Capacitive Transformerless Power Supply Calculator

A capacitive power supply uses the reactance of an AC-coupling capacitor to drop line voltage rather than a traditional wire-wound transformer. The primary reactive impedance of the capacitor limits the available alternating current based on the supply frequency. The core formulas implemented in this calculator are:

Input Current: I_in = (&rad5;2 × V_rms - V_z) / ((1 / (π × f × C)) + 2R)

Output Voltage: V_out = V_z - V_d

Where V_rms is the root-mean-square supply voltage, V_z is the Zener diode clamp voltage, f is frequency, C is capacitance, R is resistance, and V_d is any subsequent forward voltage drop.

Let's walk through a practical design scenario. Suppose you want to power a low-drain microcontroller circuit from a standard AC mains supply.

Given Parameters:

• RMS Voltage (V_rms): 120 V
• Frequency (f): 60 Hz
• Capacitance (C_1): 1.0 μF (0.000001 F)
• Resistance (R_1): 100 Ω
• Zener Voltage (V_z): 12 V
• Diode Voltage Drop (V_d): 0.7 V

Step-by-Step Calculation:

1. Calculate capacitive reactance: X_c = 1 / (π × 60 × 0.000001) ≈ 2652.58 Ω.
2. Calculate total impedance including resistance: Z_total = 2652.58 + (2 × 100) = 2852.58 Ω.
3. Calculate peak input voltage: &rad5;2 × 120 V ≈ 169.71 V.
4. Compute input current: I_in = (169.71 - 12) / 2852.58 ≈ 0.0553 A (or 55.3 mA).
5. Compute regulated output voltage: V_out = 12 V - 0.7 V = 11.3 V.

Never Touch Circuit Components: Transformerless power supplies are directly connected to high-voltage AC mains. There is no galvanic isolation, posing a severe electric shock hazard. Always enclose your final build in an insulated, non-conductive casing.

Include a Safety Discharge Resistor: Always place a high-value bleed resistor in parallel with the dropping capacitor. This safely discharges the capacitor when the unit is unplugged, preventing nasty residual shocks.

Keep Current Draw Low: These circuits are strictly meant for low-current applications (typically under 50mA to 100mA). Drawing higher currents requires dangerously large capacitors and oversized Zener diodes that dissipate excessive heat.