LLC Converter Capacitive and Inductive Regions

Simplified LLC Resonant Converter Operation for Beginners

Introduction

LLC Resonant Converter is a good topology for DC-DC conversion due to its soft switching feature. The current in primary switching devices will only flow when the voltage is zero. This is zero voltage switching or ZVS. An ideal LLC will operate at resonance. At resonance, the switching frequency is equal to the tank circuit resonant frequency.

The tank circuit resonant frequency is govern by the series inductance and series capacitance or the so called resonant inductance and resonant capacitance. At resonance, the gain of the LLC converter is unity. There is only a single point in which the resonance will occur. Outside resonance, the LLC will still operates well but there are some drawbacks that needs to be addressed by the design engineer.

LLC Resonance Converter Topology Variants

Single Phase LLC

For low power application, single phase is more preferable because the current on the power devices is only small. Single phase means that there is only one path for the current. Below diagrams are examples of single phase LLC.

Splitting Resonant Capacitor Half Bridge LLC with Full Wave Center Tap Secondary Using MOSFETs
Non-Splitting Resonant Capacitor Half Bridge LLC with Bridge Diodes Secondary

Single phase LLC can be configured as half bridge or full bridge. In above diagrams, Lr denotes the resonant inductor, Cr refers to resonant capacitor while Lm symbolizes the transformer magnetizing inductance. In actual application, there is no inductance across the transformer because it is just art of the transformer primary. The diagrams above are only showing the representation of the magnetizing inductance to emphasize the LLC (Lr, Lm and Cr).

Half Bridge LLC

A half bridge LLC means that there is only one pair of switching devices in the primary side like the diagrams above. They are both half bridge configurations since there are only S1 and S2 which form a single pair. In the first diagram, the equivalent resonant capacitance (the Cr in the second diagram) is the sum of the Csplit_A and Csplit_B.

Half bridge variant is mostly use in low power since the effective voltage across the LLC resonant network is only half the level of Vin. This results to a higher current in the resonant network, so the power devices may have high power loss.

Full Bridge LLC

Below is a full bridge LLC converter. There are two pairs of switching devices in the primary section (S1/S2 and S3/S4). Each pair will not conduct at the same time but it is S1 and S4 that turn on together as well as S2 and S3.

Full bridge is more popular at higher power application because the effective voltage across the LLC network is the whole Vin. This results to a smaller current in the resonant network.

Full Bridge LLC

Secondary Circuit Configuration

The secondary circuit configuration are either using diodes or switches. Switch is could be BJT, IGBT or MOSFET. First diagram above uses a MOSFETs switch while the second diagram uses a diodes.

Using a diode is simpler than using a switch because it requires no control mechanism. On the other hand, switch needs a control mechanism that synchronizes to the switches in the primary making it complex to implement.

The advantage of using a switch however is low voltage drop and low power loss. This means, high system efficiency.

Three-Phase LLC

Three-phase LLC is commonly used for very high power applications. As compared to single phase, this variant has three power paths for the current as indicated by Phase u, Phase v and Phase w.

This schematic is credited to ROHM Semiconductor. This is part of their application note of 5kW LLC that features their Silicon Carbide MOSFET (SiC).

Three-phase LLC is can be broken down into single phase and use the same analysis as the single phase variant.

Simplified LLC Resonant Network Model

LLC converter seems difficult to understand but it is not. There is a way to simplify the circuit using the FHA or first harmonic approximation. The FHA model is very easy to understand since it only includes the resonant capacitor, resonant inductor, magnetizing inductance and the equivalent AC resistance. Read the complete explanation how it is derived here.

Equivalent AC Circuit of LLC

Gain and Turns Ratio

The gain equation for half bridge LLC is

Gain = 2 x n x Vo / Vin

Where;

n – turns ratio of the transformer (primary divide by secondary)

Vo – secondary voltage (ideally this is also the output DC voltage neglecting the voltage drop of secondary diodes or the switches)

Vin – is the input voltage across the tank or LLC network

During the design stage, the LLC gain is set to one as this is the target. With this, the turns ratio could be determined as

Turns ratio, n = Gain x Vin / (2 x Vo), since the gain is unity, then

Turns ratio, n = Vin / (2 x Vo)

For full bridge LLC, the gain is

Gain = n x Vo / Vin

And the turns ratio during the design stage is

Turns ratio, n = Vin / Vo

To learn how the gain of LLC converter becomes unity, read Why LLC Resonant Converter Gain is Unity.

Peak Gain and Gain-Frequency Curve

Aside from the gain discussed above, there is also another gain which is the peak gain. When plotted on a gain-frequency curve, this is the top most point and correspond to a single frequency which is called the peak gain frequency. Peak gain is very useful because it can indicate where to clamp the minimum switching frequency to avoid the LLC entering the capacitive region. There are two regions an LLC can go and these are capacitive and inductive regions. Complete discussion about it will follow in the next section.

The vertical red line in the figure below denotes the peak gain of an LLC converter. The yellow vertical line is showing the LLC unity gain on the other hand.

LLC Gain -Frequency Curve Emphasizing the Peak Gain and Unity Gain

A gain-frequency curve is an illustration in graphical format like above. It is very important because it can give idea where the unity gain frequency as well as the peak gain frequency. This can easily be plotted using the simplified LLC circuit using FHA. Read How to Derive LLC Converter AC Circuit and and LLC Converter Gain-Frequency Curve for complete details.

LLC Quality Factor (Q)

In LLC the term quality factor is also popular. For an RLC circuit, this is the measure of selectivity. It is also defined as the characteristic impedance divided by equivalent ac resistance. In general, low Q circuits are wideband while high Q circuits are narrow band. Higher loads has higher while lower loads has low Q.

Resonant Frequencies

There are two resonant frequencies in LLC converter. The first one is due to the series inductor (Lr) and series capacitor (Cr). In below derivation, the resonant inductor and resonant capacitor are referred as Lres and Cres respectively.

The second resonant frequency is due to the combination of Lmag and Lres. This will likely to happen at very light load or absolute no load. At absolute no load, Rac is open circuit thus the equivalent circuit is a series circuit of Cres, Lres and Lmag.

LLC Converter Modes of Operation

At Resonance (Fswitch = Fresonant)

LLC can operate in three modes. First is at resonance. This means that the switching frequency of the LLC equates to the first resonant frequency discussed above. This is the ideal scenario an LLC converter must behave in order to maximize the soft switching action. Below are the attributes of operation at resonance frequency.

  • The tank or the resonant network input current (Ires) is near perfect sinusoid (critically discontinuous) because the reactive inductance and reactive capacitance cancels each other. See below plots.
  • Input voltage to the tank or the resonance network leads current because of Lmag
  • Before the current (I_Q1 and I_Q2) on the MOSFET starts to increase, the drain voltage is already zero therefore no switching losses (soft switching, ZVS)
  • Secondary current (Isec) is softly commutated
  • Magnetizing current (Imag) is triangular
Waveforms of LLC when Operating at Resonance

Above Resonance (Fswitch>Fresonant)

The characteristics of LLC at above resonance are below.

  • Tank input current (Ires) is continuous and not a perfect sinusoid
  • Resonant choke peak current is low
  • Lower magnetizing current
  • Input voltage to the tank leads current
  • Before the current on the MOSFET starts to increase, the drain voltage is already zero therefore no switching losses (soft switching, ZVS)
  • Lower peak current on MOSFET but not softly commutated that maybe a liability in terms of efficiency
  • Secondary current is not softly commutated (but has lower peak and RMS value)
Waveforms of LLC when Operating above Resonance

At above resonance, there is a big tendency that the LLC converter is very noisy and may have issue in EMC. This is because the switching frequency becomes higher.

Below Resonance (Fswitching<Fresonant)

The attributes of LLC operating below resonance are below.

  • Tank input current (Ires) is discontinuous
  • High peak current seen by the resonant choke (prone to saturation)
  • Magnetizing current (Imag) is high and core losses are also high (watch out core saturation). This is not good on efficiency.
  • Input voltage to the tank leads current as courtesy of Lmag
  • Before the current on the MOSFET starts to increase, the drain voltage is already zero therefore no switching losses (soft switching, ZVS).
  • Higher peak and RMS current on MOSFET. This is not good on efficiency.
  • Secondary current is softly commutated but has high peak and RMS value. This is not good on efficiency. This is also result to a higher ripple current on the output capacitors.
Waveforms of LLC when Operating Below Resonance

The drawback of this operating mode is higher losses on the power devices both primary and secondary due to the increase in rms value of the currents. The transformer loss will be high as well.

Capacitive and Inductive Regions

LLC converter may go to capacitive and inductive regions. The former is undesired while the latter is the desired one.

Both regions are separated by the peak gain. On the right of the peak gain is the inductive region and this is where LLC must operate. On the left side of the peak gain on the other hand is the capacitive region and this is not good for LLC.

Capacitive and Inductive Regions of LLC Converter

How to Avoid Capacitive Region

The simplest way to avoid capacitive region is to clamp the minimum switching frequency above the peak gain frequency.

Clamping the Switching Frequency above the Peak Gain Frequency to Avoid Capacitive Region

Boost Mode and Buck Mode

These terms are also used in LLC. For boost mode, the gain is higher than 1. This means the switching frequency will be lower than the resonant frequency.

Boost Mode of LLC

For buck mode, the LLC gain is lower than unity. This results to a switching frequency higher than the resonant frequency.

Buck Mode LLC

Resonant Network Current

This is the current that flows to the resonant inductor (Lr or Lres), resonant capacitor (Cr or Cres) and the primary winding of the transformer. Take note that this current is a peak value.

Derivation of LLC Converter Resonant Network Current

Where;

Io – is the output current

n – is the transformer turns ratio

Vo – is the output voltage (neglecting the drop of the secondary diodes or switches)

L – is the magnetizing inductance Lmag

Freq – is the operating switching frequency. At resonance, Freq is equal to the resonant frequency.

Eff – is the efficiency and it is part of the equation to somehow get the maximum level of the primary current. At ideal case however, this can be neglected.

Resonant Capacitor RMS Current and Voltage

The resonant capacitor (Cr or Cres) rms current is

Irms Cr = 0.707 x Ipri

Its voltage is derived below

LLC Resonant Capacitor RMS Current and Voltage Derivation

Primary Switch Current and Voltage

The current in each switch (half bridge LLC) or pair of switches (full bridge LLC) is following the half wave shape. The rms value is

Irms primary switch = 0.5 x Ipri

LLC Primary Switch Current Derivation

Regardless of half bridge or full bridge LLC, the voltage that the switches will see is ideally the level of the input voltage (Vin). However, once the LLC converter operates at above resonance, there is significant spike on top to the ideal voltage.

Transformer Magnetizing Current

This is the current that the transformer core can see. Actual measurements using scope can’t detect it. The determination of this value relies on calculation. See below derivation.

Derivation of Magnetizing Current of LLC Converter

Secondary Current

The secondary current shape of the LLC is just the same with the primary current just differs in the magnitude. On the other hand, the current after the diode or the secondary switch but before the output capacitor is a full wave shape since the secondary diodes or switches configuration is full wave or bridge. The shape is a perfect full wave if the LLC is at resonance.

LLC Converter Secondary Current Waveform

The value of Idc is just the LLC DC output current. For a full wave, the DC value is

Idc fullwave = (2 / pi) x Ipeak

Since the DC value is known, the Ipeak is can be determined by re-arranging the equation as

Ipeak = (pi / 2) x Idc full wave

For full bridge rectification using diode as the diagram in the left below shows, the diodes D1 and D3 will conduct at the same time as well as D2 and D4 are together also.

Either diode pairs will only see half wave current shape. Thus, the Irms and Idc of these diodes are

Irms diode = 0.5 x Ipeak

Idc diode = 0.308 x Ipeak

In the same manner, if the secondary rectification configuration is same as the second diagram above, each MOSFET will see half wave current only. Thus, the Irms and Idc are also

Irms MOSFET = 0.5 x Ipeak

Idc MOSFET = 0.308 x Ipeak

Output Capacitor Ripple Current

The ripple current of the output capacitor is can be calculated using the full wave shape secondary current. See below derivation.

Derivation of Output Capacitor Ripple Current

Saturation of Transformer and Inductor

The transformer must have plenty of margins against saturation. The equation for saturation (Bsat) is

Likewise, the resonant inductor must have lot of margins from saturation. The saturation equation is

Challenges of LLC Resonant Converter

There are known challenges of using LLC resonant converter. However, these all can be mitigated by careful analysis and putting corrective actions.

  1. Higher no load or very light load ripple voltage due to the flatness of the gain
  2. Higher tank or resonant network current at startup
  3. Primary MOSFET voltage stress is high due to high frequency spikes when the converter operates above resonance.
  4. Poor EMI performance at above or below resonance (more pronounced above resonance)
  5. Short circuit protection should be fast as possible
  6. Hold up requirement suffers at below resonance
  7. Higher stress on the output capacitors when operating below resonance
  8. Thermal problems in higher voltage (more than the voltage where resonance is set) for wide range operation
  9. Lower efficiency at operation below resonance

Fell free to share your inputs, raise your questions and comments. Let’s discuss.

One comment

  1. Excellent content..just one question,not able to understand the waveforms for switching frequency more than and less than resonant frequency case ..why waveform of resonant current is like that and diode current as well ? If you could simply this that we would be great help

Leave a Reply

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed.