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Zener regulator output voltage and minimum RL

Short answer

Using Zener model Vz0=6.7V, rz=20Ω, the no-load output voltage is 6.83V. The minimum load resistance to stay in breakdown is 1.53kΩ when the supply drops to 9V.

Given Vz = 6.8 V at Iz = 5mA, rz= 20 ohms and Vs = 10 ± 1 V, Rs = 500 ohms and Izk = 0.2mA. Determine the output Voltage of Zener voltage regulator without load. Find the minimum value of load resistance such that the Zener diode operates in Zener breakdown region.

Given: Vz = 6.8 V at Iz = 5 mA, rz = 20 Ω, Izk = 0.2 mA, Vs = 10 ± 1 V, Rs = 500 Ω.

Zener model

Vz0 = Vz − rz Iz = 6.8 − 0.1 = 6.7 V (Zener = 6.7 V source in series with 20 Ω)

(a) Output voltage without load (Vs = 10 V)

I = (10 − 6.7)/(500 + 20) = 6.346 mA

Vo = 6.7 + 20 × 6.346 mA = 6.83 V

For Vs = 9 V: Vo = 6.7 + 20 × 4.423 mA = 6.79 V; for Vs = 11 V: Vo = 6.87 V. So a ±1 V supply change changes Vo by only ±40 mV (±0.04 V).

(b) Minimum load resistance to stay in breakdown

At the limit, Iz = Izk = 0.2 mA, and Vo = 6.7 + 20 × 0.0002 = 6.704 V.

Worst case is the lowest supply, Vs = 9 V:

Is = (9 − 6.704)/500 = 4.592 mA

IL = Is − Izk = 4.592 − 0.2 = 4.392 mA

RLmin = 6.704 V / 4.392 mA = 1.53 kΩ

(At the nominal 10 V supply, Is = 6.592 mA, IL = 6.392 mA, and RLmin = 1.05 kΩ.)

Answer: Vo (no load) = 6.83 V; RLmin ≈ 1.5 kΩ (worst case, Vs = 9 V).

✓ Answer checked by Claude Opus 5.5 (high effort)

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