LLC's most complete calculation routine

The ever-rising demand for higher power density in switching power supplies has been constrained by the physical dimensions of passive components. Utilizing higher operating frequencies significantly reduces the size of critical components like transformers and filters. However, excessive switching losses present a significant barrier to achieving such high-frequency operations. To mitigate these losses and enable high-frequency operation, resonant switching technology was developed. This technology employs a sinusoidal approach to power delivery, allowing switching devices to perform soft switching. As a result, switching losses and noise are dramatically reduced. Among various resonant converters, the simplest and most commonly used is the LC series resonant converter, where the rectifier-load network is connected in series with the LC resonant network, as illustrated in Figure 1 [2-4]. In this configuration, the LC resonant network functions as a voltage divider alongside the load. By adjusting the driving voltage’s frequency, the impedance of the resonant network can be altered. The input voltage is then distributed between the resonant network's impedance and the reflected load. Due to this voltage division, the DC gain of the LC series resonant converter is always less than one. Under light load conditions, the load impedance is much larger than the resonant network's impedance, meaning nearly all the input voltage is applied directly to the load. This poses challenges in regulating the output under light loads. To address this issue, the theoretical resonant frequency would need to be infinitely high. To overcome the limitations of series resonant converters, LLC resonant converters were proposed [8-12]. An improvement over the LC series resonant converter, the LLC resonant converter incorporates a shunt inductor placed in the primary winding of the transformer, as shown in Figure 2. The introduction of a shunt inductor increases the circulating current within the primary winding, enhancing circuit performance. While this concept may not initially seem intuitive, it gained attention when applied to high-input-voltage applications, where switching losses outweigh on-state losses, thus improving overall efficiency. In most practical designs, the shunt inductor is implemented using the transformer's magnetizing inductance. The circuit diagram of an LLC resonant converter closely resembles that of an LC series resonant converter, with the sole distinction being the magnetizing inductance values. The excitation inductance in an LLC resonant converter is significantly larger—typically 3 to 8 times—that of the LC series resonant converter. This is usually achieved by increasing the air gap in the transformer. LLC resonant converters offer numerous advantages over series resonant converters. They regulate output voltage across a broad range of power and load variations while maintaining a relatively stable switching frequency. Zero voltage switching (ZVS) is achievable throughout the entire operational range. Additionally, inherent parasitic parameters, such as junction capacitance, transformer leakage inductance, and magnetizing inductance of all semiconductor devices, can be utilized to implement soft switching. This article delves into the working principles of LLC resonant converters, the design of transformers and resonant networks, and the selection of components. Practical design examples are provided to guide readers step-by-step through the design process, making this information invaluable for those working with LLC resonant converters. LLC Resonant Converter and Fundamental Approximation Figure 3 illustrates a schematic diagram of a half-bridge LLC resonant converter. Here, Lm represents the magnetizing inductance, acting as the shunt inductor; Lr refers to the series resonant inductor; and Cr denotes the resonant capacitor. Figure 4 displays a typical waveform of an LLC resonant converter. Assuming the operating frequency aligns with the resonant frequency, determined by the resonance between Lr and Cr, a substantial excitation current (Im) forms, freely circulating in the primary winding without contributing to energy transfer. The primary current (Ip) comprises the excitation current and the current reflected from the secondary back to the primary. Generally, the LLC resonant topology comprises a three-stage circuit, as depicted in Figure 3: a square wave generator, a resonant network, and a rectifier network. The square wave generator produces the square wave voltage Vd by alternately driving switches Q1 and Q2 with a 50% duty cycle. Continuous switching often introduces a small dead time. This generator can be configured as either a full bridge or a half bridge. The resonant network consists of a capacitor, transformer leakage inductance, and magnetizing inductance. It filters out higher harmonic currents. Fundamentally, even when a square wave voltage is applied, only sinusoidal current flows through the resonant network. The current (Ip) lags behind the voltage applied to the resonant network (i.e., the fundamental component of the square wave voltage Vd is applied to the totem pole of the half bridge), enabling the MOSFET to switch on at zero voltage. As shown in Figure 4, the MOSFET turns on when the voltage across it is zero, at which point the current flows through the anti-parallel diode. The rectifier network generates a DC voltage, utilizing a rectifier diode and a capacitor to rectify the AC. This network can be designed as a full-wave rectifier bridge or a center-tapped configuration with a capacitive output filter. The filtering effect of the resonant network can be analyzed using the fundamental approximation principle, deriving the voltage gain of the resonant converter. It is assumed that the fundamental component of the square wave voltage is input to the resonant network and the electrical energy is transferred to the output. Since the secondary side rectifier circuit can act as an impedance transformer, its equivalent load resistance differs from the actual load resistance. Figure 5 outlines the derivation of this equivalent load resistance. The primary circuit is replaced by a sinusoidal current source Iac, appearing at the input of the rectifier. Since the average value of |Iac| equals the output current Io, Iac can be described as: Note: Vo refers to the output voltage. Since the harmonic components of VRI do not involve power transmission, the AC equivalent load resistance can be calculated using (VRIF/ Iac): Considering the transformer turns ratio (n=Np/Ns), the primary equivalent load resistance can be described as: An AC equivalent circuit can be obtained using the equivalent load resistance, as shown in Figure 6. As shown, Vd and VRO in the figure refer to the fundamental component of the driving voltage Vd and the reflected output voltage VRO (nVRI), respectively. Using the equivalent load resistance obtained in Equation 5, the characteristics of the LLC resonant converter can be derived. Using the AC equivalent circuit shown in Figure 6, the formula for calculating the voltage gain M can be obtained: Figure 7 illustrates the difference in Q values and m=3, fo=100kHz and fp=57kHz. The gain expressed by Equation 6 is shown. As seen from Figure 7, the LLC resonant converter exhibits a voltage gain characteristic that is nearly independent of the load when the switching frequency is near the resonant frequency fo. This is a remarkable advantage of the LLC type resonant converter over traditional series resonant converters. Therefore, it is assumed that the converter operates near the resonance frequency, reducing the switching frequency fluctuation. The operating range of the LLC resonant converter is subject to peak gain (up to maximum gain), which is labeled '*'. It should be noted that the peak voltage gain does not appear near fo or fp. The frequency at which the peak voltage gain is obtained is between fp and fo, as shown in the figure. As the load becomes lighter, the Q value decreases, shifting the peak gain frequency toward fp and reducing the peak gain. Hence, for resonant network design, the full load condition is the worst-case scenario. Integrated Transformer Considerations For practical design purposes, it is usually necessary to implement the magnetic device (series inductance and shunt inductance) using the concept of an integrated transformer, where the leakage inductance is used as a series inductance and the excitation inductance is used as a parallel inductance. When constructing the magnetic element in this manner, it is essential to refine the equivalent circuit in Fig. 6 to Fig. 8 because there is leakage inductance not only at the primary but also at the secondary. Failing to account for the leakage inductance of the transformer secondary often results in design errors. When dealing with actual transformers, it is advisable to use equivalent circuits with Lp and Lr, since these inductance values can be easily measured at the primary by separately opening and shorting the secondary windings. In the actual transformer, Lp and Lr can be measured on the primary side under the condition that the secondary winding is open and shorted, respectively. When handling real transformers, it is prudent to employ equivalent circuits featuring Lp and Lr, as these inductance values can be readily measured at the primary by independently opening and shorting the secondary windings. In an actual transformer, Lp and Lr can be measured on the primary side when the secondary winding is open and shorted, respectively. A virtual gain MV is introduced in Figure 9, which is caused by the leakage inductance of the secondary side. Using the improved equivalent circuit of Figure 9, the gain expression of Equation 6 can be adjusted to obtain the gain expression of the integrated transformer: Working Mode and Maximum Gain Considerations The LLC resonant converter can operate at a lower or higher resonant frequency (fo), as shown in Figure 10. Figure 11 displays the current waveforms of the primary and secondary transformers for each mode of operation. Operating below the resonant frequency (Case I) enables the secondary rectifier diode to achieve soft commutation, although the loop current is larger. As the operating frequency decreases and deviates from the resonant frequency, the circulating current significantly increases. Operating above the resonant frequency (Case II) allows for a reduction in the circulating current, but the rectifier diode cannot achieve soft commutation. For high-output-voltage applications, such as plasma display panels (PDPs), it is recommended to operate below the resonant frequency because the reverse recovery losses of the rectifier diodes in this type of application are comparable. On the other hand, when operating above the resonant frequency, the on-state loss is smaller than when operating below the resonant frequency. For low-output-voltage applications, such as liquid crystal display (LCD) TVs or laptop adapters, good efficiency is exhibited. Because of this type of application, the secondary rectifier diode is suitable for Schottky diodes, and the reverse recovery problem is irrelevant. However, when operating at the upper resonant frequency, operating at light loads causes a large increase in switching frequency. When operating above the resonant frequency, the frequency jump function is needed to prevent the switching frequency from rising sharply. Maximum Gain and Peak Gain Requirements Above the peak gain frequency, the input impedance of the resonant network is inductive, and the input current (Ip) of the resonant network lags behind the voltage (Vd) applied to the resonant network. Thus, the MOSFET can achieve zero voltage turn-on (ZVS), as shown in Figure 12. Below the peak gain frequency, the input impedance of the resonant network is capacitive, and Ip leads Vd. When operating in the capacitive range, during the switching process, the body diode of the MOSFET is reversely recovered, causing severe noise. Another problem with entering the capacitive range is that the output voltage is out of control due to the inverse of the gain slope. The minimum switching frequency should be appropriately higher than the peak gain frequency. The appropriate input voltage range for the LLC resonant converter is determined by the peak voltage gain. Therefore, the resonant network should be designed to ensure that the gain curve has sufficient peak gain and can cover the entire input voltage range. However, below the peak gain point, the ZVS condition is lost, as shown in Figure 12. Therefore, when determining the maximum gain point, it is required to reserve some margin, ensuring stable ZVS operation during the load transient and startup phases. Typically, for the actual design, 10-20% of the maximum gain is selected as the margin, as shown in the figure. Under a given condition, even if the peak gain is obtained using the gain formula 6, it is difficult to express the peak gain in a clear form. To simplify analysis and design, a simulation tool can be used to obtain the peak gain, as shown in Figure 14. The figure shows the peak gain (up to the maximum gain) as the value of Q changes for different values of m. It can be seen that by reducing the m and Q values, a higher peak gain can be obtained. For a given resonant frequency (fo) and Q value, decreasing m means that the magnetizing inductance is reduced, which will result in an increase in the circulating current. Naturally, a trade-off should be made between the available gain range and the conduction loss. Characteristics of the FSFR Series The FSFR family integrates a pulse frequency modulation (PFM) controller and a MOSFET specifically designed for zero voltage switching (ZVS) half-bridge converters with minimal external components. The internal controller includes an undervoltage lockout, an optimized high-side/low-side gate driver, a temperature-compensated precision current-controlled oscillator, and a self-protection circuit. Compared to discrete MOSFET and PWM controller solutions, the FSFR family reduces total cost, component count, size and weight while increasing efficiency, productivity and system reliability. Design Steps This section provides design steps based on the schematic shown in Figure 17. The integrated transformer has a center tap and the input voltage comes from a pre-regulator-power factor corrector (PFC). A DC/DC converter with a 192W/24V output has been selected as a design example. The design specifications are as follows: - Nominal input voltage: 400VDC (PFC stage output) - Output: 24V/8A (192W) - Hold time requirement: 20 milliseconds (50Hz power frequency) - PFC output DC capacitor: 220μF [[STEP-1] Determining the Various Indicators of the System] [[STEP-2 Determines the Maximum and Minimum Voltage Gain of the Resonant Network] According to the discussion in the previous section, in order to reduce switching frequency fluctuations, the LLC resonant network should typically be designed to operate near the resonant frequency (fo). Since the LLC resonant converter is powered by the PFC output voltage, the PFC nominal output voltage should be accommodated in order to design the operating frequency of the converter at fo. As can be seen from Equation 10, the gain at fo is a function of m (m = Lp / Lr). The gain at fo is determined by the choice of m values. Although a high peak gain can be obtained when the value of m is small, an excessively small value of m causes a deterioration in the coupling of the transformer and a decrease in efficiency. Typically, setting m to 3 to 7 allows the voltage gain at the resonant frequency (fo) to be 1.1 to 1.2. After the value of m is selected, the voltage gain at the nominal output voltage of the PFC can be described as: Core: EER3542 (Ae=107 mm2) Skeleton: EER3542 (horizontal/segment type) 6. Experimental Verification In order to verify the validity of the design process in this instruction manual, the converter design example was built and tested. All circuit components involved in the design example have been adopted. Figure 30 and Figure 31 show the operating waveforms at full load and no load for the nominal input voltage. It can be seen that due to the resonance effect, the drain-source voltage (VDS) of the MOSFET drops to zero before turn-on, achieving zero voltage switching. Figure 32 shows the resonant capacitor voltage and primary current waveform at full load. The peak value of the resonant capacitor voltage and the primary side current are 325V and 1.93A, respectively, which closely match the calculated value of the eighth step in the design process chapter. Figure 33 shows the resonant capacitor voltage and primary side current waveform for an output short circuit condition. For the output short-circuit condition, when the primary current is greater than 3A, the overcurrent (OCP) acts. The maximum voltage of the resonant capacitor is slightly higher than the calculated value of 419V, because the 1.5μs turn-off delay makes the OCP operating current slightly higher than 3A (refer to the FSFR2100 product specification). Figure 34 shows the voltage and current waveforms of the rectifier diodes under full load and no load conditions. The voltage stress is slightly higher than the calculated value in the ninth step due to the voltage overshoot caused by the stray inductance. Figure 35 shows the ripple waveform of the output voltage under full load and no load conditions. The ripple of the output voltage matches the design value in the ninth step. Figure 36 shows the efficiency measurements for different load conditions. The efficiency at full load is approximately 94%. Graphic I network

Wireless CPE

What is 5G CPE?

Definition of 5G CPE
CPE stands for Customer Premise Equipment. The so-called front end refers to the equipment in front of the customer's terminal equipment. When we use Wi-Fi, if the distance is far, or there are more rooms, it is easy to appear signal blind spots, resulting in mobile phones or ipads or computers can not receive Wi-Fi signals. The CPE can relay the Wi-Fi signal twice to extend the coverage of Wi-Fi.

What are the benefits of CPE?
Through the following comparison table, it is not difficult to understand the technical advantages of CPE products:

* Currently, the global 5G FWA service is mainly in the Sub-6GHz band, with only the United States and Italy supporting the millimeter wave band.

* 5G CPE integrates the low cost of Wi-Fi and the large bandwidth of 5G, combining the advantages of the two to form a strong complement to traditional fiber broadband.

The relationship between 5G, FWA and CPE
It can be said that FWA (Fixed Wireless Access) will be the most down-to-earth application of 5G technology. FWA business plays a key role in enabling "connecting the unconnected." FWA is a low-cost, easy-to-deploy flexible broadband solution. Compared with wired access technology, FWA has been an ideal choice for deploying broadband in many countries and regions because it does not need to obtain rights of way, dig trenches and bury cables, and drill holes through walls. The development of 5G technology is further promoting the development of FWA.

FWA services (including 4G and 5G) have reached 100 million users. FWA is no longer a niche service; The FWA industry as a whole has been supported by numerous suppliers. Why is that? In the 5G era, 5G CPE receives 5G signals from operator base stations and then converts them into Wi-Fi signals or wired signals to allow more local devices to get online. For operators, the initial user penetration rate of 5G is low, and the investment is difficult to realize quickly; The CPE business can use the idle network to increase revenue for operators, so major operators vigorously promote the development of 5G CPE.

FWA services can be used for both home (To C) and business (To B), and customers have different requirements for CPE devices when using FWA services in different application environments, resulting in consumer grade 5G CPE and industrial grade 5G CPE (similar to home routers and industrial routers).

In 2020, the global market size of 5G CPE will reach 3 million units, and it is expected that in the next five years, the market size of 5G CPE will maintain a compound growth rate of more than 100%, reaching 120 million units in 2025, with a market value of 60 billion yuan. As an important market for 5G CPE, China's 5G CPE market size will reach 1.5 million units in 2020 and is expected to reach 80 million units in 2025, with a market value of 27 billion yuan.

The difference between 5G CPE and other devices
CPE can support a large number of mobile terminals that access the Internet at the same time, and the device can be directly inserted with a SIM card to receive mobile signals. CPE can be widely used in rural areas, cities, hospitals, units, factories, communities and other wireless network access, can save the cost of laying wired networks.

A Router is a hardware device that connects two or more networks, acts as a gateway between networks, and is the main node device of the Internet. Routers use routes to determine the forwarding of data. If it is a home router, it does not support a SIM card slot, and can only receive signals by connecting to optical fiber or cable and then convert it into WI-FI to provide a certain number (several) of terminal devices to surf the Internet.

Industrial 5G CPE is equivalent to 5G industrial routers, and the technology of the two is not very different. On the one hand, the industrial 5G CPE converts 5G network signals into WiFi signals for transmission, and on the other hand, the data received by the WiFi network is converted into 5G network signals for uploading. In addition, industrial 5G CPE generally supports routing functions.

5G CPE trends
According to a research report, after evaluating the products of some mainstream 5G CPE suppliers, many institutions believe that the development of 5G CPE products will continue in two aspects: one is to support mmWave and Sub-6 GHz at the same time; Second, the design will pay attention to humanized operation and installation. The industry development trend will accelerate the demand for 5G in the medical, education and manufacturing industries due to the epidemic, and 5G FWA will promote global 5G CPE shipments.

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