LLC converter control method: hybrid optimal trajectory control

1. Scope and Purpose

This page provides a general functional description and design guidelines for a 3 kW LLC isolated DC/DC resonant converter, controlled using the novel HOTC, to improve transient response and address the AI server market.

2. Introduction

Power supplies with high efficiency, power density, and low EMI are highly desired in power electronics applications. Resonant converters can meet these requirements thanks to their low switching losses, which allow operation at higher frequencies. In particular, the LLC converter stands out for its wide output voltage regulation capability, ensuring soft switching over the entire operating range, as well as ZCS on the secondary side over certain frequency ranges, which further increases efficiency. However, the main drawbacks of this topology are its slow response to variations in the output load, which generates large output voltage over- and undershoots, as well as its high sensitivity to input voltage variations, which generally requires design trade-offs to optimize the converter for a wide input voltage range.

3. Overview LLC resonance converter

Fig1: Full bridge LLC converter

An LLC resonant converter mainly consists of four parts: an inverting bridge (full‑bridge or half‑bridge), a resonant tank, a high‑frequency transformer, and a rectifier stage (full‑bridge or center‑tapped). The choice of the primary side structure depends on the RMS current, which in a half‑bridge is twice that in a full‑bridge for the same transferred power. On the secondary side, the choice depends mainly on the output voltage, with center‑tapped rectifiers being dominant in low‑voltage applications.

Fig2: Equivalent circuit

In a simplified description, the switching bridge generates a square‑wave voltage to excite the LLC resonant tank. The resonant tank acts as a filter that removes the higher‑order harmonics and allows the fundamental component (FHA) to pass, resulting in a sinusoidal resonant current. This current is then scaled by the transformer and rectified by the output rectifier stage. Finally, the output capacitor filters the rectified AC current and provides a DC output voltage.

3.1. Resonant Tank Design

The design of a resonant converter is a challenging task and requires more effort to achieve optimization compared to the design of PWM converters. Current state-of-the-art LLC design methods are based on the First Harmonic Approximation (FHA), which is generally used to determine the transfer ratio of the resonant converter. The FHA approach assumes that the power transfer from the source to the load through the resonant tank is entirely associated with the fundamental harmonic of the Fourier series expansion of the currents and voltages involved. The harmonics of the switching frequency are then neglected, and the waveforms in the tank are assumed to be purely sinusoidal at the fundamental switching frequency.

3.1.1. DC Gain Characteristics

Using the FHA (First Harmonic Approximation) method, the resonant tank gain can be theoretically calculated by analyzing the equivalent resonant circuit shown in fig2.

$$G\left(Q,m,F_{x}\right)=\left|{\frac {V_{LLCout}(s)}{V_{IN}(s)}}\right|={\frac {F_{x}^{2}(m-1)}{\sqrt {{(m.F_{x}^{2}-1)}^{2}+F_{x}^{2}.\left(F_{x}^{2}-1\right)^{2}.{(m-1)}^{2}.Q^{2}}}}$$

Where,

$(Quality\ factor)$	$$Q={\frac {\sqrt {L_{r}/C_{r}}}{R_{ac}}}\ \ \ \ \ \ \ \ \$$
$(Reflected\ load\ resistance)$	$$R_{ac}={\frac {8}{\pi ^{2}}}.{\frac {N_{P}^{2}}{N_{s}^{2}}}.R_{0}\ \ \ \ \$$
$(Normalized\ switching\ frequency)$	$$F_{x}={\frac {f_{s}}{f_{r}}}\ \ \ \$$
$(Resonant\ frequency)$	$$f_{r}={\frac {1}{2\pi {\sqrt {L_{r}{.C}_{r}}}}}\ \ \ \$$
$(Ratio\ of\ total\ primary\ inductance\ to\ resonant\ inductance)$	$$m={\frac {L_{r}+L_{m}}{L_{r}}}\ \ \ \ \$$

Based on the gain equation, the normalized voltage gain versus normalized switching frequency characteristic of the LLC resonant converter is plotted for several values of m and Q to illustrate how these parameters affect the gain characteristic of the LLC resonant converter.

Fig3 : Gain plot for different m and Q values

The selection of the factor m depends on several parameters, the most critical being the magnetizing inductance L_m. A low m factor, implying a low L_m value, results in higher RMS current, leading to increased conduction losses in the primary power MOSFETs, as well as higher turn-off switching losses and higher copper losses in the resonant inductor.

Regarding transformer copper losses, a low value of L_m typically implies fewer winding turns. This reduction in the number of turns leads to a lower resistance, which would normally reduce losses. However, this advantage is often offset by the fact that a lower L_m results in a much higher magnetizing current. This increased current raises the overall RMS current in the windings, which can ultimately lead to higher total copper losses despite the lower resistance.

Nevertheless, lower values of m offer significant advantages, such as achieving a higher boost gain, maintaining a narrower frequency modulation range, and requiring a shorter dead time to achieve Zero Voltage Switching (ZVS).

3.1.2. Design steps

• Transformer ratio

$$n={\frac {V_{in,nom}}{V_{out}}}$$

• Calculate min, max gain

This is the required gain at the extreme values of the input voltage range.

Maximum gain:	$$G_{\max }=n.{\frac {V_{out}}{V_{in,min}}}$$
Minimum gain:	$$G_{\min }=n.{\frac {V_{out}}{V_{in,max}}}$$

• Calculate m value

The m parameter is determined based on the maximum switching and resonant frequencies. For better efficiency, the value of m should be as high as possible.

$$m=1+{\frac {L_{m}}{L_{r}}}$$

At light load, the gain is the following:

$$G\left(Q,F_{x}\right)=G\left(0,F_{x}\right)=\left|{\frac {1}{1+{\frac {L_{r}}{L_{m}}}-{\frac {\frac {L_{r}}{L_{m}}}{F_{x}^{2}}}}}\right|\Rightarrow G_{\min }=G\left(0,F_{xmin}\right)=\left|{\frac {1}{1+{\frac {L_{r}}{L_{m}}}-{\frac {\frac {L_{r}}{L_{m}}}{F_{xmin}^{2}}}}}\right|$$

$$=>{\frac {L_{r}}{L_{m}}}={\frac {1-K_{\min }}{K_{\min }}}.{\frac {F_{xmin}^{2}}{F_{xmin}^{2}-1}}\ with\ F_{xmin}={\frac {f_{\max }}{f_{r}}}$$

• Select Qmax

${\textstyle Q_{\max }}$ is determined based on the minimum switching and resonant frequencies. Once ${\textstyle m}$ is calculated, the optimal approach for selecting ${\textstyle Q_{\max }}$ is to plot the normalized voltage gain versus the normalized switching frequency, for different values of ${\textstyle Q}$, using the calculated ${\textstyle m}$ value as shown in the figure below. From these curves, select the ${\textstyle Q_{\max }}$ that achieves the required maximum gain at the minimum switching frequency. This optimization process may require several iterations. If the maximum gain remains insufficient at the minimum frequency, the value of ${\textstyle m}$ must be recalculated; specifically, lowering the target minimum switching frequency allows for a reduction in the ${\textstyle m}$ factor.

Fig4 : Qmax selection

• Resonant components values

After selecting the values for m and ${\textstyle Q_{\max }}$, the theoretical resonant tank components can then be calculated using the following equations:

$$R_{ac,min}={\frac {8}{\pi ^{2}}}.{\frac {N_{P}^{2}}{N_{s}^{2}}}.{\frac {V_{o}^{2}}{P_{omax}}}\ ,Q_{\max }={\frac {\sqrt {L_{r}/C_{r}}}{R_{ac,min}}}\ \ ,f_{r}={\frac {1}{2\pi {\sqrt {L_{r}{.C}_{r}}}}}\ ,\ m={\frac {L_{r}+L_{m}}{L_{r}}}\$$

• Operation regions

According to the switching frequency, the LLC converter operation can be divided into two regions, as shown below:

• 

  Fig6: Capacitive and inductive regions
  

  Fig5: ZVS timing

To achieve zero-voltage switching (ZVS) on the primary side, the converter must operate in the inductive region over the entire input-voltage and load-current range and must never enter capacitive-region operation, which would cause hard switching on the primary side and lead to efficiency drifting outside the target.

However, this condition is not sufficient, as it is necessary to provide enough dead time to ensure that sufficient energy is available to charge and discharge the drain ‑source capacitances (Cds) of the primary full-bridge MOSFETs within the dead-time interval ${\textstyle T_{D}}$, which means:

$$I_{ZVS}=C_{ZVS}.{\frac {V_{dc}}{T_{D}}},V_{dc}=4.L_{m}.{\frac {I_{ZVS}}{T_{sw}}}\Rightarrow T_{d}\geq 4.L_{m}.C_{ZVS}.F_{sw}$$

With,

$$C_{ZVS}={4.C}_{oss}+C_{stray}$$

C_stray: Midpoint half bridge parasitic capacitance.

According to the switching frequency, there are three operating modes for the LLC converter within the inductive region. The figure below illustrates the typical waveforms of an LLC resonant converter operating at, below, and above the resonant frequency:

Fig7:Operating mode of LLC converter

I_Q5,8 and I_Q7,6: correspond to the current flowing through the synchronous rectifier switches Q7, Q6, Q5, and Q8.

I_Lr: resonant current flowing through Lr.

I_Lm: magnetizing current flowing through Lm.

V_mid-point: square-wave voltage generated by the primary full bridge and applied to the resonant tank input.

• At resonant frequency ${\textstyle (f_{x}=1\Rightarrow f_{s}=f_{r})}$:
  

The resonant tank has unity gain, and the transformer turns ratio is designed so that, at nominal input voltage, the converter operates at this point with maximum power.

• Above resonant frequency ${\textstyle (f_{x}>1\Rightarrow f_{s}>f_{r})}$:
  

The converter operates in this mode at higher input voltage or light load, where a step-down gain is required.

• Below resonant frequency ${\textstyle (f_{x}<1\Rightarrow f_{s}<f_{r})}$:
  

The converter operates in this mode at lower input voltage and high load, where a step-up gain is required. In this operating mode, zero‑current switching (ZCS) is also achieved on the secondary side, which makes this operating mode commonly used.

4. HOTC Theory Basis introduction

It is usually admitted that CMC (Charge Mode Control) offers a significant advantage of transient regulation due to its simple first-order response. This advantage arises from the linear relationship between control and input power. The reasoning can also be explained as follows:

LLC is characterized by two distinct phases of power transfer:

1. High-side on/Low-side off: During this phase, half of the power charges the resonant capacitance ${\textstyle C_{r}}$, while the remaining half is transferred to the secondary side.
2. High-side off/Low-side on: In this phase, the charge stored in ${\textstyle C_{r}}$ is transferred to the secondary side.

The resonant current, which exhibits a sinusoidal waveform and operates near the resonance frequency, can be defined as follows:

$$I_{r}(t)=\ C_{r}{\frac {dV_{cr}}{dt}}\ \sim \ C_{r}.\mathrm {\Delta } V_{cr}.f_{sw}$$

The input power (related to the output power) of a resonant converter can be calculated with the equation below. The equation shows that the input power has a linear relationship with the voltage difference around resonant capacitor${\textstyle {\mathrm {\Delta } V}_{cr}}$.

$$P_{in}=\ V_{in}.C_{r}.{\mathrm {\Delta } V}_{cr}.f_{sw}$$

Controlling the input power to meet the output power under the power conservation law requires controlling the voltage across the resonant capacitance. The switching period is then modulated as a function of the time when the${\textstyle V_{cr}}$ waveform crosses ${\textstyle V_{threshold}}$ (The high and low thresholds can be symmetric, assuming a ${\textstyle V_{cr}}$ sinusoidal behavior):

Fig8:Transient load impact on Vcr

The linearity of control ensures that the only pole to handle is related to the output capacitance, as demonstrated by rigorous partial derivation in:

$$\ {\frac {\mathrm {\Delta } v_{0}}{\mathrm {\Delta } v_{thH}}}\sim \ {\frac {R_{L}}{1+sC_{0}R_{L}}}$$

First-order behavior is determined by the output capacitance and load condition, so it moves accordingly. This behavior, in accordance with the unitary gain slope, is used as an indicator of the HOTC algorithm's efficiency, while following an optimal current trajectory as demonstrated in the following sections.

4.1. Fundamental equations

Fig9: Current and resonant voltage waveforms

An LLC full bridge generates a square waveform, which can be analyzed using Fourier series. The behavior of the LLC topology is fundamentally bandpass at the resonant frequency. This means that only the sinusoidal component at the resonant frequency passes through, while harmonics are filtered.

To achieve optimal performance, LLC topology operates with switching frequencies close to the resonant frequency. This operation is characterized by a resonant current, which follows a sinusoidal formula in Mode I: the high-side switch Q1 is on, and the low-side switch Q2 is off.

$$i_{Lr}(t)=\ I_{pk}\sin {(\omega t+\ \varphi )}$$

The LLC converter has two main current components on the primary side: the reflected rectifier current (secondary current scaled by the turns ratio) and the magnetizing current of the transformer. These two currents are orthogonal (90º degrees out of phase) because the magnetizing current ${\textstyle I_{Lm}\ }$is reactive (inductive), lagging the voltage, and the reflected current ${\textstyle I_{rec}}$ is in phase with the load current. Since these two components are perpendicular in the complex plane, the peak of the resonant current can be expressed as:

$$I_{Lr}={\sqrt {\left({\frac {I_{rec}}{n}}\right)^{2}+I_{L_{m}}^{2}}}$$

The magnetizing current ${\textstyle I_{Lm}}$, driven by high inductance ${\textstyle Lm}$, and based on initial conditions of magnetizing voltage and its null value around the middle of the half period, we can deduce that:

$$I_{m}=\ {\frac {nV_{0}}{4L_{m}f_{r}}}$$

The rectification current is linked to load current by:

$$I_{rec}={\frac {\pi }{2}}I_{Load}$$

Based on previous equations:

$$I_{pk}={\sqrt {{\frac {V_{in}^{2}}{16L_{m}^{2}f_{r}^{2}}}+\ {\frac {\pi ^{2}I_{Load}^{2}}{4n^{2}}}}}$$

And

$$v_{cr}(t)=-{\frac {I_{pk}}{{\omega C}_{r}}}\cos {(\omega t+\ \varphi )}$$

Knowing that:

$$i_{Lr}\left(T_{zcd}\right)=\sin \left(\omega T_{zcd}+\ \varphi \right)=0$$

$$\varphi =\ -2\pi {\frac {T_{zcd}}{T_{r}}}$$

4.2. Intermediate verification

Plant described later has been simulated, and two signals plotted:

${\textstyle V_{cr}}$ as sensed from Plant

dbg signal generated based on modelized Vcr as described from previous equations.

Here below code from PSIM to illustrate such modeling:

phi = (double)TIMA_ZCD/PeriodRes;

phi = -2*pi_c*phi

double omega = 2*pi_c*fsw;

out[6] = (-Ipk/(Cr*omega))*cos(omega*TIMA_CNT*Ts_c + phi);

In plots below we can check high level of concordance between sensed Vcr and modelized version. Such check was done at various parameters of load, frequencies, …

Fig10: Model and simulated resonant voltage waveforms

4.3. HOTC regulation approach

Now, based on the charge control approach, we intend to resolve the equation of:${\textstyle V_{cr}(t)=\ V_{th}}$ as an indication of switching period ensuring the lowest losses.

${\textstyle V_{cr}(t)}$ model as previously described is reliable approximation to sensed voltage in steady state, however during load transition, we cannot rely on it.

This motivates the need for a voltage representation to a function ensuring a fast transition to the optimal trajectory when dynamic load transition is detected.

The capacitor voltage ${\textstyle V_{cr}}$ is related to the charge stored capacitively in tank. Opening the high-side transistor removes the direct voltage source, forcing ${\textstyle V_{cr}}$ to a specific level. The capacitor discharges rapidly through the resonant inductor and the low-side transistor conduction path. The resonant tank current flowing through the capacitor causes the ${\textstyle V_{cr}(t)}$ voltage to drop quickly due to the capacitor's energy release.

Hence, we take advance from ${\textstyle (\omega t+\ \varphi )}$ qualification as a small angle at PWM switching to use Taylor approximation:

$$\cos(\omega t+\ \varphi )\approx 1-\ {\frac {{(\omega t+\ \varphi )}^{2}}{2}}$$

Fig11: Small angle of Vcr at switching

Since modelized ${\textstyle V_{cr}(t)}$ allow to target the optimal trajectory at load transitions, resolution of ${\textstyle V_{cr}(t)=\ V_{th}}$, equation will lead to match the optimal period if ${\textstyle V_{cr}(t)}$ is a bell-shaped function, since parabolic bell with axis of symmetry will cross the bell support at point O(T,0). T is the period of the optimal trajectory for Voltage Resonant, deduced from efficient input power equaling output.

Welch-type parabolic window is used for this purpose with radius of ${\textstyle {\sqrt {\frac {2I_{pk}}{I_{pkmax}}}}}$

${\textstyle V_{cr}(t)}$ is approximated as follows:

$${I_{pk}\cos }(\omega t+\ \varphi )\approx I_{pk}-\ I_{pkmax}{\frac {{(\omega t+\ \varphi )}^{2}}{2}}$$

The figure below, extracted from a PSIM simulation, shows bell-shaped waveforms.

Fig12: Vth intersection with bell-shaped function

The figure below illustrates the effect of Welch-type substitution in reaching the optimal trajectory. This is named a hybrid control, as it uses a steady-state approximation without losing the fast placement to the optimal current when a new load is detected.

This approach provides a major advantage: maintaining the same control. Let’s compare this with a major trajectory type control: SOTC (Simplified Optimal Trajectory Control). This control, despite its interest and accuracy, suffers from the complexity of switching between proportional-integral (PI) control and trajectory control, which may bring discontinuity when switching from one scheme to another. ${\textstyle I_{th}}$ is proportional to the initial ${\textstyle V_{th}}$used in crossing equation. This is a PI output monitoring the level of output voltage gap with the output voltage reference.

Here below a summary of HOTC equations:

$$\varphi =\ -2\pi {\frac {T_{zcd}}{T_{r}}}$$

$$I_{pk}={\sqrt {{\frac {V_{in}^{2}}{16L_{m}^{2}f_{r}^{2}}}+\ {\frac {\pi ^{2}I_{Load}^{2}}{4n^{2}}}}}$$

$$T=\ {\frac {1}{2\pi f_{r}}}({\sqrt {{\frac {2}{I_{pkmax}}}(I_{pk}\left(I_{Load}\right)+I_{th})}}-\ \varphi )$$

4.4. Intermediate verification

Fig13: DFC and Model at Load transition

In the simulation, the DFC (direct frequency control) method was run, while ${\textstyle V_{cr}(t)}$ model converge very fast the expected and optimal trajectory (red), the ${\textstyle V_{cr}(t)}$ of the plant goes through slow and oscillatory regulation before meeting the model trajectory. Model based converge very fast to target waveform, while sensed voltage (with DFC regulation) is evolving slowly to target value.

We see slow and oscillatory (green) regulation while probing the resonant voltage model (red).

Fig14: HOTC and Model at Load transition

In this figure, HOTC control was applied instead of DFC, leading to a fast convergence of both model and sensed voltages to the final level, which is relevant to an efficient power transfer.

4.5. Qualitative explanation

The resonant voltage model serves as the reference for waveform generation because it is derived from ideal power efficiency conversion. The threshold voltage ${\textstyle V_{th}}$, determined by the output voltage difference from the reference, intersects with the model waveforms to reach the peak value. Due to regulation error, an increase in Vth compensates for the growing mismatch with reference. This process projects the optimal trajectory onto the switching period. Using a bell-shaped function, specifically the Welch function in the HOTC concept, accelerates the achievement of this target. Projection onto the bell support provides a period that is closer to the model peak than the initial function.

A very high value of Welch function radius (using >> ${\textstyle I_{pk}(maxload)}$) helps to decrease undershoots and overshoots, so margins at frequency analyse, but may impact crossover frequency value by lowering it.

5. Simulation performances

Used Plant for simulation has higher Lm/Lr, which is linked to lower gain (performance) but better efficiency. Output capacitance is selected to match the target ripples.

Parameters	Values	Comment
Vdc	400V	Nominal input voltage
fr	116230Hz	Resonant frequency
Cr	75nF	Resonant capacitance
Lr	25uH	Resonant inductance
Lm	225uF	Magnetizing inductance
C	300e-12uH	Parasitic capacitance
a_sp	7.5	Primary/Secondary ratio
Vref	53.5 V	Output voltage
P_l	Vref*5	Lite load
P_f	Vref*56	Full load
P_hl	Vref*56/2	Half load
Ts	Ts=1e-8	Simulation Sampling. It needs to be consistent with the Time step.
fsw_min	30kHz	Min switching frequency
fsw_max	300Khz	Max switching frequency

Results were generated for many use cases and compared with other control methods: DFC, TSC (Time Shift Control) and CMC (Charge Mode Control). We extract here below a mix of cases:

• Transient response: comparison with TSC
• Open loop response: comparison with DFC
• Closed loop response: comparison with CMC
• Transient and frequency response

Usecase: C0=6000uF, 0-FullLoad (57A)

• 

  Fig15: TSC transient response

• 

  Fig16:TSC transient response

Find below a summary of use cases results:

Conditions	TSC	HOTC	M-CRPS Limits
C0=1000uF, 0-FullLoad (57A)	3.42V 6.4%	2.04V 3.8%	8%
C0=1000uF, 0-HalfLoad (57/2 A)	2.77V 5.1%	1.43V 2.6%	5%
C0=4000uF, 0-FullLoad (57A)	3.52V 6.5%	1.45V 2.7%	8%
C0=6000uF, 0-FullLoad (57A)	2.8 V 5.2%	0.97V 1.8%	8%
C0=1000uF, 0-FullLoad (57A), Czcd=220u	4.47V 8.3%	1.87V 3.4%	8%

Note

HOTC (regarding TSC) allows matching M-CRPS limits

5.1. Open loop response

As shown in the figures below, the DFC case exhibits the complexity of a multiple poles-zeros response, which results in less effective compensation. Conversely, figure demonstrates that the HOTC open-loop frequency response simplifies the system order. The dependency of the transfer function on output capacitance is analyzed using various values, confirming its close behavior to charge control.

• 

  Fig17:DFC Open loop response

• 

  Fig18:HOTC Open loop response

5.2. Closed loop response

Charge control implementation:

A charge-control scheme compares the control capacitor voltage ${\textstyle V_{cr}}$ to a threshold ${\textstyle V_{th}}$. Each crossing event terminates a switching cycle. As the load or input conditions change, the rate at which ${\textstyle V_{cr}}$ reaches ${\textstyle V_{th}}$ varies, making the switching frequency inherently dependent on how fast ${\textstyle V_{cr}}$ crosses ${\textstyle V_{th}}$.

• 

  Fig19:CMC control

• 

  Fig20:CMC control (cycle)

Below, the charge control frequency response profile with compensation initially designed for full load. The stability is hampered at half-load, with a high dependency on load:

Fig21:Bode Plot of CMC with same coefficients at different load

HOTC frequency response profile (compensation designed for full load initially, enough crossover frequency to keep fair performance at half load):

The system maintains a marginally higher gain at full load, but the overall gain does not change dramatically between half and full load in this frequency range. Full load gives a modestly higher plant gain, but the overall bandwidth and roll‑off characteristics are similar. Controller crossover frequency can therefore be kept similar for different load conditions, though full‑load gain must be considered when setting compensation to maintain adequate phase margin.

At higher frequencies, the system becomes significantly more phase‑lagged under full load than under half load. This occurs starting from 5-6khz, which may reduce the gain margin because of anticipated crossing of -180 degrees. Obtained Gain margin is, however, enough for stability.

Fig22:Bode Plot of HOTC with same coefficients at different load

5.3. Tools for HOTC design:

An excel file for HOTC control dimensioning is provided (see snapshot below). This excel file (file provided on demand for customers) also includes FHA gain, Quality factor, inductance ratio, ripple and different hardware parameters to assess the plant behavior seamlessly and in advance.

Fig23:HOTC equation computation

6. HOTC control method implementation

Fig24:HOTC Digital control implementation

The control method is similar to Direct Frequency Control (DFC); the power transistors switch at a variable frequency with a fixed duty cycle of 50%. However, in this implementation the switching period is provided by the HOTC algorithm, which requires the output current measurement and the zero‑crossing detection of the resonant inductor current ${\textstyle I_{Lr}}$. This control method consists of two main loops, an outer loop running at a fixed frequency that provides the ${\textstyle V_{th}}$ through the controller (PID), and an inner loop running at the switching frequency that provides the operating period based on the HOTC algorithm.

6.1. Hardware requirement

Fig25:LLC–HOTC Block Diagram

To implement this control technique, an analog comparator circuit must be placed after the current transformer (CT) to measure the time interval between the start of the period and the zero-crossing of the inductor current ${\textstyle I_{Lr}}$. The measurement process, as well as the use of the measured value is described in the block diagram shown below.

6.2. HRTIM configuration

The HRTIM is programmed to control the primary power switch of the LLC converter as described hereafter.

The master timer and timers A and B operate in continuous mode, and all counters are reset at the master timer period. The preload register is disabled so that any modified values in the registers are considered immediately.

The PWM outputs are configured as follows:

• HRTIM_CHA1 (Q1): Set on Master timer period event, reset on Master timer CMP1.
• HRTIM_CHA2 (Q2): Complementary output of HRTIM_CHA1 with dead-time insertion.
• HRTIM_CHB1 (Q3): Set on Master timer CMP1, reset on Master timer period event.
• HRTIM_CHB2 (Q4): Complementary output of HRTIM_CHB1 with dead-time insertion.

An ISR is triggered at the beginning of each period to process the HOTC algorithm, which calculates the operating period that will be applied immediately before the end of the first half‑period.

Fig26:LLC converter operating waveforms

Fig27:System Block for LLC current mode (HOTC) and peripherals

7. Experimental results

7.1. LLC 3KW

To verify the validity of the proposed control method, the experiment was performed on a 3kW Full Bridge LLC resonant converter:

Fig28:LLC 3KW

Design parameters are shown in the table below.

Specification
Input Voltage Output Voltage Output Power	400V 52V 1.5kW
Switch
Min Switching frequency Max Switching frequency	85kHz 300kHz
Resonant tank
Transformer ratio Resonant capacitance Resonant inductance	30:4 75nF 25uH
Control
Microcontroller	STM32G474
Output filter specification
Output capacitance	6720uF

The figures below show the test results for load transients from 2A to 25A and from 25A to 2A, respectively, with a step load slope of 1 A/µs. These figures compare the transient responses of two control methods: the conventional voltage-mode control (DFC) and the HOTC method using a PID controller. As shown in the waveforms, the HOTC method achieved 26% less overshoot, 20% less undershoot, and 32% shorter settling time compared to the voltage-mode control, highlighting a significant improvement in transient response performance.

• 

  Fig29:DFC/HOTC overshoot/settling time

• 

  Fig30:DFC/HOTC undershoot/settling time

7.2. LLC 15W

Advanced analysis was run on LPLV board (12V-7.5V, 2A load) using DFC and HOTC. This LLC HAT is described in the table below:

Fig31:LLC 15W Board

Specification
Input Voltage Output Voltage Output Power	12V 7.5V 15W
Switch
Min Switching frequency Max Switching frequency	100kHz 300kHz
Resonant tank
Transformer ratio Resonant capacitance Resonant inductance Magnetizing inductance	33:1 400nF 0.3uH 6.4uH
Control
Microcontroller	STM32G474
Output filter specification
Output capacitance	47uF

Below are the results with fine-tuned parameters, resulting in high bandwidth for HOTC involving a guaranteed stability.

Results of comparison between DFC and HOTC in Half and Full loads:

	Stability criteria	DFC FL	DFC HL	HOTC FL	HOTC HL
Fc	> 800Hz	3.4Khz	3.4Khz	8.9 Khz	8.9 Khz
Gain margin	>= 6 db	8.3	10	6	9
Phase margin	>= 45 degree	64	65	52	64

Parameters that influence the frequency analysis are:

• SW tuning for Kp, Ki, phase correction in HOTC equation to adjust the approximation of null angle, and Ipkmax parameter. Tools for HOTC and tuning session will describe this tuning
• Injection amplitude for which we look for a compromise between steady state and AC sweep precision. Hence, third-party tools allow “shaped level feature changing the output level over frequency.” This is also a used technique with the frequency profiler tool used for LLC analysis.
• MCU Peripherals configuration is major factor for a fast response. This includes:
  • Fast ADC and short sampling time, with enough precision
  • Fast control loop, allowing to enhance the period prediction
  • HRTimer high precision for a period settling close enough to the optimal trajectory

See below screenshots of a set of results:

• 

  Fig32:DFC Full Load frequency profile

• 

  Fig33:DFC Half load frequency profile

• 

  Fig34:HOTC Full load frequency profile

• 

  Fig35:HOTC Half Load frequency profile

8. Conclusion

This page introduces a novel LLC resonant control method featuring a new control algorithm: HOTC. Dynamic behavior characterization was performed using PSIM simulations, which demonstrated that HOTC effectively reduces the system order, thereby simplifying the control of the LLC converter. Prototype experiments revealed a substantial improvement in dynamic load performances, making this solution ideal for data server power supplies that require high responsiveness.