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A direct current (DC) electrical charge of some 9 to 48 volts that is sent along a microphone cable to energize the transducer is known as phantom power. The phrase “phantom power” is a result of the fact that there is no visible means of conductivity, no extra electrical line running from the DC power source to the microphone nor is the added DC voltage noticeable in the audio path. In other words, phantom power does its job of essentially powering the microphone invisibly and without interfering with the alternating current (AC) used for the actual audio reproduction and traveling in the same cable.
Phantom power essentially energizes the diaphragm and capacitors inside a condenser microphone, also known as a capacitor microphone. Condenser microphones are today considered the microphone of choice for quality audio reproduction but require a DC power source for proper functioning. Power sources for this DC voltage include a mixing desk, a battery or a power box. Phantom power energizes the transducer element inside the microphone, thereby polarizing the transducer’s diaphragm and capacitor to essentially turn sound waves into electrical impulses. The energized element captures the audio input, ordinarily a voice or instrument, and returns the audio signal as alternating current (AC) to the preamp in the mixing desk. The electrically reproduced audio signal is undisturbed by the phantom power and is able to be amplified and/or recorded without distortion.
The audio signal produced by a condenser microphone is considered alternating current to be transferred from electrical energy into sound at the mixing desk. This AC current, however, is neither designed nor utilized to energize the condenser microphone’s transducer. That’s where phantom power comes in, to subtly power the audio reproduction elements within the microphone itself.
This is accomplished, in part, by using a direct injection (DI) box. The DI box allows the DC voltage to be carried along a lengthy electrical line or wire and to overcome the impedance, the resistance, inherent in the wire length. Using a three-pin XLR plug, two of the pins send both AC and DC electrical current along the microphone cable to the transducer. The DC current powers the capacitor and the AC current carries the audio signal and is returned via the two pins within the plug. The third pin in the XLR plug is the ground. Thus the DI box allows a single, long microphone wire to conduct, with little resistance, both phantom power and AC current through the XLR plug and cable to energize and polarize the microphone’s diaphragm and capacitor.
A DI has nothing to do with Phantom (Unless it is a unit that generates its own).
DI boxes convert a Hi-Z signal (ie a guitar) to a Lo-Z signal (like a microphone). They use either electronic circuitry or a passive impedance matching transformer to do this.
You have two half working explanations in there but the combination of the two make little sense.