Communications Satellite Corp. announced plans yesterday to acquire Amplica Inc., a California microwave equipment company, for $57 million. The deal, if approved by Amplica stockholders, would be the largest takeover in Comsat history.

The merger already has been approved by Amplica's board of directors and principal stockholders and could be completed as soon as Jan. 1. Comsat paid $13.50 in cash apiece for the company's outstanding stock, which closed Friday on the over-the-counter market at 12 1/2 bid, 13 asked.

In a brief announcement, the company said the deal is still subject to "certain conditions" such as the approval of the remaining stockholders.

The company, which is based in Newbury Park, Calif., just outside Los Angeles, specializes in manufacturing microwave amplifiers, which are attached to earth stations to punch up signals received from satellites.

"One immediate reason for our interest stems from our interest in direct broadcasting," Comsat President Joseph Charyk said yesterday. The company's chief executive said Amplica-produced equipment that could be used in Comsat's proposal, now before the Federal Communications Commission, to beam television directly to homes via satellite.

Charyk said in an interview that the purchase also was based on Amplica's "impressive growth and performance" record. "The kind of position this company has established in the marketplace makes it an attractive acquisition," Charyk said.

Amplica's performance has improved steadily over the past several years, with revenues rising from $3.7 million in 1978 to $6.3 million in 1979. Last year sales climbed to $9.2 million, and in the first six months of this year the company reported sales of $6.2 million. Profits have risen from $225,000 in 1978 to $844,000 last year and to $732,000 for the first half of 1981.

Until yesterday's announcement, Comsat's largest purchase had been the 1978 buy-out of Environmental Research & Technology Inc., a cash deal of just under $20 million. Comsat also made two smaller acquisitions.