Table 5-16 of the AM3358 datasheet shows a single channel can be sampled as fast as 200 kSPS. We've found that whether we sample at 20 kSPS or 200 kSPS the ADC channel does not show a rise time faster than 400us and a fall time time faster than 300us. That puts the maximum analog bandwidth for a TSC_ADC channel at about 1.5KHz. Is that correct?
Changing the source driving the load from 10 ohm to 1 ohm makes no difference in rise and fall time, so this appears to be an internal limitation.