Design 6 V Zener regulator, regulation factor

Given: Vz = 6 V at Iz = 20 mA, Izk = 2 mA, Pzmax = 500 mW, rz = 20 Ω. Vin = 12 V ± 20 % → Vin(min) = 9.6 V, Vin(max) = 14.4 V.

Circuit

 Vin o----[ R ]-----+------+----o Vo ≈ 6 V
                    |      |
                  (Dz)    [RL]
                    |      |
                   GND    GND

Zener model

Vz0 = Vz − rz Iz = 6 − 20 × 0.02 = 5.6 V. So Vz(Iz) = 5.6 + 20 Iz.

Maximum Zener current and R

Pz = Vz0 Iz + rz Iz² = 0.5 W → 20 Iz² + 5.6 Iz − 0.5 = 0 → Iz(max) = 71.2 mA (Vz = 7.02 V).

Worst case for the Zener power: Vin(max) with no load:

R ≥ (14.4 − 7.02)/71.2 mA = 103.6 Ω → choose the standard value R = 110 Ω

Maximum load current

At Vin(min), the Zener must stay at the knee current Izk = 2 mA (Vz = 5.6 + 0.04 = 5.64 V):

IR = (9.6 − 5.64)/110 = 36 mA

IL(max) = IR − Izk = 36 − 2 = 34 mA (RL(min) ≈ 5.64/34 mA = 166 Ω)

Voltage regulation factors

Line regulation: ΔVo/ΔVin = rz/(R + rz) = 20/(110 + 20) = 0.154 V/V = 154 mV/V. For the full input swing of 4.8 V (9.6 V to 14.4 V), Vo changes by about 0.74 V. At no load: Vo = 6.2 V at 9.6 V; 6.95 V at 14.4 V; and 6.58 V at 12 V nominal. In percent: line regulation ≈ 0.154 × 100/6.6 = 2.3 % per volt of input change.

Load regulation: ΔVo/ΔIL = −(rz ∥ R) = −(20 × 110/130) = −16.9 Ω (−16.9 mV per mA). For the full load swing of 34 mA, Vo falls by about 0.57 V.

Note: because the Zener current at the design point differs from 20 mA, Vo is about 6.6 V and not exactly 6 V; to obtain exactly 6 V the Zener current should be set at 20 mA (R about 300 Ω at no load), but then IL(max) falls.

Answer: R = 110 Ω; IL(max) = 34 mA; line regulation 154 mV/V; load regulation −16.9 mV/mA.