Hi Guys, thanks for your replies.
Here's the link to the RT8059 datasheet
http://www.richtek.com/assets/product_file/RT8059/DS8059-05.pdf
Here's the schematic of the constructed circuit
**broken link removed**
Here's a picture of the breadboard circuit
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Here's a picture of the copper stripboard circuit
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The circuit feedback network resistors are R1 = 1M ohm; and R2 = 200k ohm.
From the formula in the datasheet, this should give an output voltage of 3.6V.
I have an LED and 100 ohm resistor in series as the load (basic 5mm indicator LED, forward voltage ~2.4V)
The circuit is powered by an 18650 li-ion battery, which I've measured regularly and it has a stable output.
I've been using a digital multimeter to measure the output voltage from the circuit. The output voltage typically starts at 1.4V and drops steadily at a rate of approximately 100mV per second. The voltage sporadically rises and falls, without settling at a stable level. I've noticed that touching the ground wire with my finger causes the output voltage to rise significantly.
Spec, I suspect as you said, that the type of components and their layout are the important factor for stability - the datasheet discusses this, however, I don't have the ability to make a PCB with the appropriate layout! Any suggestions about how to construct the circuit with the components in the required layout but without a custom made PCB?
Ronsimpson, I am in Dublin, Ireland.
Thanks again guys.