EXHIBIT 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

The Board of Directors

Power Integrations, Inc.:

We consent to the incorporation by reference in the registration statements on Forms S-8 (Nos. 333-122370, 333-119015, 333-112135, 333-102676, 333-42194, 333-56381, 333-69871, 333-83083, 333-59564, and 333-86270) of Power Integrations, Inc. of our reports dated March 15, 2005, with respect to the consolidated balance sheets of Power Integrations, Inc. as of December 31, 2004 and 2003, and the related consolidated statements of income, stockholders’ equity, and cash flows for each of the years in the three-year period ended December 31, 2004, and the related financial statement schedule, management’s assessment of the effectiveness of internal control over financial reporting as of December 31, 2004, and the effectiveness of internal control over financial reporting as of December 31, 2004, which reports appear in the December 31, 2004 annual report on Form 10-K of Power Integrations, Inc.

/s/    KPMG LLP

Mountain View, California

March 15, 2004