A diode itself has no input or output.
The circuit containing the diode usually has an input and an output, maybe even more than one of each. The output of this circuit will depend on far more than the diode as well as depending on the type of diode used.
Theoretically: if a diode is connected across the secondary output of a stimulated transformer, you would read a half wave at the frequency of the source across diode.
Such a circuit would cause any real diode to explode due to lack of any current limiting and the resulting high power dissipation in the diode.
Hence "Theoretical". That's kind of what "Theoretical" means.
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The effect of diode voltage drop as the output voltage is that the input voltage will not be totally transferred to the output because power loss in the diode . The output voltage will then be given by: vout=(vin)-(the diode voltage drop).
It depends on how the diode is damaged. There are generally two cases. One, the diode is shorted, and conducts with a low impedance in both directions. The other, the diode is open, and does not conduct, having a high impedance, in both directions. The effect depends on the particular circuit. In a power supply, a shorted diode will often blow the fuse, while an open diode will result in no output, or in high ripple voltage output. Is it possible that diode has normal voltage output but wrong current,meaning low mA?
A free wheeling diode is used to suppress or eliminate flyback. In ULN2803, the free wheeling diode protects the output.
The output degrades to a half-wave rectifier.
sharp reverse breakdown function