Design Example: Automobile Ignition System

An inductor opposes rapid changes in current by creating a collapsing magnetic field. When the ignition switch opens abruptly, this rapidly collapsing magnetic field generates a high voltage across the inductor. This voltage amplification allows a 12-volt car battery to produce the 24 kilovolts needed to create a spark across the spark plug's air gap, igniting the fuel-air mixture.

A spark plug consists of two electrodes separated by an air gap. When high voltage is applied between these electrodes, a spark forms across the gap, igniting the fuel-air mixture in the engine cylinder. The spark persists until all energy stored in the inductor is exhausted in the spark discharge, ensuring reliable engine combustion.

An inductor's voltage is proportional to the rate of current change. When the ignition switch is closed and current rises steadily through the spark coil, it eventually stabilizes at a constant level. At this steady state, the rate of current change becomes zero, making the inductor voltage zero as well.

The final steady-state current through a spark coil is determined by dividing the battery voltage by the coil's resistance. For a 12-volt battery and a known coil resistance, this ratio yields the maximum current the coil can sustain. This calculation is essential for designing an ignition system that operates reliably with a small car battery.

Energy stored in inductors is released when the switch opens and the magnetic field collapses rapidly. This stored energy is discharged across the spark plug's air gap, creating the high voltage needed to ignite fuel. In the design example, the spark coil stores 57.6 millijoules, which generates 24 kilovolts at the spark gap during a 2-microsecond switch opening.

The charging time for a spark coil depends on its inductance and resistance values. In the design example with a 20-millihenry coil and a 12-volt supply, the coil reaches full charge in 20 milliseconds. This charging period allows current to rise steadily until it stabilizes, preparing the system to generate a spark when the switch opens.

The voltage across the spark gap is determined by the inductor's voltage relationship and the rate of current change during switch opening. When a 20-millihenry spark coil with steady-state current collapses in 2 microseconds, it generates approximately 24 kilovolts across the air gap. This high voltage is sufficient to ionize the air and create the spark that ignites the fuel-air mixture.