The present invention uses two transistors instead of a sensing resistor to provide a constant current source for a load such as an array of light emitting diodes ("LEDs"). In the present invention, a bias current is applied to a branch of the circuit. The drain-to-source voltages of two transistors are matched. The voltage at the gate of both transistors is controlled based on the bias current and the drain-to-source current of the first of the two transistors. The second of the two transistors is sized such that source current of the second transistor is a multiple of the source current of the first transistor for a given gate voltage. By the techniques of this invention, the load current in a circuit is efficiently kept constant at a multiple of the input bias current.