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I've been looking at the LM78xx.

schematic

simulate this circuit – Schematic created using CircuitLab

The notes state:

enter image description here

So, input and output must be referenced to ground. C1 removes power line noise/ ripple and C0 improves switching stability.

Why was .33uF selected for the input capacitor and .1uF selected for the output capacitor?

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  • \$\begingroup\$ In short, voltage regulators are analog devices and those values minimize the instability of the regulator circuit. \$\endgroup\$ – Ignacio Vazquez-Abrams May 2 '16 at 23:50
  • \$\begingroup\$ @IgnacioVazquez-Abrams But the real question is why such specific values are used on the capacitors? I believe that some range of values are acceptable. \$\endgroup\$ – Bradman175 May 3 '16 at 1:51
  • \$\begingroup\$ Probably because they were most convenient, most modern regulators will run fine with just about any capacitor (within reason) \$\endgroup\$ – Sam May 3 '16 at 7:39
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Strongly related: Capacitor Sizes for 7805 Regulator

Anyway, these values are actually not critical, especially for these kind of regulators (linear regulators made out of a NPN transistor). Those can be made stable with almost any input/output capacitor values, or even no capacitors at all. Those values have been suggested in the datasheet because they provide a good compromise between cost/size and stability/noise immunity for a large range of output current. Just trust the guys that settled on those values.

Note that for LDO (low dropout) type of regulators, however, the capacitor values are more critical, because the stability of those regulators depend on the capacitor values (mainly the output capacitor). In this case, it is clearly indicated in the datasheet, sometimes with a graph indicating the stable region (with capacitance vs output current). In addition to the capacitor value, the capacitor ESR can also be relevant for LDO stability.

A link that provide informative data regarding capacitor roles in regulators (and for all kind of regulators): http://www.ti.com.cn/cn/lit/wp/snoa842/snoa842.pdf

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