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The measured input Z of my outdoor base coil loaded 3 meter vertical (1/2 inch aluminum pipe) above ground radials antenna is measured as 57 + j0 ohms. The j0 means it is resonant and this was measured at 1680 kHz. The loading coil inductance (L) is 260 uH.
From this the antenna system bandwidth can be calculated as BW = R/(2*pi*L) which equals 34.9 kHz so the audio high frequency cutoff for AM is half this = 17.5 kHz.
As an experiment, the audio cutoff of my transmitter was measured to be 20 kHz measured at the output of the modulator at the input to the final RF stage. The receiver, a BC-1004-C, has a measured audio cutoff at 17 kHz with the IF wide open. The overall system bandwidth from transmitter audio input to receiver audio output was measured as 17 kHz (high cutoff) so the receiver BW dominates and the transmitter/antenna system BW is at least greater than this.
For my installation, increasing the diameter of the pipe would have no noticeable effect and is not worth the effort.
To repeat this calculation using the AMT-5000 the audio bandwidth of this transmitter needs to be known and also the Q (or RF resistance) of the loading toroid needs to be known. The Q of my loading coil was measured to be 147 (R = 19 ohms) so if the AMT-5000 specs. are similar then similar results would be expected providing the antenna system R is comparable to my 57 ohm reading.
Since the Q of the loading toroid and the audio bandwidth for the AMT-5000 is not known to me I cannot make an accurate prediction but I expect that if your ground resistance is comparable to mine then the bandwidth will be adequate using a 1/2 inch diameter radiator.
The only sure way to know is for you to try a narrow and wide radiator and do a “listen” test or better yet a measurement of bandwidth for any difference. If a difference is found then the good news is that a lower bandwidth means lower losses compared to my system.