Optimal digital power control using LLC resonant converters
April 30, 2012 | Bilal Akin and Daniel Chang | 222904514
Bilal Akin, PhD and Daniel Chang of Texas Instruments Incorporated (TI) describe a digital power control implementation using line level control (LLC) resonant converters based on a flexible, 32-bit, low-cost, high-performance microcontroller. Key elements of digital power control are explored; including duty cycle control, dead-band adjustment in real time, frequency control, and adaptive thresholds for maintaining different safe operation regionsWith the availability of new low-cost, high-performance microcontrollers (MCUs), the benefits of digital power control can be introduced to a wide range of embedded, industrial and control applications. Traditional analog systems are susceptible to factors such as drift, aging of components, variations caused by temperature and component tolerance degrading. Developers are also limited to classical control implementations. In addition, analog-based systems offer little flexibility to accommodate different environmental operating conditions or even simple changes in system requirements.
When designed using a digital approach, portions of the power system can be implemented in software, resulting in a level of flexibility that enables a single architecture to provide optimal performance across a range of applications and operating conditions. With software-based control algorithms, developers can:
- Ensure precise and predictable system behavior through configuration – both in the factory and at power up – to adjust for component tolerance issues
- Improve efficiency through the use of advanced algorithms (i.e., non-linear, multi-variable, etc.), which are not feasible to implement in analog-based systems
- Maintain performance over an extended system lifetime through dynamic recalibration
- Support multiple systems with a single controller
- Increase system reliability through self-diagnostics
- Enable intelligent management through a communications link
- Simplify system design by allowing developers to work with model tools and C rather than having to rework analog designs with every requirement change
- Reduce system cost by supporting other system functions on the same MCU
Tuning of the voltage compensator using coefficients during an active load will show the flexibility of the implementation, and the use of programmable soft start/stop capabilities and slew rate control will demonstrate how to avoid inrush current and reduce audible noise. Finally, developers will learn how hybrid burst mode control dramatically increases light-load and stand-by efficiency.
Digital control with microcontrollers
Consider the right MCU to provide all of the necessary performance and peripherals needed to control a system with a single stand-alone controller. MCUs with ample headroom and specialized peripherals will enable developers to implement more advanced control algorithms to further improve performance while lowering system cost.
Few microcontrollers have an architecture optimized for digital control applications with advanced architectural features to enhance high-speed signal processing. The main CPU core needs built-in DSP capabilities such as a single cycle 32 x 32-bit multiply and accumulate (MAC) unit to greatly speed processing of computations. Integrated control peripherals, such as the analog-to-digital converter (ADC) and PWMs, are designed to be very flexible and easily adapt to almost any use with very little software overhead. For example, the ADC has a programmable auto-sequencer that cycles through samples in a specific order so that values are ready when the application needs them. With more intelligent control peripherals and a powerful CPU core, control loops run tighter, both improving the dynamic nature of control algorithms and resulting in better disturbance behavior.
Microcontrollers need to provide the significant PWM features needed for real-time digital control including:
- Duty cycle control for soft start-up avoids inrush currents and enables various burst mode configurations to enhance light-load efficiency
- Real-time dead band adjustability guarantees ZVS at all operating points and optimizes efficiency
- Trip-zone and internal comparator options enable instantaneous PWM disabling to ensure system reliability and safety
- High-resolution frequency adjustment capabilities down to 150 ps for precise output voltage regulation
LLC resonant converters
One of the well-known digital power topologies is the resonant convertor. While offering high efficiency and low noise, the most common resonant topologies have several significant limitations. For example, the converter is theoretically incapable of regulating under no- or light-load conditions and wide frequency variation is necessary to regulate the output over full load range. Under light-load conditions, small resonant currents cause a loss of zero voltage switching (ZVS). In addition, re-circulating energy will degrade high line or light-load efficiency.
The LLC resonant topology’s simple structure overcomes the drawbacks of conventional resonant topologies. Advantages of the LLC resonant topology include:
- Full ZVS operation for primary side switches is possible because the magnetizing inductance (Lm) of the transformer is relatively small when compared to an ideal transformer
- High-efficiency and high-power density from no-load to full-load ZVS due to reduced switching losses without degrading output voltage regulation
- Low electromagnetic interference (EMI) and reduced filtering requirements due to ZVS, and switching takes place under conditions of zero drain voltage
- No need for external parallel series inductors because of an integrated transformer. Magnetizing and leakage inductors also serve as a part of the topology
- Reduced turn-off losses since switches are turned off under low-current conditions
- Low-voltage stresses (limited to two times output voltage) and zero current switched (ZCS) operation on the secondary rectifier due to the absence of a secondary filter inductor. In addition, ZCS of secondary diodes removes its reverse recovery problem
Embedded comparators and trip zones within the microcontroller need to provide programmable protection in case of a short circuit, overload, overvoltage, brown-out, etc. In the control software, soft-start/stop capabilities avoid inrush current and reduce audible noise. A programmable soft transient option limits the slew rate while the system follows a given reference voltage level. A smoother startup profile without causing overshoots or high inrush current is achieved through gain adjustment by means of hybrid duty cycle and frequency control. Light-load efficiency is increased by running the system in burst mode, which involves on/off control of the half-bridge pulse width modulators (PWMs). Finally, the additional peripherals on the microcontroller should allow the user to control the synchronous rectifiers.
Click on image to enlarge.
Fig. 1a System-level block diagram of an LLC resonant converter
Click on image to enlarge.
Fig. 1b digital control system
On the secondary side, various combinations of diode circuits or synchronous rectification methods improve the overall efficiency as shown. The microcontroller can be located at the primary or secondary side, depending on application requirements.
The transformer leakage and magnetizing inductances serve as a part of LLC topology to minimize the cost and size. Alternatively, leakage inductance can be implemented externally during prototyping to simplify design and troubleshooting. In addition, the ability to use an external inductor provides flexibility to optimize resonant tank design to address specific manufacturing difficulties and design trade-offs. Some common resonant tank design trade-offs are system efficiency, operating frequency, output accuracy, conversion ratio, conduction vs. switching losses, system frequency resolution, maximum/minimum achievable frequency and variable input-output requirements.
Figure 2 shows single-stage LLC converter control software flow, which is partitioned into two sections: high-speed, high-priority code used for control related algorithms and low-speed, low-priority code used for initialization and background tasks.
The high-speed code is typically written for maximum efficiency in order to enable greater-bandwidth control loops. This code is called using interrupt service routines (ISRs) which are able to interrupt the background tasks when called. For an LLC converter, which operates with variable switching frequency, two ISRs running asynchronously might be used. One ISR would be used to handle the control loop algorithm and called at a fixed frequency to avoid violating sampling and control theory. A second ISR would be used to handle the PWM modules updates and called at the PWM switching frequency (variable) in order to allow simultaneous updates and minimize delay between control loop calculation and update.
The slower background loop is executed in the remaining time interval when no ISRs are active. This is where system tasks such as instrumentation, soft-start, on/off delays, protection mechanisms, active load control and communications are executed. A task state machine has been implemented as part of the background code. Tasks are arranged in groups (A1, A2, A3..., B1, B2, B3..., C1, C2, C3...) and executed according to three CPU timers that are configured with user-defined periods of 1 ms, 5 ms, and 7.5 ms respectively. Tasks are executed in a “round-robin” manner within each group. For example, if group B executes every 5 ms and has 3 tasks, each “B task” will execute once every 15 ms. “Slow” tasks can be written in C, whereas the more time critical resonant converter control algorithm is written in assembly code.
Click on image to enlarge.
Figure 2: LLC resonant converter control software flowchart
SR PWM timing considerations
Synchronous rectifier (SR) current has a positive half-wave sinusoidal shape. Ideal SR timing would have the MOSFET on during non-zero positive current and off at all other times, the same way a diode conducts. This means the SR would turn on at zero current just as current begins and turns off at zero current just as current ends, achieving Zero Current Switching (ZCS).
SR turn on timing can be easily obtained based on primary side switch timing. This is because SR current starts flowing at the beginning of the half period, when the primary side switch turns on. By setting the SR PWM to turn on at the same time or slightly after its corresponding primary side half-bridge PWM, ZCS can be achieved during SR turn on. SR turn off timing is more difficult to obtain. This is because the SR turn off current zero crossing point is variable with frequency. Above the resonant frequency, SR current actually never reaches zero before the end of the half period. In this situation, SR turn off timing is simply at the end of the half period. Even though ZCS is not achieved, this provides the minimum power loss. At the resonant frequency, SR current reaches zero at the end of the half period. In this situation, SR turn off timing is also at the end of the half period, but ZCS can be achieved. Below the resonant frequency, SR current reaches zero before the end of the half period.
This results in three possible scenarios. First, if SR turn off occurs too late, negative current can flow backwards through the SR MOSFET which is undesirable and can lead to component damage. Second, if SR turn off occurs too early, ZCS is not achieved and additional power loss occurs. Third, if SR turn off occurs at the zero crossing point, ZCS is achieved. The third scenario with ZCS is the one desired.
There are many ways to set SR turn off timing. One simple method is to choose a fixed timing (relative to either the beginning or end of the half period) that ensures SR turn off at the ZCS point or earlier for all frequencies, providing some benefits of SR without risk of component damage. A second more advanced method is to adjust the SR turn off timing based on the frequency. This would allow ZCS for all frequencies but, unless the SR turn off timing is updated sufficiently fast, either of the first two scenarios for operation below resonant frequency can occur after sudden shifts in frequency. Both of these methods would also require experimentation to determine the SR turn off timings required for each implementation, which can be time consuming or impractical. A third method is to adjust the SR turn off timing based on the SR current level directly. This would require additional sense circuitry but could simplify development and reduce computational requirements.
Transient state tuning
To keep loop tuning simple and avoid the need for complex mathematics or analysis tools, the number of degrees of freedom have to be considered by remapping them to a more intuitive set of coefficients. For example, working with the five 2P2Z regulator coefficient terms (B0, B1, B2, A1, and A2) can be simplified by remapping these terms to the P, I, and D coefficient gains, each of which can be independently adjusted. This method requires a periodic transient or disturbance to be present and a means to observe the output transient while interactively making adjustments while the built-in active load on the converter board can provide the periodic disturbance (see Figure 3).
Click on image to enlarge.
Figure 3 Active load test, from full-load to no-load transient response tuning with various regulator coefficients
The compensator block has two poles and two zeros and is based on the general infinite impulse response (IIR) filter structure. The transfer function is given by:
The recursive form of the PID controller is given by the difference equation:
And the z-domain transfer function form of this is:
Comparing this with the general form, we can see that the PID is nothing but a special case of CNTL_2P2Z control where A1 = -1 and A2 = 0.
Burst mode operation
When the resonant converter is lightly loaded or not loaded, there will be significant primary current flowing through the transformer's magnetizing inductance to maintain soft switching, thereby introducing losses and significantly reducing light-load efficiency. To overcome this problem, the converter can be run in burst-mode to keep the converter's input consumption to a minimum; when the load falls below a certain value, the program will enter burst mode. Burst mode is a series of switching cycles at a nearly fixed frequency and a duty cycle spaced out by long idle periods where either switches are in OFF-state or duty cycles are set to zero as shown in Figure 4. In this way, the average value of the resonant tank current can be reduced to an almost negligible value. Furthermore, the average switching frequency will be considerably lower, thereby reducing switching losses.
Click on image to enlarge.
Figure 4: Various burst mode implementations
In this implementation, the burst mode on/off decision is based on output ripple. Since the amount of ripple is not critical at no-load, a bandwidth less than 5% of the output voltage can be defined to turn on and off burst mode. In addition, a software subroutine can be added to adjust the on/off period according to system ripple limitations. When Figure 4a is compared to Figure 4b, ON time can significantly be reduced to improve light-load efficiency. The flexible control capabilities of the microcontroller will allow developers to implement burst mode operation in a hybrid manner and adjust the duty cycle as well.
Figure 4c shows a duty cycle limited to 10%. This allows the system to obtain smoother transients, reduce inrush current and lower stress on components. Depending upon the system specifications, developers can select an optimal combination of all these alternatives to obtain the highest light- or no-load efficiency.
In addition to the burst mode, the hybrid approach enables soft-starting of the converter. LLC converters initially tend to draw huge currents that can be controlled by increasing the switching frequency up to three times higher values. By means of a hybrid approach, inrush current can be efficiently suppressed at relatively low switching frequencies.
Many OEMs are turning to digital power control technology to improve system performance and efficiency. Advanced topologies, such as those based on LLC resonant converters, bring many benefits to OEMs and end-users, including lower system cost, better responsiveness, higher reliability, and optimal power efficiency. By using the flexibility of a programmable approach with integrated hardware components, OEMs can quickly and easily customize operation and maximize efficiency across a wider range of operation than is possible with analog-based implementation. The high level of integration of the Piccolo MCU architecture also optimizes overall performance while lowering system cost by integrating complete system functionality on a single chip. OEMs will experience fast return on investment through system-cost optimization, long-term software and tool compatibility, and the ability to leverage the expansive portfolio across all their power control applications.
 Chun-An Cheng, et al. "Efficiency Study for a 150W LLC Resonant Converter" IEEE Power Electronics and Drive Systems, 2009, Taipei.
 B. Yang: Topology Investigation for Front End DC/DC Power Conversion for Distributed Power System, PhD dissertation, Virginia Polytechnic Institute and State University, 2003
 H. Choi: Analysis and Design of LLC Resonant Converter with Integrated Transformer, Applied Power Electronics Conference, APEC 2007 - Twenty Second Annual IEEE Feb. 2007
 Ya Lui, “High Efficiency Optimization of LLC Resonant Converter for Wide Load Range”, Master Thesis, Virginia Polytechnic Institute and State University 2007
Bilal Akin is an Application Engineer with TI's C2000 Embedded Control Group, Texas Instruments Incorporated, Dallas. He received B.S. and M.S. degrees in electrical engineering from Middle East Technical University, Ankara, Turkey, in 2000 and 2003, respectively, and the Ph.D. degree in electrical engineering from Texas A&M University in 2007. From 2005 to 2007, he was an R&D Engineer with Toshiba Industrial Division, Houston, TX. From 2007 to 2008, he was a Postdoctoral Research Associate with Texas A&M University. Bilal's research interests are advanced control methods in motor drives, real-time fault diagnosis of industrial systems, digital power management, and various DSP based industrial applications.
Daniel Chang is an Application Engineer with TI's C2000 Embedded Control Group, Texas Instruments Incorporated, Dallas. He received B.S. and M.S. degrees in electrical engineering from the University of Illinois at Urbana-Champaign, in 2004 and 2008, respectively. Daniel's interests include advanced digital control, real-time control systems, and digital power supply design.
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