup$ Hi Phil, and welcome to ham.stackexchange.com! Nice first answer! $\endgroup$
    – rclocher3
    Jul 12 at 15:58
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I have an Icom IC-T81A that will transmit and receive on 6 meters.

https://www.universal-radio.com/catalog/ht/3795.html

Or at least it did at one time. I haven't used that feature in a long time and my IC-T81A has seen better days. I haven't even powered it up in quite some time.

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