A linear RF transmitter (100) includes a forward path including a baseband signal combiner (109) and an RF (radio frequency) power amplifier (123), and a linearizing control loop from an output (127) of the RF power amplifier to an input of the combiner (109). A feedback control path (105, 107) of the loop delivers a baseband error control signal to the combiner. The transmitter further includes a test signal generator (102) to apply to the combiner in a closed loop level training mode a test signal comprising a voltage Vin which increases with time in a non-linear manner approaching an asymptotic limit such that in response an output signal produced by the combiner is a voltage Ve which is substantially constant over a period of time.