Abstract: This paper introduces the thermal design of a brushless motor controller for electric bicycles. This includes an introduction to the controller's working principle, calculation of MOSFET power loss, analysis of the thermal model, calculation of steady-state temperature rise, selection of thermally conductive materials, and thermal simulation. Keywords: Electric bicycle controller, MOSFET, thermal design 1. Introduction Power MOSFETs have been widely used in electric bicycle controllers due to their advantages such as low drive current and fast switching speed. However, improper design and use can frequently damage MOSFETs. Once damaged, the drain and source of the MOSFET short-circuit, and the wafer is usually severely burned. Most users cannot accurately analyze the cause of MOSFET damage. Therefore, reliability design of MOSFETs is crucial during the design phase. Common MOSFET failure modes include overcurrent, overvoltage, avalanche breakdown, and exceeding the safe operating area. Ultimately, these failures are caused by excessively high wafer temperatures, making thermal design extremely important when designing a controller. The MOSFET junction temperature must be calculated to ensure that the MOSFET junction temperature does not exceed its maximum allowable value during operation. 2. Introduction to Brushless Motor Controllers Brushless motors, due to their advantages such as high torque, long lifespan, and low noise, have been widely used in various fields. Their working principle is also well-known and will not be detailed here. Domestic electric vehicle motor controllers typically operate in a three-phase, six-step configuration. The power stage schematic is shown in Figure 1, where Q1 and Q2 are the upper and lower transistors of phase A; Q3 and Q4 are the upper and lower transistors of phase B; and Q5 and Q6 are the upper and lower transistors of phase C. All MOSFETs use AOT430. The MOSFETs operate in a pairwise conduction mode, with the conduction sequence being Q1Q4→Q1Q6→Q3Q6→Q3Q2→Q5Q2→Q5Q4→Q1Q4. The controller output is achieved by adjusting the PWM pulse width of the upper bridge, with the PWM frequency generally set to 18kHz or higher. When the motor and controller operate in one phase (assuming Q3 on phase B and Q6 on phase C), there are two operating states in each PWM cycle: State 1: Q3 and Q6 are on, and current I1 flows to ground through Q3, motor coil L, Q6, and current sensing resistor Rs. State 2: Q3 is off, Q6 is on, and current I2 flows through motor coil L, Q6, and Q4. This state is called freewheeling state. In State 2, if Q4 is on, the controller is in synchronous rectification mode. If Q4 is off, I2 flows through the body diode of Q4, which is called asynchronous rectification mode. The sum of the currents I1 and I2 flowing through motor coil L is called the controller phase current, and the average current I1 flowing through the current sensing resistor Rs is called the controller line current. Therefore, the controller phase current is larger than the controller line current. 3. Power Consumption Calculation The power loss of the controller MOSFET increases with the increase of motor load. When the motor is stalled, the MOSFET loss of the controller reaches its maximum (assuming the controller is at full output). For ease of analysis, we assume that when the motor is stalled, the upper transistor of phase B operates in PWM mode, the lower transistor of phase C is always on, and the lower transistor of phase B operates in synchronous rectification mode (see Figure 1). The waveforms when the motor is stalled are shown in Figures 2-5. The power loss is calculated as follows: 3.1 Power loss of the upper B-phase tube: 3.1.1 Turn-on loss of the upper B-phase tube (t1-t2), see Figure 2; 3.1.2 Turn-off loss of the upper B-phase tube (t3-t4), see Figure 3; 3.1.3 Conduction loss of the upper B-phase tube (t5-t6), see Figure 4; Total loss of the upper B-phase tube: Phs(Bphase) = Phs(turn on) + Phs(turn off) + Phs(on) = 5.1 + 3.75 + 7.5 = 16.35W 3.2 Power loss of the lower B-phase tube: 3.2.1 Freewheel loss of the lower B-phase tube (t7-t8), see Figure 5; PLS(Bphase) = PLS(freewheel) = I2 × Rds(on) × (1-D) = 402 × 0.015 × (1-20/64) = 16.5 W 3.3 The power loss of the lower C-phase transistor is calculated as follows because the lower C-phase transistor is always on: PLS(Cphase) = PLS(on) = I² × Rds(on) = 40² × 0.015 = 24 W. The total power loss of the controller is: Ptatal = PHS(Bphase) + PLS(Bphase) + PLS(Cphase) = 16.35 + 16.5 + 24 = 56.85 W. 4. Thermal Model Figure 5 shows the typical installation structure and thermal model of TO-220. Thermal resistance is similar to electrical resistance, so we can consider Rth(ja) as several small resistors connected in series, resulting in the following formula: Rth(ja) = Rth(jc) + Rth(ch) + Rth(ha) Where: Rth(jc) — Thermal resistance from the junction to the MOSFET surface Rth(ch) — Thermal resistance from the MOSFET surface to the heat sink Rth(ha) — Thermal resistance from the heat sink to the environment (related to the heat sink mounting method) Figure 6 Thermal resistance model Generally, heat flows from the junction to the heat sink via conduction, and from the heat sink to the environment via conduction and convection. Rth(jc) is determined by the device, so for a system, if the MOSFET is fixed, to obtain a smaller thermal resistance, we can choose a better thermally conductive material and mount the MOSFET well on the heat sink. 5. Calculation of Steady-State Temperature Rise From the AOT430 datasheet, we can obtain the following parameters: Tjmax = 175℃ Rth(jc)max = 0.56 ℃/W 5.1 Calculation of Temperature Rise from MOSFET Junction to its Surface During Motor Operation (Because the upper and lower transistors only operate for one-third of the time during motor operation, the average power should be divided by 3): 5.1.1 Steady-State Temperature Rise from Upper Transistor Junction to Power Transistor Surface 5.1.2 Steady-State Temperature Rise from Lower Transistor Junction to Power Transistor Surface 5.2 Calculation of Temperature Rise from MOSFET Junction to its Surface When the Motor is Stalled 5.2.1 Steady-State Temperature Rise from Phase B Upper Transistor Junction to Power Transistor Surface Tjc = Tj - Tc = Phs × Rth(jc) = 16.35 × 0.56 = 9.2℃ 5.2.2 The steady-state temperature rise from the junction of the lower MOSFET in phase B to the surface of the power transistor is Tjc = Tj - Tc = PLS × Rth(jc) = 16.5 × 0.56 = 9.24℃. 5.2.3 The steady-state temperature rise from the junction of the lower MOSFET in phase C to the surface of the power transistor is Tjc = Tj - Tc = PLS(Cphase) × Rth(jc) = 24 × 0.56 = 13.44℃. From the above calculations, it can be seen that the temperature rise of the MOSFET (lower MOSFET) that is always conducting in the controller is the largest when the motor is stalled. Therefore, the MOSFET temperature rise during motor stall should be a key consideration in the design. 6. Selecting a suitable thermal conductive material Figure 7 shows the thermal conductivity curves of the SilPad series thermal conductive materials for the TO-220 package as a function of pressure. Figure 7 6.1 When the thermal conductive material is SilPad-400 and the pressure is 200psi, its thermal resistance Rth(ch) is 4.64 ℃/W. Therefore: Tch = Tc - Th = PLS × Rth(ch) = 24 × 4.64 = 111℃ 6.2 The thermally conductive material is SilPad-900S. At a pressure of 200psi, its thermal resistance Rth(ch) is 2.25℃/W. Therefore: Tch = Tc - Th = PLS × Rth(ch) = 24 × 2.25 = 54℃ It can be seen that different thermally conductive materials have a significant impact on temperature rise. To reduce the junction temperature rise of the MOSFET, we can choose a better thermally conductive material to obtain better thermal conductivity, thereby achieving our design goals. To make the controller more reliable, we usually control the MOSFET surface temperature below 100℃. This is because other high-energy pulses may occur during use, such as short circuits in motor phase lines or sudden increases in load. 7. Thermal Simulation: Since it is difficult to determine the thermal resistance from the heat sink surface to the environment in practical applications, it is difficult to perform thermal design entirely through calculation. Therefore, we can use thermal simulation software to perform simulations to achieve our design objectives. Simulation conditions: Ptotal = 56.85W, Ta = 45℃, controller heatsink size: 70mm × 110mm × 30mm, natural air cooling, MOSFET installation as shown in Figure 8. Figure 8 MOSFET Installation Diagram 7.1 Thermal Simulation of the Controller During Motor Operation As shown in Figure 9, the temperature rise of the lower MOSFET is significantly higher than that of the upper MOSFET. 7.2 Thermal Simulation of the Controller During Motor Stall As shown in Figure 10, the lower MOSFET, which is continuously conducting during stall, is the hottest, with a temperature approaching 150℃. As shown in Figure 11, the MOSFET temperature rise has not stabilized after 100 seconds of stall. If stall continues, the MOSFET will inevitably burn out. Therefore, if the heatsink size in the simulation is used, stalling cannot be continuous; appropriate protective measures must be taken. We can use a gap protection method, that is, when the motor stalls, stall for a period of time, then protect for a period of time, ensuring that the MOSFET temperature does not exceed the maximum junction temperature. Figure 12 shows a transient temperature rise diagram for 1.5s stall and 1.5s protection. As shown in the figure, this method can effectively protect the MOSFET. Figure 10: Temperature rise diagram during stall. Conclusion: Thermal design of the controller is very important in the product design stage. We must calculate the temperature rise through power consumption calculation, thermal model analysis, thermal simulation, etc. At the same time, the most severe application environment should be considered during the design. Finally, the correctness of our thermal design should be verified through actual test.