An auxiliary circuit for outputting a supplying voltage or a detection signal includes a normally-on device and a signal processing circuit. A drain terminal of the normally-on switching device is coupled to a first terminal, a gate terminal of the normally-on switching device is coupled to a second terminal. An input voltage between the first terminal and the second terminal switches between two different levels. The signal processing circuit is configured to output the supplying voltage or the detection signal according to a voltage at a source terminal of the normally-on switching device.