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TPS7A88: Alternative solution for TPS7A8801 for the better thermal

Part Number: TPS7A88
Other Parts Discussed in Thread: TPS7A85, TPS74401

Hi team, 

Customer is going to design TPS7A8801 for 5.5Vin and 3.3Vout with 0.6Aload. For a simple calculation :

(5.5-3.3)*0.6 = 1.32W

Tj = 85 + RθJA * 1.32 = 85 + 33*1.32 = 128.9 degC (The customer system usually has a temperature of 85 degC)

The recommended junction temperature range is -40 to 125 degC so I guess TPS7A8801 is not a proper device for this application. Even though I suggest that customer uses other device with the higher current rating such as TPS74401 and TPS7A85, the thermal problem would be same or worse because RθJA of TPS7A8801 is lower than others. 

This power rail is for powering clock device so they need to use LDO. Could you advise any solution for this application.