The trick is that the current transformer has a maximum volt*second product on the secondary so if the secondary voltage is too high, the transformer will saturate. Any current transformer you find should have this specification.
I'm trying to understand this part. There's a maximum of voltage, integrated over time? For what time period?
Exactly, the maximum volt*time product that the transformer will support before saturation is a constant. Transformers intended for power line use specify this differently; they include a maximum secondary voltage or load resistance and assume a 50 or 60 Hz AC only input.
The Tektronix design I mentioned used a roughly 9 volt shunt regulator on the secondary side of the current transformer which limited the secondary voltage preventing saturation. But they also included a 15 volt shunt zener diode as protection to prevent the secondary from going open circuit which is very bad in a current transformer. So their design supported more than 9 volts across the secondary but this was pretty easy for them to do; they built their own custom transformer and it was operating at 10's of kHz lowering the volt*time product compared to a 60 Hz transformer. I used their design as an example of what can be done.
What if we were to use this CT; how does it apply? http://cdn.sparkfun.com/datasheets/Sensors/Current/ECS1030-L72-SPEC.pdf
In this case the numbers to look at are the specified secondary DC resistance of 250 ohms, the 10 ohm load resistance, and the 300mV output voltage. Nothing more is needed in aa normal 60 Hz application.
Assuming it could be rectified, 300mV across 10 ohms only yields 30 milliamps and 9mW. Of course we should know that because 60 amps divided by the turns ratio of 2000 is 30 milliamps. The actual secondary voltage which we cannot access is 30 milliamps across 260 ohms or 7.8 volts. Divided by the winding ratio of 2000, this burdens the primary side with 3.9 millivolts.
At some point as we raise the load resistance, the transformer will saturate and the output will drop but the specifications do not say anything about that; it will have to be measured to see if the transformer is suitable.
Note that there are lots of low voltage energy harvesting ASICs now which could directly operate off of a low voltage AC source to charge a capacitor or battery. It should be possible to use these with a standard AC current transformer and it would probably be less expensive than procuring a better transformer.