Making LM317 output voltage adjustable down to 0 V
To get the LM317 down to zero volts you need to bring the control pin down to -1.25 V.



Figure 1. This dual LM317 circuit consists of a current limiter based around LM317(1) and a voltage regulator based around LM317(2). The voltage regulator section is relevant to this post as it is adjustable down to zero volts. Source: ON-Semi datasheet.


The control pin of LM317(2) is pulled low by Q2 which is wired as a simple constant current sink pulling several milliamps from the adjust pin.
D3 and D4 clamp the top of Q2 at two diode drops (2 x 0.7 V) below zero (-1.4 V).
The 240 \$\Omega\$ resistor and 5k pot can then adjust from zero up to the supply limit.


The problem with this circuit is that you need to generate a negative supply capable of sinking the few milliamps. My answer to Smartest way to use current limit using LM317? (where I explained the current limiting section) may help in this regard.







simulate this circuit &ndash; Schematic created using CircuitLab

Figure 2. If a centre-tapped transformer is used the negative rail can be generated quite easily. In this example a half-wave rectified signal is smoothed by C2 which doesn't have to be very large.