Input Capacitor and Over Voltage Protection Circuit Design. Application Note

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1 AN13 Input Capacitor and Over-Voltage Protection Circuit Design Input Capacitor and Over Voltage Protection Circuit Design Application Note Prepared by Leo Zhang and Hongqiang Qin February 018 AN13 Rev. 1.1 MonolithicPower.com 1 9/18/018 MPS Proprietary Information. Patent Protected. Unauthorized Photocopy and Duplication Prohibited. 018 MPS. All Rights Reserved.

2 AN13 INPU CAPACIOR AND OVER-VOLAGE PROECION CIRCUI DESIGN ABLE OF CONENS ABSRAC... 3 WHY MECHANICAL ENERGY IS RECYCLED O HE INPU RAIL... 3 DESIGN PROCEDURE... 4 DESIGN SUMMARY... 6 APPENDIX 1: DEAILED DERIVAION OF INPU CAPACIANCE CALCULAION... 7 APPENDIX : OVER-VOLAGE PROECION CIRCUI DESIGN DEAILS... 9 AN13 Rev. 1.1 MonolithicPower.com 9/18/018 MPS Proprietary Information. Patent Protected. Unauthorized Photocopy and Duplication Prohibited. 018 MPS. All Rights Reserved.

3 AN13 INPU CAPACIOR AND OVER-VOLAGE PROECION CIRCUI DESIGN ABSRAC In a motor control system, the mechanical energy may be recycled back into the DC input rail during periods when the motor speed decreases. In real applications, it is necessary to add enough input capacitance to absorb this energy. A DC over-voltage protection (OVP circuit may also be required. his application note describes how to choose the input capacitor value and how to design the OVP circuit. WHY MECHANICAL ENERGY IS RECYCLED O HE INPU RAIL When the motor speed is decreasing, the controller may generate a negative torque to slow the speed of the motor. he motor now works as a generator, which converts mechanical energy into electrical energy. his energy is recycled back into the DC input rail. Figure 1 shows the control system model. e b L Figure 1: Motor Control System Model From the model above, we can get the electrical torque using Equation (1: d b J (1 dt e L Where e is the electrical torque generated by the motor, ω is the angular speed of the motor, J is the inertia of the rotor and load, b is the friction ratio, and L is the load torque. In most cases, b is a very small value and can be disregarded. he electrical torque can be expressed with Equation (: d e J L ( dt From the sign of e, we can determine whether or not mechanical energy has been converted to electrical energy. If e < 0, mechanical energy is recycled back to the DC input rail. If e > 0, no mechanical energy is recycled. Figure : Energy Recycling during Motor Speed Decrease AN13 Rev. 1.1 MonolithicPower.com 3 9/18/018 MPS Proprietary Information. Patent Protected. Unauthorized Photocopy and Duplication Prohibited. 018 MPS. All Rights Reserved.

4 AN13 INPU CAPACIOR AND OVER-VOLAGE PROECION CIRCUI DESIGN As Figure shows, the recycled electrical energy charges the input capacitor. If there is insufficient capacitance on the DC input rail, a high-voltage spike occurs and may damage the power stage. If it is not practical to fit enough capacitance on the input rail, an OVP circuit can also be used to discharge the energy and limit the input rail voltage. DESIGN PROCEDURE he energy recycled back into the DC input rail is related to many factors, such as the rate of speed deceleration, the mechanical load, and the motor characteristic parameters. o simplify the calculation, assume that the motor deceleration speed is constant (see Figure 3. Figure 3: Motor Speed Curve During the deceleration period, the motor speed starts to decrease from rpm 1 at time t 1 and becomes rpm at time t. he angular speed at t 1 can be calculated with Equation (3: rpm1 1 rad s (3 60 he angular speed at t can be calculated with Equation (4: rpm rad s (4 60 he angular acceleration can be calculated with Equation (5: d 1 (5 dt t t 1 Input Capacitance Calculation From Equation (, the electrical torque can be expressed as Equation (6: d e J L J L (6 dt he power consumption from the input bus can be expressed with Equation (7: P in Pe PR Pe e ( J L P 3I R R rms s (7 AN13 Rev. 1.1 MonolithicPower.com 4 9/18/018 MPS Proprietary Information. Patent Protected. Unauthorized Photocopy and Duplication Prohibited. 018 MPS. All Rights Reserved.

5 AN13 INPU CAPACIOR AND OVER-VOLAGE PROECION CIRCUI DESIGN Where P in is the input power from the DC rail, P R is the power of the motor winding resistor, and I rms is the RMS value of the winding phase current. During speed deceleration, P e becomes negative and the motor works as a generator. he energy is charged back to the input rail as shown in Equation (8: t t t in L rms s M L R (8 E P dt ( J 3 I R dt= ( P P P dt Where P M is the mechanical power change during speed deceleration, P L is power consumed by the mechanical load, and P R is the power consumed by the winding resistors. Supposing at t x, when P M - P L - P R = 0, the energy charged back reaches the maximum value. he input DC bus maximum voltage (V max at t x can be calculated with Equation (9: tx 1 Emax Pindt Cin ( Vmax Vnom (9 Where V max is the maximum voltage value of the input bus, and V nom is the nominal voltage value of the input bus. For easy calculation, it is suggested to use an MPS spreadsheet tool to calculate how much input capacitance is needed with a given maximum allowed voltage. Please contact an MPS FAE for this spreadsheet. he detailed derivation is shown in Appendix 1. Over-Voltage Protection (OVP Circuit Design If the input capacitor value cannot be as large as the value calculated above due to space or other limitations, it is necessary to add an OVP circuit at the DC rail input. You can use a comparator to detect when the DC bus voltage increases. When the DC input voltage is above the required clamping voltage value (V clamp, a comparator outputs high logic, which can be used to turn on a MOSFE to clamp the input voltage (see Figure 4. Figure 4: Protection Circuit Using a Comparator When the voltage is larger than V clamp, the MOSFE turns on, and current flows through the resistor to discharge excess energy. he bleeding resistor design guidelines are shown below. Resistor value limitation: A resistance value too large causes the peak DC voltage to exceed the allowed clamping voltage. For most cases, a resistor with several ohms to tens of ohms is sufficient. hermal limitation: A power-rating resistor too small makes the resistor too hot when absorbing energy. For most cases, a resistor with few watts power rating is enough to handle the energy. Please see Appendix for the calculation details of how to design this circuit. AN13 Rev. 1.1 MonolithicPower.com 5 9/18/018 MPS Proprietary Information. Patent Protected. Unauthorized Photocopy and Duplication Prohibited. 018 MPS. All Rights Reserved.

6 AN13 INPU CAPACIOR AND OVER-VOLAGE PROECION CIRCUI DESIGN DESIGN SUMMARY he energy recycled back into the DC rail causes a voltage spike. It is necessary to add enough input capacitance to absorb this energy. If it is impossible to add enough capacitance, add a voltage clamping circuit at the DC input rail. Following the design procedures described in this application note should help you understand the principles of how to choose the input capacitor value and how to design the protection circuit correctly. You can also use an MPS spreadsheet tool to calculate the required values quickly. Please contact an MPS FAE for this spreadsheet. AN13 Rev. 1.1 MonolithicPower.com 6 9/18/018 MPS Proprietary Information. Patent Protected. Unauthorized Photocopy and Duplication Prohibited. 018 MPS. All Rights Reserved.

7 AN13 INPU CAPACIOR AND OVER-VOLAGE PROECION CIRCUI DESIGN APPENDIX 1: DEAILED DERIVAION OF INPU CAPACIANCE CALCULAION he power recycled from the mechanical side can be calculated with Equation (10: E t t t ( Pe PR dt ( e PR dt ( J L 3 I rms Rs dt (10 he motor electrical torque ( e provided by the motor can be calculated with Equation (11 and Equation (1: e C I C I (11 peak rms J (1 e L Where C (N*m/A is the torque constant of motor. he energy back to DC input rail can be expressed with Equation (13: E( t t t ( P P dt e If P e > P R, energy is recycled back and stored in the input capacitor. Figure 4 shows an E(t vs. t plot. R J J L 3 ( Rs dt (13 C P ( t P ( t e R Figure 5: Energy Recycled Back against Lasting ime E(t reaches the maximum value at t x when P e(t = P R(t, t x and ω x are shown in Equation (14 and Equation (15: Rs J tx (14 C 1 /( J x 1 L t (15 he maximum energy generated by the inertia load can be calculated with Equation (16: x 1 EM J( 1 x (16 AN13 Rev. 1.1 MonolithicPower.com 7 9/18/018 MPS Proprietary Information. Patent Protected. Unauthorized Photocopy and Duplication Prohibited. 018 MPS. All Rights Reserved.

8 AN13 INPU CAPACIOR AND OVER-VOLAGE PROECION CIRCUI DESIGN he energy consumed by the load torque can be calculated with Equation (17: ( 1 x EL L tx (17 he energy consumed on the winding resistance can be calculated with Equation (18: E L I 3( peak R t s x J L 1.5 Rs ( C Given the maximum allowed input voltage (V max, the input capacitance can be calculated with Equation (19: ( EM EL ER Cin (19 V V max nom t x (18 AN13 Rev. 1.1 MonolithicPower.com 8 9/18/018 MPS Proprietary Information. Patent Protected. Unauthorized Photocopy and Duplication Prohibited. 018 MPS. All Rights Reserved.

9 AN13 INPU CAPACIOR AND OVER-VOLAGE PROECION CIRCUI DESIGN APPENDIX : OVER-VOLAGE PROECION CIRCUI DESIGN DEAILS If the input capacitor value cannot be as large as the calculated value due to space or other limitations, a smaller capacitor value should be used. However, this means that when energy is recycled into the DC input rail, the peak voltage may exceed the allowed maximum voltage. herefore, an OVP circuit must be added at the DC rail input. A comparator over-voltage detection circuit can be used to implement a protection circuit with a bleed resistor (see Figure 6. ref R bleed Figure 6: Protection Circuit Using a Comparator When the voltage is larger than V clamp, the MOSFE turns on, and current flows through the resistor to discharge excess energy. he voltage on the capacitor is latched at V clamp. he energy stored on the capacitor at V clamp can be calculated with Equation (0: 1 EC Cbus ( Vclamp Vnom (0 Where C bus is the input capacitor value. When the OVP circuit is active, set the angle speed and time (ω bleed, t bleed with Equation (1: t t (1 bleed 1 1 he mechanical energy change can be calculated with Equation (: 1 EM J 1 bleed ( he energy consumed by the load torque can be calculated with Equation (3: 1 bleed EL L tbleed (3 he energy consumed on the winding resistor can be calculated with Equation (4: bleed E 3R I t t (4 R s rms 1 bleed he protection circuit starts to work when Equation (5 is satisfied: Ebleed EM EL ER EC 0 (5 ω bleed and t bleed can be calculated from Equations 0-5. AN13 Rev. 1.1 MonolithicPower.com 9 9/18/018 MPS Proprietary Information. Patent Protected. Unauthorized Photocopy and Duplication Prohibited. 018 MPS. All Rights Reserved.

10 AN13 INPU CAPACIOR AND OVER-VOLAGE PROECION CIRCUI DESIGN he power that the resistor must dissipate can be calculated with Equation (6: P P P 3R I (6 bleed e R e s rms Where P bleed is at its maximum when ω = ω bleed and can be calculated with Equation (7: P R I (7 bleed _max e bleed 3 s rms Bleed Resistor Selection he maximum power dissipated is P bleed_max. he maximum bleed resistor value can be calculated with Equation (8: Pbleed _max Rmax (8 V Select the bleed resistor R < R max. he total energy to be discharge can be calculated with Equation (9: clamp E E E (9 total C _max C he average power can be calculated with Equation (30: P avg E t t Ensure that the resistor can handle the pulsed power. total bleed (30 Bleed MOSFE Selection he peak current can be calculated with Equation (31: V clamp he peak voltage of the MOSFE should be larger than V clamp. I (31 R NOICE: he information in this document is subject to change without notice. Users should warrant and guarantee that third party Intellectual Property rights are not infringed upon when integrating MPS products into any application. MPS will not assume any legal responsibility for any said applications. AN13 Rev. 1.1 MonolithicPower.com 10 9/18/018 MPS Proprietary Information. Patent Protected. Unauthorized Photocopy and Duplication Prohibited. 018 MPS. All Rights Reserved.

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