How do you calculate hold-up time for an SMPS?
3 Answers
The hold-up time in a Switch Mode Power Supply (SMPS) is the duration that the power supply can maintain its output voltage within specified limits after the input power is lost or drops below a certain threshold. It is an important parameter for ensuring that sensitive electronic devices remain operational during brief interruptions in power.
### Steps to Calculate Hold-Up Time
1. **Determine Output Voltage and Load Current**:
- Identify the nominal output voltage (\(V_{out}\)) and the load current (\(I_{load}\)) drawn by the connected load.
2. **Calculate Output Capacitor Value**:
- The hold-up time (\(t_{hold}\)) can be influenced by the output capacitance (\(C_{out}\)). Larger capacitance will result in longer hold-up time. The required capacitance can be calculated based on the output voltage variation.
3. **Voltage Variation**:
- Decide the allowable voltage drop (\(ΔV\)) during hold-up time. This is typically defined by the specifications of the connected load.
4. **Use the Formula**:
- The hold-up time can be calculated using the formula:
\[
t_{hold} = \frac{C_{out} \cdot ΔV}{I_{load}}
\]
Where:
- \(t_{hold}\) = Hold-up time (in seconds)
- \(C_{out}\) = Output capacitance (in Farads)
- \(ΔV\) = Allowable output voltage drop (in Volts)
- \(I_{load}\) = Load current (in Amperes)
### Example Calculation
- If you have:
- \(C_{out} = 1000 \mu F = 1000 \times 10^{-6} F\)
- \(ΔV = 5 V\)
- \(I_{load} = 1 A\)
- Substitute the values into the formula:
\[
t_{hold} = \frac{(1000 \times 10^{-6} F) \cdot (5 V)}{1 A} = 0.005 s = 5 ms
\]
This means the SMPS can maintain the output voltage for approximately 5 milliseconds after the input power is lost, given the specified conditions.
### Considerations
- Ensure that the output capacitance is rated for the voltage levels in your application.
- The hold-up time will vary depending on the actual load current and the characteristics of the load.
This calculation provides a theoretical estimate; actual performance may vary based on other factors like temperature, capacitor aging, and the behavior of the load during the hold-up period.
### Steps to Calculate Hold-Up Time
1. **Determine Output Voltage and Load Current**:
- Identify the nominal output voltage (\(V_{out}\)) and the load current (\(I_{load}\)) drawn by the connected load.
2. **Calculate Output Capacitor Value**:
- The hold-up time (\(t_{hold}\)) can be influenced by the output capacitance (\(C_{out}\)). Larger capacitance will result in longer hold-up time. The required capacitance can be calculated based on the output voltage variation.
3. **Voltage Variation**:
- Decide the allowable voltage drop (\(ΔV\)) during hold-up time. This is typically defined by the specifications of the connected load.
4. **Use the Formula**:
- The hold-up time can be calculated using the formula:
\[
t_{hold} = \frac{C_{out} \cdot ΔV}{I_{load}}
\]
Where:
- \(t_{hold}\) = Hold-up time (in seconds)
- \(C_{out}\) = Output capacitance (in Farads)
- \(ΔV\) = Allowable output voltage drop (in Volts)
- \(I_{load}\) = Load current (in Amperes)
### Example Calculation
- If you have:
- \(C_{out} = 1000 \mu F = 1000 \times 10^{-6} F\)
- \(ΔV = 5 V\)
- \(I_{load} = 1 A\)
- Substitute the values into the formula:
\[
t_{hold} = \frac{(1000 \times 10^{-6} F) \cdot (5 V)}{1 A} = 0.005 s = 5 ms
\]
This means the SMPS can maintain the output voltage for approximately 5 milliseconds after the input power is lost, given the specified conditions.
### Considerations
- Ensure that the output capacitance is rated for the voltage levels in your application.
- The hold-up time will vary depending on the actual load current and the characteristics of the load.
This calculation provides a theoretical estimate; actual performance may vary based on other factors like temperature, capacitor aging, and the behavior of the load during the hold-up period.
The hold-up time in a **Switch Mode Power Supply (SMPS)** refers to the duration for which the power supply can maintain a regulated output voltage after the input power (AC mains) has been interrupted or dropped below a certain threshold. Calculating the hold-up time is important to ensure that the power supply can sustain output long enough during short power interruptions.
### Basic Equation:
The hold-up time is determined by the energy stored in the input bulk capacitor(s) and the power drawn by the load. The main factors involved are:
1. **Energy stored in the capacitor (W)**: \( W = \frac{1}{2} C V_{in}^2 \)
- \( C \) = Capacitance of the bulk capacitor (Farads)
- \( V_{in} \) = Input voltage to the capacitor before interruption (Volts)
2. **Power consumed by the load (P)**: This is the output power of the SMPS which needs to be supported during the hold-up time.
\( P = V_{out} \times I_{out} \)
- \( V_{out} \) = Output voltage of the SMPS
- \( I_{out} \) = Load current
3. **Hold-up time (t)** is determined by the time it takes for the capacitor to discharge from the initial voltage \( V_{in} \) to a lower threshold voltage \( V_{min} \) at which the SMPS can no longer maintain regulation.
### Hold-up Time Formula:
To calculate the hold-up time, use the following formula:
\[
t = \frac{C \times (V_{in}^2 - V_{min}^2)}{2 \times P}
\]
Where:
- \( t \) = Hold-up time (seconds)
- \( C \) = Bulk capacitor value (Farads)
- \( V_{in} \) = Initial capacitor voltage (volts)
- \( V_{min} \) = Minimum voltage the capacitor can discharge to while maintaining regulation (volts)
- \( P \) = Power consumed by the load (Watts)
### Steps to Calculate Hold-up Time:
1. **Determine Input Voltage**: Measure or find out the rectified DC voltage (typically the peak of the AC voltage after rectification) applied to the bulk capacitor. This is \( V_{in} \).
2. **Choose the Minimum Input Voltage \( V_{min} \)**: This is the lowest voltage at which the SMPS can still provide the required output voltage.
3. **Calculate the Power Consumption**: This is typically the output power of the SMPS, but you can also use the rated load current and output voltage to determine the total power.
4. **Capacitance of the Bulk Capacitor**: The value of the bulk capacitor is generally provided in the design of the SMPS. This is typically located at the input stage after rectification and filtering.
5. **Plug into the Formula**: Insert the values into the hold-up time formula to get the result.
### Example Calculation:
Let’s say we have the following parameters for an SMPS:
- Capacitance \( C = 470 \, \mu F \)
- Initial input voltage \( V_{in} = 380 \, V \)
- Minimum input voltage \( V_{min} = 300 \, V \)
- Output power \( P = 150 \, W \)
Using the formula:
\[
t = \frac{470 \times 10^{-6} \, F \times (380^2 - 300^2) \, V^2}{2 \times 150 \, W}
\]
\[
t = \frac{470 \times 10^{-6} \times (144400 - 90000)}{300}
\]
\[
t = \frac{470 \times 10^{-6} \times 54400}{300}
\]
\[
t = \frac{25.568}{300}
\]
\[
t \approx 0.085 \, seconds
\]
So, the hold-up time would be approximately **85 milliseconds**.
### Conclusion:
The hold-up time of an SMPS is crucial in applications where a brief power interruption can cause issues, such as in sensitive electronic equipment. By ensuring adequate hold-up time, the system can remain stable during momentary input power drops.
### Basic Equation:
The hold-up time is determined by the energy stored in the input bulk capacitor(s) and the power drawn by the load. The main factors involved are:
1. **Energy stored in the capacitor (W)**: \( W = \frac{1}{2} C V_{in}^2 \)
- \( C \) = Capacitance of the bulk capacitor (Farads)
- \( V_{in} \) = Input voltage to the capacitor before interruption (Volts)
2. **Power consumed by the load (P)**: This is the output power of the SMPS which needs to be supported during the hold-up time.
\( P = V_{out} \times I_{out} \)
- \( V_{out} \) = Output voltage of the SMPS
- \( I_{out} \) = Load current
3. **Hold-up time (t)** is determined by the time it takes for the capacitor to discharge from the initial voltage \( V_{in} \) to a lower threshold voltage \( V_{min} \) at which the SMPS can no longer maintain regulation.
### Hold-up Time Formula:
To calculate the hold-up time, use the following formula:
\[
t = \frac{C \times (V_{in}^2 - V_{min}^2)}{2 \times P}
\]
Where:
- \( t \) = Hold-up time (seconds)
- \( C \) = Bulk capacitor value (Farads)
- \( V_{in} \) = Initial capacitor voltage (volts)
- \( V_{min} \) = Minimum voltage the capacitor can discharge to while maintaining regulation (volts)
- \( P \) = Power consumed by the load (Watts)
### Steps to Calculate Hold-up Time:
1. **Determine Input Voltage**: Measure or find out the rectified DC voltage (typically the peak of the AC voltage after rectification) applied to the bulk capacitor. This is \( V_{in} \).
2. **Choose the Minimum Input Voltage \( V_{min} \)**: This is the lowest voltage at which the SMPS can still provide the required output voltage.
3. **Calculate the Power Consumption**: This is typically the output power of the SMPS, but you can also use the rated load current and output voltage to determine the total power.
4. **Capacitance of the Bulk Capacitor**: The value of the bulk capacitor is generally provided in the design of the SMPS. This is typically located at the input stage after rectification and filtering.
5. **Plug into the Formula**: Insert the values into the hold-up time formula to get the result.
### Example Calculation:
Let’s say we have the following parameters for an SMPS:
- Capacitance \( C = 470 \, \mu F \)
- Initial input voltage \( V_{in} = 380 \, V \)
- Minimum input voltage \( V_{min} = 300 \, V \)
- Output power \( P = 150 \, W \)
Using the formula:
\[
t = \frac{470 \times 10^{-6} \, F \times (380^2 - 300^2) \, V^2}{2 \times 150 \, W}
\]
\[
t = \frac{470 \times 10^{-6} \times (144400 - 90000)}{300}
\]
\[
t = \frac{470 \times 10^{-6} \times 54400}{300}
\]
\[
t = \frac{25.568}{300}
\]
\[
t \approx 0.085 \, seconds
\]
So, the hold-up time would be approximately **85 milliseconds**.
### Conclusion:
The hold-up time of an SMPS is crucial in applications where a brief power interruption can cause issues, such as in sensitive electronic equipment. By ensuring adequate hold-up time, the system can remain stable during momentary input power drops.
The hold-up time of a Switched-Mode Power Supply (SMPS) refers to the amount of time the power supply can continue to provide the required output power after the input power is interrupted. It's primarily determined by the energy stored in the bulk capacitor(s) on the input side of the power supply.
### Steps to Calculate Hold-Up Time:
1. **Find the total energy stored in the capacitor:**
The energy stored in a capacitor is given by the formula:
\[
E = \frac{1}{2} C V^2
\]
Where:
- \( E \) is the energy in joules (J),
- \( C \) is the capacitance in farads (F),
- \( V \) is the voltage across the capacitor in volts (V).
2. **Determine the minimum operational input voltage:**
The minimum voltage at which the power supply can still operate, denoted as \( V_{\text{min}} \), is crucial in this calculation.
3. **Calculate the available energy:**
The usable energy stored in the capacitor is the difference in energy between the full voltage and the minimum operating voltage. This is given by:
\[
E_{\text{usable}} = \frac{1}{2} C (V_{\text{input}}^2 - V_{\text{min}}^2)
\]
Where:
- \( V_{\text{input}} \) is the normal input voltage (before the interruption),
- \( V_{\text{min}} \) is the minimum input voltage at which the SMPS can operate.
4. **Determine the output power:**
Let \( P_{\text{out}} \) be the power consumed by the load at the output of the SMPS. This should be in watts (W).
5. **Calculate hold-up time:**
Finally, the hold-up time \( t_{\text{hold-up}} \) is calculated by dividing the available energy by the output power:
\[
t_{\text{hold-up}} = \frac{E_{\text{usable}}}{P_{\text{out}}}
\]
This gives the time in seconds (s) that the SMPS can continue to supply power after input power is lost.
### Example Calculation:
Suppose we have:
- Input capacitor \( C = 470 \, \mu F \),
- Input voltage \( V_{\text{input}} = 400 \, V \),
- Minimum operational voltage \( V_{\text{min}} = 300 \, V \),
- Output power \( P_{\text{out}} = 100 \, W \).
Using the formula:
1. Calculate the usable energy:
\[
E_{\text{usable}} = \frac{1}{2} \times 470 \times 10^{-6} \times (400^2 - 300^2)
\]
2. Divide the usable energy by the output power to get the hold-up time.
By plugging in the values, you can get the exact hold-up time in seconds. Would you like me to calculate this example for you?
### Steps to Calculate Hold-Up Time:
1. **Find the total energy stored in the capacitor:**
The energy stored in a capacitor is given by the formula:
\[
E = \frac{1}{2} C V^2
\]
Where:
- \( E \) is the energy in joules (J),
- \( C \) is the capacitance in farads (F),
- \( V \) is the voltage across the capacitor in volts (V).
2. **Determine the minimum operational input voltage:**
The minimum voltage at which the power supply can still operate, denoted as \( V_{\text{min}} \), is crucial in this calculation.
3. **Calculate the available energy:**
The usable energy stored in the capacitor is the difference in energy between the full voltage and the minimum operating voltage. This is given by:
\[
E_{\text{usable}} = \frac{1}{2} C (V_{\text{input}}^2 - V_{\text{min}}^2)
\]
Where:
- \( V_{\text{input}} \) is the normal input voltage (before the interruption),
- \( V_{\text{min}} \) is the minimum input voltage at which the SMPS can operate.
4. **Determine the output power:**
Let \( P_{\text{out}} \) be the power consumed by the load at the output of the SMPS. This should be in watts (W).
5. **Calculate hold-up time:**
Finally, the hold-up time \( t_{\text{hold-up}} \) is calculated by dividing the available energy by the output power:
\[
t_{\text{hold-up}} = \frac{E_{\text{usable}}}{P_{\text{out}}}
\]
This gives the time in seconds (s) that the SMPS can continue to supply power after input power is lost.
### Example Calculation:
Suppose we have:
- Input capacitor \( C = 470 \, \mu F \),
- Input voltage \( V_{\text{input}} = 400 \, V \),
- Minimum operational voltage \( V_{\text{min}} = 300 \, V \),
- Output power \( P_{\text{out}} = 100 \, W \).
Using the formula:
1. Calculate the usable energy:
\[
E_{\text{usable}} = \frac{1}{2} \times 470 \times 10^{-6} \times (400^2 - 300^2)
\]
2. Divide the usable energy by the output power to get the hold-up time.
By plugging in the values, you can get the exact hold-up time in seconds. Would you like me to calculate this example for you?