Introduction:
A three-phase series inverter is a type of voltage source inverter that converts DC power into three-phase AC power. It consists of six power electronic switches, typically insulated gate bipolar transistors (IGBTs) or MOSFETs, which are controlled to generate the desired output waveform. The circuit configuration of a three-phase series inverter is such that the output frequency is determined by the firing frequency of the switches.

Explanation:
The firing frequency of a three-phase series inverter refers to the rate at which the switches are turned on and off to create the desired output waveform. This frequency determines the number of times the output waveform repeats within a given time period, which is typically measured in hertz (Hz).

Relationship between Firing Frequency and Output Frequency:
The firing frequency of a three-phase series inverter is directly related to the output frequency of the AC waveform it produces. The output frequency is determined by the number of times the switches are fired within one complete cycle of the output waveform.

Three-Phase AC Waveform:
A three-phase AC waveform consists of three separate sinusoidal waveforms, each with a phase difference of 120 degrees. In one complete cycle of the waveform, each of the three phases goes through one positive and one negative half-cycle. Therefore, the total number of half-cycles in one complete cycle is six.

Firing Frequency and Switching Pattern:
To generate a three-phase AC waveform, the switches in the series inverter are fired in a specific pattern. Each switch is turned on and off at a particular time, depending on the desired output waveform. This switching pattern repeats every half-cycle of the output waveform.

Relationship between Firing Frequency and Output Frequency:
Since there are six half-cycles in one complete cycle of a three-phase AC waveform, the switches in the series inverter must be fired six times within one complete cycle. Therefore, the firing frequency of the switches is six times the output frequency of the AC waveform.

Conclusion:
In a three-phase series inverter, the firing frequency is six times the output frequency. This relationship is based on the fact that there are six half-cycles in one complete cycle of a three-phase AC waveform. By controlling the firing frequency, the inverter can generate the desired output frequency and waveform.