About

A capacitive (transformerless) power supply uses a series-connected film capacitor to drop mains AC voltage to a lower DC level without a transformer. The capacitor's reactance X_c limits current flow, replacing the bulky iron-core transformer in low-power applications. Miscalculating the dropping capacitor C₁ by even 10nF can push load current outside safe bounds, overheat the zener clamp, or cause capacitor rupture under surge. This calculator solves the reactance equation for the required X-rated (safety-class) capacitor value, computes bleeder and surge-limiting resistor ratings, estimates ripple voltage, and outputs a complete bill of materials with proper voltage derating. It assumes resistive or near-resistive loads and single-phase mains. Results approximate real-world behavior under steady-state conditions. Transient inrush at switch-on and capacitor aging effects are noted but not fully modeled.

Formulas

The capacitive reactance at mains frequency determines current delivery capability:

X_c = 12πfC

The RMS current delivered through the dropping capacitor, assuming V_mains ≫ V_out:

I_RMS ≈ V_mainsX_c ≈ 2πfCV_mains

Solving for the required capacitance given a desired load current:

C = I_load2πf ⋅ V_mains

This simplified form is valid when V_out << V_mains. The exact form uses:

C = I_load2πf ⋅ √V_mains² − V_out²

Zener power dissipation is estimated as:

P_zener = V_zener × (I_RMS − I_load)

Peak inrush current at switch-on:

I_surge = V_peakR_surge = V_mains × √2R_surge

Where: f = mains frequency in Hz, C = dropping capacitor in F, V_mains = RMS mains voltage, V_out = regulated DC output voltage, I_load = desired DC load current, R_surge = surge limiting resistor in Ω.

Reference Data

Parameter	Typical Value	Notes
Mains Voltage (EU)	230 V_RMS	Peak: 325 V
Mains Voltage (US)	120 V_RMS	Peak: 170 V
Mains Voltage (JP)	100 V_RMS	Peak: 141 V
Mains Frequency (EU/Asia)	50 Hz	Standard grid
Mains Frequency (US/JP)	60 Hz	Standard grid
X2 Capacitor Rating	275 V_AC	Minimum for 230V mains
X1 Capacitor Rating	440 V_AC	Enhanced impulse withstand
Bleeder Resistor	1 MΩ	Discharge within 1s
Surge Resistor	47 - 100 Ω	Limits inrush; 0.5 - 2W
Max Practical Load	50 - 100 mA	Above this, use a transformer
Zener Derating	60%	Max continuous power ≤ 60% of rated
Capacitor Tolerance (Film)	±10%	Polyester/Polypropylene typical
Safety Standard (IEC)	IEC 60384-14	X/Y safety capacitor classes
E6 Cap Values (nF)	100, 150, 220, 330, 470, 680	Common X2-rated film caps
E6 Cap Values (μF)	1.0, 1.5, 2.2, 3.3	Larger X2-rated film caps
Common Zener Voltages	3.3, 5.1, 6.8, 9.1, 12, 15, 24 V	Standard E24 zener series
Bridge Rectifier Drop	1.4 V	2 diode drops typical
Peak Inrush (worst case)	V_peak ÷ R_surge	Occurs at voltage peak switch-on

Frequently Asked Questions

X-rated capacitors (X1, X2 per IEC 60384-14) are designed to fail open-circuit, preventing fire if the capacitor degrades. A standard polyester or ceramic capacitor can fail short-circuit under mains transients, creating a direct short across the mains. X2 capacitors are rated for 275 VAC continuous with impulse withstand of 2.5 kV. Never substitute with electrolytics or non-safety-rated types.

Practical limit is approximately 50-100 mA. At higher currents, the required dropping capacitor becomes physically large (several µF X2-rated), the zener dissipation becomes excessive, and efficiency drops below 5%. For loads above 100 mA, a switch-mode power supply or transformer-based design is safer and more efficient.

Capacitive reactance is inversely proportional to frequency: X_c = 1 ÷ (2πfC). At 60 Hz, the same capacitor delivers 20% more current than at 50 Hz. If you design for a 50 Hz grid and deploy on 60 Hz, the zener will see excess current and may overheat.

After the supply is disconnected from mains, the X-rated capacitor retains charge at mains-peak voltage (up to 325 V for 230 V mains). A 1 MΩ bleeder resistor discharges a 1 µF capacitor to safe levels (below 60 V) within approximately 1 second. Without it, touching the plug pins after disconnection risks lethal shock. IEC 60065 requires discharge to below 60 V within 1 second.

The surge resistor limits peak inrush current when the circuit is switched on at mains voltage peak. A 100 Ω resistor limits inrush to 3.25 A on a 230 V mains (325 V peak). Smaller values (47 Ω) allow faster capacitor charging but higher surge. The resistor must be rated for pulse energy, typically 0.5-2 W wirewound or metal oxide type.

Only with additional regulation and filtering. The output has significant ripple (proportional to load current divided by filter capacitor value) and no galvanic isolation from mains. A 78xx linear regulator after the zener clamp improves regulation. However, any fault in the circuit exposes the load to mains potential. For safety-critical applications, use an isolated supply.

The full capacitor-limited current flows through the zener diode. The zener must be rated to dissipate P = V_zener × I_RMS continuously. If the zener is undersized, it will overheat and fail short, potentially causing the fuse or capacitor to blow. Always size the zener for full no-load dissipation.