The present invention provides a high peak current, low duty cycle, pulse type transformer with two methods of increasing the coupling coefficient between the primary and secondary windings. The first method provides an increased coupling coefficient for a pulse type transformer of a coreless design by increasing the number of secondary turns in proximity to a number of primary turns by providing multiple primary windings and multiple secondary windings configured in layers or winding bays in an alternating secondary, primary, secondary, primary configuration. The second method provides an increased coupling coefficient for a pulse type transformer with a magnetic core that utilizes a non-uniform cross-sectional area along the magnetic path where the cross-sectional area is increased within the primary and secondary windings. Both methods significantly increase the coupling coefficient in applications where the transformer is subjected to high peak current applications such as capacitive discharge circuits typically used in strobe circuits, electric fence controllers, and high performance ignition systems for automobile, motorcycle, or marine engines.