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Zener

Example Iz = 31.36 mA — Pz = 160 mW (zener) — PR = 216.4 mW (resistor)

$I_z=\frac{V_{\mathrm{in}}-V_z}{R}-I_{\mathrm{load}}$ — the zener must stay reverse-biased with Iz > 0 to regulate.

LM317

R1 sets the reference current path (OUT to ADJ); R2 sets how much extra voltage is added on top of the 1.25 V reference. Iadj (a few tens of µA) is ignored here, as it usually is for a first-pass estimate.

Example Vout = 5 V — headroom (Vin − Vout) = 7 V

$V_{\mathrm{out}}=1.25\text{V}\times (1+\frac{R_2}{R_1})$

The 1.25 V reference sits between OUT and ADJ; R1 is usually a fixed 220–240 Ω.

Example Nearest E24: R1=240 Ω, R2=750 Ω → Vout = 5.156 V (+3.1%)