Preface:In the lead up to a larger commercial project, I'm building a "small" 1kW CLLC resonant converter as a sort of pilot to develop and test my design methods and models. This project in itself isn't intended for any practical purpose other than learning. The project is expected to be mostly an implementation following existing methods and reference designs, nothing particularly creative or secret sauce for now. There's ample existing literature out there but a lot of it is either esoteric academia or vendor white papers so hopefully I can contribute something both down-to-earth pragmatic and component vendor impartial to the community and bring people along for the ride in the process (
perhaps release an open source reference at the end). Of course not being entirely altruistic, I also hope people will be able to catch any errors and provide suggestions and constructive criticism.
Index:--------------------------------
Bibliography - this post[writing up]
System Specs - this post
Topology Choice - this post
Critical Component Selection - this post
First Harmonic Analysis
-Analytical Exploration - this post
-Numerical Values and Simulation -
LTSpice ModelsNonlinear Time Domain Analysis
-Simplified model frequency responseAdditional Component Selection - todo
System Implementation Review - todo
Subsystem Design-Testing - todo
Complete System Build - todo
Complete System Validation -todo
[more to come?]
--------------------------------
Questions/Footnotes:--------------------------------
Inductance Required for \$C_{oss}\$ Charging -
Solution by gae_31SPICE Diodes and ConvergencePicking a DSP MCULight load gain--------------------------------
BibliographyJee-Hoon Jung, Ho-Sung Kim, Ho-Sung Kim, Myung-Hyo Ryu, Ju-Won Baek "Design Methodology of Bidirectional CLLC Resonant Converter for High-Frequency Isolation of DC Distribution" IEEE Transactions on Power Electronics 28(4):1741-1755, April 2013,
Section III.A (pg. 1745-1746) https://www.researchgate.net/publication/260496284_Design_Methodology_of_Bidirectional_CLLC_Resonant_Converter_for_High-Frequency_Isolation_of_DC_Distribution_Systems H. Huang "Designing an LLC Resonant Half-Bridge Power Converter" SLUP263, Texas Instruments, 2010,
pg. 15 https://www.ti.com/seclit/ml/slup263/slup263.pdf (Lm max error?)
F. Di Domeninco, J. Hancock, A. Steiner, J. Latly "600 W half bridge LLC eval board with 600 V CoolMOS™ C7 and digital control by XMC™" AN_201411_PL52_005, Infineon Technologies, 2016-04-21,
pg. 25 https://www.infineon.com/dgdl/Infineon-ApplicationNote-600W-HB-LLC-Evalboard-with-C7600V-and-digital-control-by-XMC-AN-v01_00-EN.pdf?fileId=5546d46253f6505701544cc1d15c20d7 (Lm max error?)
"Bidirectional CLLLC Resonant Dual Active Bridge (DAB) Reference Design for HEV/EV Onboard Charger" TIDUEG2C, Texas Instruments, March 2020,
Section 2.2.1.3 (pg. 11) https://www.ti.com/lit/ug/tidueg2c/tidueg2c.pdf A. Scuto "Half bridge resonant LLC converters and primary side MOSFET selection" AN4720, STMicroelectronics, August 2015,
https://www.st.com/resource/en/application_note/dm00207043-half-bridge-resonant-llc-converters-and-primary-side-mosfet-selection-stmicroelectronics.pdfJ. Luo, J. Wang, Z. Fang, J. Shao, J. Li "Optimal Design of a High Efficiency LLC Resonant Converter with a Narrow Frequency Range for Voltage Regulation" Energies
2018,
11, 1124.
pg 5-7 https://www.mdpi.com/1996-1073/11/5/1124Bouvier, Y.E.; Serrano, D.; Borović, U.; Moreno, G.; Vasić, M.; Oliver, J.A.; Alou, P.; Cobos, J.A.; Carmena, J. "ZVS Auxiliary Circuit for a 10 kW Unregulated LLC Full-Bridge Operating at Resonant Frequency for Aircraft Application" Energies
2019,
12, 1850. pg. 9-13
https://www.mdpi.com/1996-1073/12/10/1850 (Introduces new circuit elements to help ZVS range)
M. O'Loughlin "Improving ZVS and Efficiency in LLC Converters" SLUA923, Texas Instruments, December 2018
https://www.ti.com/lit/an/slua923/slua923.pdf (Poor estimation of Ippk)
S. Maniktala "Understanding and using LLC Converters to Great Advantage" Microsemi, 2013
https://www.microsemi.com/document-portal/doc_download/129464-understanding-and-using-llc-converters-to-great-advantage (Long winded, Conversational)
R. Nielsen "LLC and LCC resonance converters Properties Analysis Control" Runo's Power Design, August 2013
http://www.runonielsen.dk/LLC_LCC.pdf (Interesting discussion of control, also good clear engineering explanation of concepts)
System Target SpecsInput voltage: 40V-60V, 50V nominal
Output voltage: 40V-60V, 50V nominal
Power: 1kW nominal, 200W min to 1.2kW peak
Efficiency: >97% peak, >95% full range
Power density: >1kW/L
BidirectionalNotes on Targets- Input and output voltage set around 60VDC maximum for safety (DC voltage exposure limit).
- AC intermediate and tank voltage potentially dangerous but high frequency should prevent involuntary muscle contraction, main danger of burns.
- 1:1 nominal voltage ratio for simplicity, also not far from application ratio
- 1kW power trying to stay somewhat close to final application in at least magnitude of current and thus class of components and design
- 20% minimum load similar application
- 120% load head room also desirable
- Efficiency targets just below achieved performance of other reference designs
- Would be nice to achieve and test bidirectional functionality
Topology: Dual Active Bridge CLLCThe dual active bridge CLLC topology appears to be ideal for our system requirements due to overall high performance: best efficiency, best power density and bidirectionality; this is reflected in current industry trends towards resonant CLLC conversion solutions. LLC is nearly the same topology and has less complexity but CLLC symmetry allows bidirectionality. There are known difficulties in regulating LLC converter outputs but the intended application has simple output regulation requirements (battery charging over limited range) though it would be good to have a generally applicable design/method. Galvanic isolation provided by the topology is also a bonus. The dual active bridge configuration means full bridge input drive and output synchronous rectification is used to enable maximum utilisation of components (particularly magnetics) and minimisation of losses whilst enabling bidirectionality.
Alternative PWM topologies:Some of the other options available are PWM based conversion topologies i.e. buck-boost types (including SEPIC, Cuk, flyback), push-pull, non-resonant half bridge and non-resonant full bridge.
All these PWM options are non-resonant thus do not provide soft-switching or zero-voltage-switching (ZVS) i.e. they are hard-switching. This means the transistors used for switching are turned on under significant applied voltage. This is an issue because parasitic capacitance across the transistor causes charge to build up across the transistor with applied voltage which at turn-on is dumped through the transistor resulting to lost energy as heat and EMI. This is particularly an issue then operating at very high frequencies and voltages where this turn-on loss becomes a significant limit to system performance.
The buck-boost type topologies also rely on significant energy stored in an inductor to perform conversion which places extra demand on the magnetics used with higher DC flux and larger flux swings which tend to result in larger overall magnetics requirements and magnetics losses. By comparison, push-pull, half-bridge and full-bridge "true" transformer (not flyback mutual inductor "transformer") based topologies primarily use direct \$\frac{d\Phi}{dt}\$ flux swing coupling to perform conversion which means both flux and flux swings tend to be lower making them more suitable for higher current applications.
Buck-boost type topologies apart from flybacks are also not galvanically isolated which is potentially a safety issue in some applications.
Alternative resonant topologies are: Series resonant, Parallel Resonant, LLC and CCL.
These topologies and their variant forms use some form of resonant tank to which the output is coupled via a transformer. By performing switching across a resonant/reactive tank, switching can be coordinated such that turn-on occurs during zero voltage across the transistor. The difficulty with such topologies is that regulation of output is more complex, typically relying on frequency modulation in order to modulate impedances whilst maintaining ZVS. Between these different flavours of resonant topology, there are some different characteristics such as their response loads and frequency but among them LLC is known to be able to be tuned to have the most useful response. Sam Ben-Yaakov has a excellent video lecture on the topic here:
CLLC is simply a modification of LLC with added secondary series capacitance in order to produce symmetry.
The potential for advanced, mixed-frequency/phase/PWM control systems using modern DSP is also opening up flexibility and performance of resonant topologies.
A fairly detailed albeit not exhaustive overview of switch mode topologies with their advantages and disadvantages can be found here:
M. Kamil "Switch Mode Power Supply (SMPS) Topologies (Part I)" AN1114, Microchip Technology, 2007,
http://ww1.microchip.com/downloads/en/appnotes/01114a.pdfNote on CLLC vs CLLLC:The topology presented and analysed by me here I think should technically be called
CLLLC but terminology in the literature is inconsistent. I came across this PhD dissertation today which makes a clear distinction between the two
https://vtechworks.lib.vt.edu/handle/10919/77686. However, if you search for CLLC you'll find many papers presenting and discussing circuits with a discretely modelled LC secondary tank. So far CLLC seems to be more commonly used to describe the topology I'm using here so I'm going with that term.
Critical Component Selection and Component Driven Operational ParametersI’m taking a slightly different, (hopefully) more pragmatic approach to design compared to literature here. The optimal design is constrained by available critical components capable of handling system requirements. Thus rather than first setting operational parameters based on high level system requirements then finding components to fit calculated values, instead the highest performance components available are found first then system operating parameters adjusted to optimise their implementation.
Note on operating frequency: Higher operating frequency means smaller capacitors and inductors can be used but increasing frequency has a limit due to increasing losses with higher operating frequency; particularly in the semiconductor and magnetic components. Lower operating frequency reduces switching losses but requires larger capacitors and inductors to reduce resonant frequency and circuit impedances. The maximum power density is achieved by selecting the components which enable highest frequency operation with acceptable losses.
Ferrite CoreResonant frequency: ~300 kHz
Switching frequency range: 300 kHz-700 kHz
Recommended frequency range of modern power ferrites. High frequency required to achieve power density targets.
\$A_e\$ =200mm² to 600mm²
\$l_g\$ = 0.1mm to 2.0mm
\$B_{max}\$ =50mT
Specs for acceptable size and cost cores intended for HF power applications. Note \$B_{max}\$ is loss/thermally limited well below saturation for HF applications. My main contenders for core material: Epcos-TDK N49 (N87 and N97 for <500kHz), Ferroxcube 3F36, Fair-Rite 79.
Feasible inductance calculated later based on manufacturer recommended maximum flux at operating frequency, reasonable core gap, and peak magnetising current for reasonable size and cost cores.
MOSFET\$C_{oss}\$ = 620 pF
\$t_d > t_{off}\$ = 51 ns
\[L_{m(Cossmax)}< \frac{t_d}{16 C_{oss} f_{sw(max)}} = \frac{60n}{16*620p*800k}=7.56uH \label{eq:LmCossmax} \]
Not sure about the above formula for maximum inductance required for MOSFET body diode biasing based on MOSFET output capacitance calculation. I can’t find reference with derivation nor have I been able to derive it myself can get the same value as literature.
Edit: The \$f\$ value used should actually be \$f_{r}\$ the primary series resonant frequency. \$f_{sw(max)}\$ which is larger than \$f_{r}\$ will produce a tighter bound however probably isn't actually necessary for ZVS as calculated by the above equation.
Values are from datasheet specifications of TK46A08N1. Possible alternative: CSD19503KCS.
Optimal MOSFET selected based on cost vs estimated loss balance. Beware high switching losses due to high frequency operation. An approximate power loss of a single MOSFET under hard switch-on (but not reverse recovery) for comparative purposes can be calculated:
\[P_{MOSFET} = \frac{1}{2} I_{D(RMS)}^2 R_{D(on)}+ \frac{1}{2}V_{DS} I_{D} (T_{rise}+T_{fall}) f_{sw}+ \frac{1}{2} V_{DS}^2 C_{oss} f_{sw}+ Q_{G} V_{GS} f_{sw} \label{eq:P_MOSFET}\]
Resonant Capacitor\$C_r\$ < 400 nF
Limit based on available values for MLCC C0G capacitors. Maximum of 4 paralleled 100nF. Will need parallel capacitors to handle resonant currents. For X7R, X6S, etc. capacitors current handling is too low and less stable capacitance will cause operating point drift. Film capacitors cannot handle high frequency voltage swings; excessive heating, likely reliability issues.
First Harmonic AnalysisIt is useful to analyse and understand the CLLC circuit as an approximate, linearised, first harmonic equivalent to develop a “first order” intuitive understanding of the circuit behaviour.
Above is a simplified model for a full bridge CLLC converter operating in one direction. A square wave input source feeds a series LC resonant tank in series with a transformer represented as an ideal transformer with a discrete magnetising inductance parallel to the primary winding. The transformer secondary outputs to another LC tank followed by a full bridge rectifier to a smoothing capacitor and resistive load.
The non-linear model can be simplified to the above linear network. Secondary side components are replaced with “reflected” equivalents according to the transformer ratio and the non-linear rectified DC load is replaced with an equivalent power resistive load. Equations for the linearised components are:
\[R_{ac}=\frac{8}{\pi^2} R_L\]
\[R_{ac}'=N^2 R{ac}\]
\[L_{rs}'=N^2 L_{rs}\]
\[C{rs}'=C_{rs}/N^2\]
\[V_{out}'=NV_{out}\]
Reactances are by definition:
\[X_p=j(2\pi f L_{rp} - 1/(2fCrp))\]
\[X_s'=j(2\pi f L_{rs}' - 1/(2fCrs')) = j N^2(2\pi f L_{rs}-1/(2\pi f C_{rs}))\]
\[X_m=j2\pi f L_m\]
\$j\$ is the imaginary coefficient
GainA “gain” M for the network can then be easily found using series-parallel simplification:
\[M = \frac{N V_{out}}{V_{in}} = \frac{V_{out}'}{V_{in}} =\frac{ X_m||(X_s'+R_{ac}')}{X_p+X_m||(X_s'+R_{ac}')} \frac{R_{ac}'}{X_s'+R_{ac}'} \label{eq:M_series_parallel}\]
\[M = \frac{X_m R_{ac}'}{X_m X_p + X_s'(X_m+X_p)+R_{ac}'(X_m+X_p)} \label{eq:M}\]
Most literature also defines a \$Q=\frac{X_p}{R_{ac}}\$ factor but I haven't found this particularly useful to cleaning up equations, better understanding general behaviour or practical application where using \$R_{ac}\$ tends to be more direct than calculating the additional \$Q\$ value.
Further Analytical ExplorationMost literature seems to skip further analytical exploration after deriving the gain function and go straight to plots with example numerical values but some general behaviours can be discerned by poking at this equation further. If you're allergic to math or otherwise have an aversion to phasor analysis then skip to the
Numerical Values and Simulation section.
There are two major points of interest, resonance of the primary tank and "resonance" of the primary tank with the transformer magnetising inductance.
Resonance of the primary tank will occur at
\[f_{rp} =\frac{1}{2\pi \sqrt{L_{rp} C_{rp}}} \]
and by definition at this operating frequency \$X_p \rightarrow 0\$. If the secondary tank is matched to the primary tank \$ X_p = X_s'\$ then at this resonance we also have \$X_s' \rightarrow 0\$
Resonance of the primary tank with the transformer magnetising will occur at
\[f_{rpm} =\frac{1}{2\pi \sqrt{(L_{rp}+L_m) C_{rp}}} \]
and by definition at this operating frequency \$X_p +X_m \rightarrow 0\$.
Gain ContinuedAt Primary ResonanceSubstituting \$X_p \rightarrow 0\$ into the equation for \$M\$ obtains the gain at resonance of primary tank
\[M_{(rp)} = \frac{R_{ac}'}{X_s'+R_{ac}'}\]
When the secondary tank is matched \$X_s' \rightarrow 0\$ this reduces to:
\[M_{(rp)} = \frac{R_{ac}'}{R_{ac}'} = 1\]
Which an also be deduced intuitively looking at the FH network. It's also noted the gain is always and completely real at this resonant frequency.
At Primary Tank + Transformer ResonanceSubstituting \$X_p +X_m \rightarrow 0\$ into the equation for \$M\$ obtains the gain at resonance of primary tank with transformer magnetising inductance
\[M_{(rpm)} = \frac{R_{ac}'}{X_p}\]
A high gain can be produced at this operating point by a smaller primary impedance relative to the load resistance. Also due to the initial resonance condition \$X_m+X_p \rightarrow 0 \Rightarrow X_p=-X_m\$
\[M_{(rpm)} = \frac{R_{ac}'}{-X_m}=\frac{R_{ac}'\sqrt{(L_{rp}+L_m)C_{rp}}}{-j L_m}\]
Thus a smaller \$L_m\$ will increase gain at primary + transformer resonance at \$f_{rpm}\$. Note this \$f_{rpm}=\frac{1}{2\pi \sqrt{(L_{rp}+L_m) C_{rp}}} \$ must be lower than the primary tank resonance frequency \$f_{rp} =\frac{1}{2\pi \sqrt{L_{rp} C_{rp}}}\$ and using a much larger \$L_m>L_{rp}\$ can push this resonant frequency \$f_{rpm}\$ far down below the primary \$f_rp\$ resonant frequency. Notably \$X_s'\$ has no effect. Intuitively, a very large \$R_{ac}'\$ will result in the first harmonic network degenerating to a high Q series LC tank consisting of the primary tank and transformer magnetising inductance which at it's resonance frequency will of course resonate and produce a very large circulating current and voltage.
It is also noted that the output gain is always and completely imaginary at this operating frequency.
Load CurrentAt Primary + Transformer Resonance\[I_{Rac(rpm)} = \frac{V_{out(rpm)}}{R_{ac}'} = \frac{N M_{(rpm)} V_{in}}{R_{ac}'} = \frac{N V_{in}\sqrt{(L_{rp}+L_m)C_{rp}}}{-j L_m}\]
This is not dependent on \$R_{ac}'\$ so the converter will theoretically operate at a constant current independent of load. Realistically, there will likely be a limit in output voltage due to the current in the primary + transformer tank.
Magnetising CurrentThe first harmonic model can also be used to derive the magnetising current \$I_m\$ which is useful for determining if the transformer field density.
\[I_m = V_{in} \frac{X_s'+R_{ac}'}{X_m X_p + X_s'(X_m+X_p)+R_{ac}'(X_m+X_p)} \label{eq:I_m}\]
At Primary Resonance\[I_{m(rp)}=\frac{V_{in}}{X_m}\]
The \$I_m\$ will only decrease for frequencies greater than \$f_{rp}\$ since both \$X_m\$ and \$X_p\$ can only increase. Magnetising current is always and completely imaginary at primary resonance frequency.
At Primary Tank + Transformer Resonance\[I_{m(rpm)} = V_{in} \frac{X_s'+R_{ac}'}{X_m X_p}\]
As before in the gain analysis, due to the initial resonance condition \$X_m+X_p \rightarrow 0 \Rightarrow X_p=-X_m\$
\[I_{m(rpm)} = V_{in} \frac{X_s'+R_{ac}'}{-X_m^2}\]
Supposition: This will typically be greater than \$I_{m(rp)}\$ unless \$X_s'+R_{ac}'\$ is very low since \$X_m\$ at this operating point will typically be much smaller due to lower frequency.
Also noting unlike the previously calculated values, this will have a complex (not completely imaginary or real) value.
Max InductanceUsing \$I_{m(rp)}\$ in the conventional equation for estimating maximum inductance for a core of given cross sectional area, core gap, magnetising current and maximum allowed flux density (ignoring winding window/wire size):
\[L_{m(Bmax)} < \frac{l_g B_{peak}^2 A_c}{\mu_0 I_{m(max)}^2} = \frac{2 \mu_0 V_{in}^2}{l_g B_{peak}^2 A_c \omega_r^2}\]
Reducing peak flux density will reduce losses and it can be seen that reducing peak flux density means increasing magnetising inductance. Alternatively, peak flux can be reduced by:
Increasing:
- Core cross sectional area
- Frequency (will have have trade-off vs Steinmetz loss)
- Gap length
Decreasing:
LC TankThe current and voltage in the resonant tank is also good to know to understand the stresses and likely losses in the resonant tank components.
Primary Side CurrentThe solution to the first harmonic network for current through the primary side inductor/capacitor is:
\[I_p = \frac{V_{in} (R_{ac}' + X_m + X_s')}{X_m X_p + X_s'(X_m+X_p)+R_{ac}'(X_m+X_p)}\]
At Primary Resonance\[I_{p(rp)} = \frac{V_{in}(R_{ac}'+X_m+X_s')}{X_m(X_s'+R_{ac}')} = \frac{V_{in}}{X_m||(X_s'+R_{ac}')}\]
The primary current is determined by the parallel impedance of the magnetising inductance and secondary side impedance as one would expect. Maintaining a higher magnetising inductance for the
transformer will ensure the tank current does not become excessive under no load (as with a normal transformer).
At Primary Tank + Transformer Resonance\[I_{p(rpm)} = \frac{V_{in}(R_{ac}'+X_m+X_s')}{X_m X_p} = \frac{V_{in}(R_{ac}'+X_m+X_s')}{-X_m^2} \]
As with primary current at primary resonance, the current is determined by magnetising inductance impedance and total secondary side impedance Xs'+Rac' but the proportionality to secondary side impedance is flipped so larger impedance results in larger current rather than smaller.
Also if \$X_s' = X_p\$ then \$ X_m+X_s' \rightarrow 0 \$
\[I_{p(rpm)} = \frac{V_{in}R_{ac}'}{-X_m^2} \]
Note this current will be completely real i.e. there will be no reactive current circulating in the tank. This also implies all input power must be dissipated via the load resistor.
Voltage Across CapacitorCapacitors are typically components with limited voltage handling capability and in the resonant tank, the capacitor could be exposed to voltages much higher than the input.
\[V_{Crp} = I_p X_{Crp} = \frac{V_{in} X_{Crp}(R_{ac}' + X_m + X_s')}{X_m X_p + X_s'(X_m+X_p)+R_{ac}'(X_m+X_p)}\]
We can also write this as a gain:
\[m_{Crp} = \frac{V_{Crp}}{V_{in}} = \frac{X_{Crp}(R_{ac}' + X_m + X_s')}{X_m X_p + X_s'(X_m+X_p)+R_{ac}'(X_m+X_p)} \]
Gain at the two resonant points is similar to the primary current but now with the capacitor impedance factor.
At Primary Resonance\[m_{Crp(rp)} = \frac{X_{Crp}(R_{ac}'+X_m+X_s')}{X_m(X_s'+R_{ac}')} = \frac{X_{Crp}}{X_m||(X_s'+R_{ac}')}\]
If smaller \$C_{rp}\$ is used or magnetising inductance is low or load impedance is low then resonant capacitor voltage increases.
At Primary Tank + Transformer Resonance\[m_{Crp(rp)} = \frac{X_{Crp}(R_{ac}'+X_m+X_s')}{-X_m^2} \]
If smaller \$C_{rp}\$ is used or magnetising inductance is low then resonant capacitor voltage increases and lower secondary side impedance \$R_{ac}'+X_s'\$ increases resonant capacitor voltage.
If \$X_s' = X_p\$ then \$ X_m+X_s' \rightarrow 0 \$
\[m_{Crp(rp)} = \frac{X_{Crp} R_{ac}'}{-X_m^2} \]
Unlike primary current at \$f_{rpm}\$, this will be completely imaginary.