If you are looking for a low drop voltage regulator that is able to provide a power supply of 1A with an output voltage of between 5V and 20V DC, National Semiconductor LM2941 Low Dropout adjustable Regulator is one that you can choose to use.
It has a typical dropout voltage of 0.5V which means that the input supply need only have to be 0.5V DC more than the desired output voltage. Its other features include internal short circuit current limit and reverse battery protection.
As shown in the schematic below, the regulator has 5 pins which consists of the ON/OFF control, Input Voltage, Output Voltage, Ground and Adjustable pins. ON/OFF is used for the purpose of switching on and off of the regulator. The capacitors C1 and E1 are to be placed as close as possible to the regulator.
The output of the circuit can be varied by varying the value of potentiometer VR1 from 5V DC to 20V DC. The input voltage is limited from 5.5V DC to 30V DC. Resistor R1 must be greater than 1K. The value of the VR1 that needs to be set is calculated from the formula given below:
VR1 = R1[(Vout/1.275) - 1] ohm
If R1=1K, Vout = 5V, VR1 should be set to 2.9K ohm.
If R1=1K, Vout = 20V, VR1 should be set to 14.7K ohm