ELECRAFT ATU L AND C CONFIGURATIONS
The reactance configuration for all Elecraft ATUs is an L-network of series inductance, with a capacitance connected to common before (radio side) or after (antenna side) the inductance (but not both) by a relay. It is a classic low pass filter. The following is based on my research and the latest firmware for the KXAT3, KAT100, KAT500, KAT2 which I own,
KAT1, Configs=1020, L=0 to 4.9 uH (16 steps), C=0 to 300 pF (32 steps)
KAT2, Configs=131068, L=0 to 20.7 uH (256 steps), C=0 to 2420 pF (256 steps)
KAT3, Configs=131068, L=0 to 17.4 uH (256 steps), C=0 to 2600 pF (256 steps)
KAT100, Configs=131068, L=0-20 uH (256 steps), C=0-2400 pF (256 steps)
KXAT1, Configs=124, L=0 to 4.5 uH (8 steps), C=0 to 140 pF (8 steps)
KXAT3, Configs=131068, L=0 to 17.4 uH (256 steps), C=0 to 2624 pF (256 steps)
KAT500, Configs=131068, L=0 to 17.37 uH (256 steps), C=0 to 2701 pF (256 steps)
T1, Configs=32764, L=0 to 7.5 uH (128 steps), C=0 to 1300 pF (128 steps)
So for both the KX1 and the K1, the T1 will offer a wider tuning range than either internal autotuner.
As always, it is always best to minimize the mismatch between the antenna and not force the autotuner to work so hard because the transmitter may be happy but the precious few watts of a QRP rig may be burned up significantly in the autotuner reactance. The word to the wise is to use matching baluns to facilitate the better match.