I have a voltage regulator circuit powered by a CT. I rectify the output AC voltage to DC voltage and provide that as an input to the regulator L7805CV. My input voltage is about 7.20V When I connect the regulator, the input drops to 4.6 V and the output is only 3.3 V instead of 5V. When I try it with another regulated voltage of about 15 V, the output is fine to 5V and there is no drop from the input side. I tried the regulator circuit with appropriate capacitors at input and output side still makes no difference. Why is there a drop only when I connect it to the CT?
The dropout of a 7805 is around 1.6V with no load, but this is not guaranteed you really need more voltage, but let's work with that. It also draws around 5mA with no output current.
To reduce the ripple voltage to (say) 0.1V you need a capacitance of 0.01s*0.005A/0.1V= 500uF. Your 0.47uF is woefully inadequate, and your measurements are suspect because they have a shipload of ripple.
That's assuming you have no other parts, however you have not entered your circuit schematic, so that's going to be it.
A Voltge transformer produces 10% higher voltage with no load and the peak is 1.4*RMS and the '05 Regulator has a TYPICAL dropout in datasheet of 2V. (old BJT technology).
This means you are expected to provide 7V Typ and 1.5times this for no load or 10.5V.
Voltage transformers have about 10 % conduction loss and achieve rated AC Vrms at rated load.
CT's have higher conduction loss if only rated for low secondary currents since the turns ratios tend to be high and only specified for lower currents at a fixed burden R load.