Capacitive Transformerless Power Supply Calculator

Capacitive Transformerless Power Supply Formula

RMS Input Voltage (\( V_{RMS} \)):

Zener Voltage (\( V_z \)):

Frequency (\( f \)):

Capacitance (\( C_1 \)):

Resistance (\( R_1 \)):

Forward Bias Voltage of Second Diode (\( V_d \)):

Input Current (\( I_{in} \)):

Output Voltage (\( V_{out} \)):

1. What is Capacitive Transformerless Power Supply Calculator?

Definition: This calculator computes the input current and output voltage for a capacitive transformerless power supply, which converts high AC input voltage to low DC voltage using a voltage divider circuit with a capacitor.

Purpose: It is used in electronics to design transformerless power supplies for low-power applications, such as LED drivers or small electronic devices, ensuring proper current and voltage levels.

2. How Does the Calculator Work?

The calculator uses the following formulas:

\( I_{in} = \frac{\sqrt{2} \cdot V_{RMS} - V_z}{2/(2 \pi f C_1 )+ 2 R_1} \)

\( V_{out} = V_z - V_d \)

Where:

\( I_{in} \): Input current (A)
\( V_{RMS} \): RMS value of the input AC voltage (V)
\( V_z \): Zener voltage (regulated DC output voltage, V)
\( f \): Frequency of the AC input voltage (Hz)
\( C_1 \): Capacitance of the voltage-dropping capacitor (F)
\( R_1 \): Resistance (Ω)
\( V_{out} \): Output voltage (V)
\( V_d \): Forward bias voltage of the second diode (V)

Steps:

Enter the RMS input voltage (\( V_{RMS} \)) with its unit (V, mV, kV).
Enter the Zener voltage (\( V_z \)) with its unit (V, mV, kV).
Enter the frequency (\( f \)) with its unit (Hz, kHz, MHz).
Enter the capacitance (\( C_1 \)) with its unit (F, mF, µF).
Enter the resistance (\( R_1 \)) with its unit (Ω, kΩ, MΩ).
Enter the forward bias voltage of the second diode (\( V_d \)) with its unit (V, mV, kV).
Convert all inputs to base units (V, Hz, F, Ω).
Calculate the input current and output voltage using the formulas.
Convert the results to the selected output units.
Display the results with 4 decimal places.

3. Importance of Capacitive Transformerless Power Supply Calculation

Calculating these parameters is crucial for:

Electronics Design: Ensuring the power supply delivers the correct DC voltage and current for the load.
Safety: Properly sizing components to handle the input current and voltage, avoiding overheating or failure.
Efficiency: Optimizing the circuit for minimal power loss in low-power applications.

4. Using the Calculator

Example: A capacitive transformerless power supply with an RMS input voltage of 230 V, a Zener voltage of 5 V, a frequency of 50 Hz, a capacitance of 1 µF, a resistance of 100 Ω, and a forward bias voltage of 0.7 V:

RMS Input Voltage (\( V_{RMS} \)): 230 V
Zener Voltage (\( V_z \)): 5 V
Frequency (\( f \)): 50 Hz
Capacitance (\( C_1 \)): 1 µF = \( 1 \times 10^{-6} \) F
Resistance (\( R_1 \)): 100 Ω
Forward Bias Voltage (\( V_d \)): 0.7 V
Input Current (\( I_{in} \)): \( \frac{\sqrt{2} \times 230 - 5}{2 \pi \times 50 \times 10^{-6} + 2 \times 100} \approx \frac{325.2691 - 5}{0.0003142 + 200} \approx 1.6010 \) A
Output Voltage (\( V_{out} \)): \( 5 - 0.7 = 4.3 \) V
Result: \( I_{in} = 1.6010 \) A (or 1601.0000 mA), \( V_{out} = 4.3000 \) V

5. Frequently Asked Questions (FAQ)

Q: What is a capacitive transformerless power supply?
A: It is a circuit that converts high AC voltage to low DC voltage using a voltage-dropping capacitor and a Zener diode, without a bulky transformer, often used in low-power applications.

Q: Why is the output voltage less than the Zener voltage?
A: The output voltage is reduced by the forward bias voltage (\( V_d \)) of the second diode, as per the formula \( V_{out} = V_z - V_d \).

Q: What is the role of the capacitor in this circuit?
A: The capacitor (\( C_1 \)) acts as a voltage-dropping element, limiting the current and reducing the high AC voltage to a lower level before rectification.