Question

How do you calculate hold-up time for an SMPS?

Answer 1

Calculating the hold-up time for a Switched-Mode Power Supply (SMPS) involves determining how long the SMPS can continue to provide power after the input power is lost, typically due to a power failure or disconnect.

Hold-up time is primarily influenced by the energy stored in the filter capacitors (typically in the output stage) and the power being drawn by the load. Here's how you can calculate it:

1. Understand the Formula for Hold-up Time

The hold-up time can be roughly estimated by the following formula:

\[
T_{hold-up} = \frac{C \cdot V_{cap} \cdot \ln\left(\frac{V_{cap}}{V_{min}}\right)}{P_{load}}
\]

Where:

1. \( T_{hold-up} \) = Hold-up time (in seconds)
   

1. \( C \) = Output capacitance (in Farads)
   

1. \( V_{cap} \) = Initial voltage across the capacitor (typically the output voltage of the SMPS)
   

1. \( V_{min} \) = Minimum voltage that the SMPS can tolerate to keep the output voltage regulation
   

1. \( P_{load} \) = Power consumed by the load (in Watts)
   

1. \( \ln \) = Natural logarithm (ln)
   

2. Breakdown of the Parameters

1. Capacitance (C): This is the value of the output capacitor, which stores the energy needed to maintain the output voltage when the input is lost.
   

  

1. Capacitor Voltage (V_cap): The voltage across the capacitor when the power is turned off. This is typically the nominal output voltage of the SMPS, such as 12V, 24V, etc.
   

1. Minimum Voltage (V_min): This is the lowest output voltage the SMPS can still operate with before it shuts down or cannot maintain proper regulation.
   

1. Load Power (P_load): This is the amount of power the connected load consumes, in watts. The higher the load power, the quicker the capacitor will discharge, reducing the hold-up time.
   

3. Calculation Example

Let's go through a simple example.

1. Assume the SMPS has a 12V output and uses a 4700µF capacitor.
   

1. The minimum voltage the SMPS can tolerate for proper operation is 9V.
   

1. The load is consuming 24W.
   

Now, plug these values into the formula.

1. Convert the capacitance to Farads:
   

   \[
   4700\ \mu F = 4700 \times 10^{-6}\ F = 0.0047\ F
   \]

1. The formula becomes:
   

   \[
   T_{hold-up} = \frac{0.0047 \times 12 \times \ln\left(\frac{12}{9}\right)}{24}
   \]

1. Calculate the logarithmic term:
   

   \[
   \ln\left(\frac{12}{9}\right) = \ln(1.3333) \approx 0.2877
   \]

1. Now, calculate the hold-up time:
   

   \[
   T_{hold-up} = \frac{0.0047 \times 12 \times 0.2877}{24}
   \]
   \[
   T_{hold-up} \approx 0.000739\ \text{seconds}
   \]

In this case, the hold-up time would be approximately 0.74 milliseconds.

4. Adjust for Practical Considerations

In practice, the actual hold-up time might be slightly different due to factors such as:

1. Load variations (constant load vs dynamic load).
   

1. Efficiency of the SMPS.
   

1. Temperature effects on the capacitor and components.
   

  
For higher accuracy, you would ideally simulate the power supply behavior with a detailed circuit model or measure the hold-up time using an oscilloscope under real conditions.

Final Thoughts

This approach gives you a basic estimation of the hold-up time, but keep in mind that the real-world performance of an SMPS might depend on various additional factors like capacitor quality, efficiency, and load characteristics.