FRANKFURT — The German chip maker Dialog Semiconductor has agreed to buy Atmel, an American rival, for about $4.6 billion, adding to a wave of deal-making in the sector as firms seek alternatives to saturated mobile phone markets.

Dialog said on Sunday that the deal would diversify its client base in automotive markets as well as in network-connected chips used in industrial gear.

The company said that Atmel shareholders would receive $4.65 in cash and 0.112 of a Dialog Semiconductor American depository share for each Atmel common share, equivalent to $10.42 per Atmel share based on Dialog’s closing price on Friday.

Shares in Dialog closed at 45.325 euros apiece on Friday, while Atmel shares closed at $7.27.

Dialog said it planned to pay for the deal with cash, $2.1 billion of debt and about 49 million Dialog American depository shares. After the transaction, Atmel shareholders will own about 38 percent of the combined group, Dialog said.