AC polarity inversion

AC polarity inversion, also known as AC phase inversion, is the swapping of the two poles of an alternating current (AC) source. A polarity inversion is neither a time shift nor a phase shift, but simply a swap of plus and minus.
For example, in a push–pull power amplifier using vacuum tubes, the signal is most often "split" by a phase splitter (aka phase inverter) stage which produces two signals, one "in phase", and the other "out of phase", that is, phase inverted. These two complementary signals then drive the two halves of the first push–pull stage, which may be either the output stage or the driver stage. The other common arrangements for driving a push-pull stage are by using an isolation transformer to produce the split signals, or by using the in-phase half of the first push-pull stage to drive the other half. A common circuit using this last technique is the long-tailed pair, often seen in television sets and oscilloscopes. 
In solid-state electronics all of these techniques can be used, and phase inversion can also be produced by the use of NPN/PNP complementary circuitry, which has no corresponding technique in vacuum tube designs. 
Polarity inversion may occur with a random or periodic, symmetrical or non-symmetrical waveform, although it is usually produced by the inversion of a symmetrical periodic signal, resulting in a change in sign. 
A symmetrical periodic signal represented by formula_1, after polarity inversion, becomes formula_2
where: