Fairchild Industries Inc. yesterday offered to purchase shares of Bunker Ramo Corp. valued at $56.1 million, in a transaction that would increase the Germantown-based company's holdings of the Illinois firm to 45 percent.

The offer, presented in a proposal to Bunker Ramo's Board of Directors, will not be considered until the board meets on Oct. 30, a company spokesman said.

Fairchild already owns more than 20 percent of the Bunker Ramo stock. Bunker Ramo, based in Oak Brook, Ill., is principally a producer of electrical connectors, information systems, and deep pile fabrics.

The Fairchild offer proposes a cash purchase of 1.7 million shares of preferred and common stock at $33 per share. Bunker Ramo opened trading on the New York Stock Exchange yesterday at $29 3/4 a share, before temporarily closing.

But the offer is contingent on the lifting of an agreement between the two companies, which bars Fairchild from further purchases of Bunker Ramo stock until Jan., 1982, unless the deal is approved by the Bunker Ramo board.

In January, Fairchild spent $27.4 million to purchase a block of Bunker Ramo from the Martin Marietta Corp. of Bethesda, which gave the company a 20.6 percent share of Bunker Ramo's outstanding shares.

But in June, Bunker Ramo's directors rejected a Fairchild offer to purchase the balance of its outstanding shares for $96 million in cash and stocks, called the offer "inadequate."

The Fairchild efforts reflect the company's interest in broadening its business base. Bunker Ramo has been a particularly successful venture in recent years, earning record sales of $18.8 million on sales of $383 million last year.

Fairchild upped its offer from the spring, when the company proposed a $28 a share purchase of the stock, although at the time Bunker Ramo was trading at 27 3/8 a share.

The two companies have historic links, since Bunker Ramo was founded in 1964 by George M. Bunker, a retired chairman of Martin Marietta.