谐振电容（MKP薄膜电容或者MLCC电容）在大功率LLC电路中可以串联使用嘛?

[海阔天空]

Can resonant capacitors (MKP film capacitors or MLCC capacitors) be used in series in high-power LLC circuits?

If the voltage rating is insufficient at high frequencies, can these capacitors be connected in series? If so, should voltage balancing resistors be added?

[ABC]

1. Can resonant capacitors be connected in series in high-power LLC circuits?

Conclusion: They can be connected in series, but only recommended as an “emergency/temporary” solution. For high-power LLC circuits, prioritize a single high-voltage, high-ripple-current dedicated resonant capacitor (e.g., MKP CBB65/85 series, industrial-grade MLCC). If series connection is unavoidable due to insufficient voltage rating at high frequency, strict voltage-sharing and current-sharing design must be implemented; otherwise there is a serious reliability risk.

Core limitations (key issues with series connection):

1. Capacitance tolerance dispersion: Even capacitors from the same batch have capacitance deviations (±5%~±10%) that cause uneven voltage division in series (voltage is inversely proportional to capacitance: U_1/U_2 = C_2/C_1 ). A capacitor with smaller capacitance will bear higher voltage and is prone to breakdown.
2. High-frequency parasitic parameter effects: LLC operating frequencies are usually 50 kHz~1 MHz. The capacitor’s equivalent series resistance (ESR) and equivalent series inductance (ESL) become more prominent at higher frequencies; when capacitors are placed in series, parasitics add up, which can shift the resonant frequency, increase losses, and cause severe heating.
3. Special risks of MLCCs: MLCCs exhibit a “DC bias effect” (the higher the voltage, the more the capacitance degrades). When used in series, unequal bias voltages further exacerbate capacitance differences, making voltage-sharing imbalance worse than with MKP. Also, MLCCs have poor ripple-current capability and are prone to failure from heating in high-power applications.

2. Is it necessary to add voltage‑balancing resistors when connecting in series?

Conclusion: Mandatory! And they must be part of a voltage-balancing circuit design—capacitors alone cannot ensure voltage sharing.

Design points for the voltage‑balancing resistors:

1. Resistance value selection principle:
   • Resistors are connected in parallel across each capacitor to form a “forced voltage-balancing loop.” The resistor value should satisfy: R \\ll X_C = 1/(2πfC) (where X_C is the capacitive reactance), ensuring the resistors dominate the voltage division and compensate for capacitance tolerance differences.
   • Example: LLC frequency 500 kHz, resonant capacitor 1 μF, \( X_C ≈ 318Ω \), then the resistor should be chosen below 1 kΩ (commonly 100~500 Ω), and power calculated by \( P = U^2/R \) (U is the rated voltage of a single capacitor), with a 2~3× margin (resistor heating increases at high frequency).
2. Resistor type selection:
   • Prefer metal-film resistors (low temperature coefficient, good high-frequency characteristics); avoid carbon-film resistors (poor stability). For high-power scenarios, use power resistors or multiple resistors in parallel.
3. Additional optimizations (for high-power scenarios):
   • Paralleled balancing capacitors: Paralleling a small-value, high-voltage, non-inductive capacitor across each series capacitor (e.g., 0.1 μF CBB) helps compensate for parasitic differences at high frequency.
   • Series balancing inductors: If ripple-current differences are large, small series inductors (nH range) can be added to suppress circulating currents, but this increases circuit complexity.

3. Alternatives to series resonant capacitors in high-power LLC (preferred)

1. Use dedicated high-voltage resonant capacitors:
   • MKP film capacitors: choose voltage rating ≥2× the bus voltage (e.g., for a 400 V DC bus, choose MKP rated 1000 V AC / 800 V DC), ripple current rating ≥2× the LLC resonant peak current, and marked for “high-frequency resonant use” (low ESR, low ESL).
   • Film capacitor modules: manufacturer-prefabricated multi-cell series modules with built-in voltage-balancing resistors and thermal design; reliability is far higher than DIY series connections.
2. Optimize the LLC topology:
   • If the bus voltage is too high (e.g., 800 V DC), consider changing from a half-bridge LLC to a full-bridge LLC to reduce voltage stress per leg, thereby lowering the voltage rating required for the resonant capacitor.

4. Risk notices

• The failure rate of DIY series capacitors is much higher than a single dedicated capacitor—especially in high-power (≥10 kW), high-frequency (≥500 kHz) scenarios—where voltage-sharing failure can lead to capacitor breakdown and catastrophic device failure.
• MLCCs are not recommended for high-power LLC resonant circuits (poor ripple and surge tolerance). Even if series-connected, they are only suitable for low-power auxiliary circuits; for high-power applications use MKP film capacitors.

5. Summary

Scenario	Series connection allowed?	Need voltage‑balancing resistors?	Recommendation priority
Small power (<1 kW), low frequency (<100 kHz) emergency use	Yes	Must add	Low
High power (≥10 kW), high frequency (≥500 kHz)	Not recommended	-	Prohibited
Dedicated high-voltage capacitors available	No need to series	-	High

[CCC]

Yes, resonant capacitors (both MKP film and C0G/NP0 MLCC types) can be used in series in high-power LLC circuits. In fact, this is a standard design practice when the resonant voltage stress exceeds the rating of a single component.

Regarding your second question: No, you generally do not use voltage-dividing resistors for resonant capacitors in high-frequency LLC circuits.

The detailed technical reasoning and design guidelines are below.

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1. Using Resonant Capacitors in Series

In high-power LLC converters, the voltage across the resonant capacitor (V_{Cr}) can be very high, often exceeding the input DC voltage (V_{in}) depending on the quality factor (Q) and load conditions.

• Why Series? If your calculated peak resonant voltage is 1200V but your preferred MLCC or MKP capacitor is rated for 630V or 1000V, putting two in series doubles the withstand capability.
• The Trade-off: Remember that series connection reduces total capacitance:1

C_{total} = \frac{C_{individual}}{N}

(Where N is the number of capacitors in series). You will likely need to place multiple strings in parallel to recover the required capacitance and handle the high resonant RMS current.2

MKP vs. MLCC in Series

• MLCC (Class 1 / C0G / NP0): These are excellent for series connection because their capacitance is extremely stable regardless of voltage, temperature, or frequency.3
• MKP (Polypropylene Film): These are also highly suitable and robust. However, they are physically larger.

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2. Why Balancing Resistors are NOT Recommended

You typically see balancing resistors across DC link electrolytic capacitors to handle leakage current differences. However, resonant capacitors operate differently:

A. Voltage Division is determined by Impedance (X_c), not Resistance

In an AC resonant circuit, the voltage across each capacitor in a series string is determined by its impedance (Z = \frac{1}{j\omega C}). The current (4$I_{resonant}$) flowing through the series string is identical for all capacitors.5 Therefore, the voltage drop across each capacitor is:

V_n = I_{resonant} \times X_{Cn} = \frac{I_{resonant}}{2\pi f C_n}

This means voltage sharing is purely a function of the capacitance tolerance.

• If C_1 = 100nF and C_2 = 100nF, they share voltage 50/50.
• If C_1 = 95nF and C_2 = 105nF, the smaller capacitor (95nF) will have higher impedance and take more voltage stress.

B. Resistors cause Power Loss

Resonant capacitors handle high-frequency AC (often 50kHz to 500kHz+). A balancing resistor effective enough to influence the voltage distribution (i.e., with impedance comparable to the capacitor’s impedance) would dissipate massive amounts of power, destroying efficiency.

• Example: A 100nF cap at 100kHz has an impedance of \approx 16\Omega. To “balance” this with a resistor, you’d need a very low resistance value, which would basically short out the circuit. High-value resistors (e.g., 100 \text{k}\Omega) are essentially “invisible” to the high-frequency current and provide no AC balancing.

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3. Critical Design Requirements for Series Connection

Since you cannot use resistors, you must ensure voltage balance through component selection and layout:

1. Tight Tolerance is Mandatory:

• Do not use standard ±10% or ±20% capacitors.
• Use ±5% (J) or ±1% (F) tolerance capacitors.
• MLCC: Use C0G/NP0 dielectric. Avoid X7R/X5R at all costs (their capacitance changes with voltage bias, leading to catastrophic runaway imbalance).
• MKP: Use high-quality polypropylene film.

2. Identical Part Numbers: Always use the exact same part number from the same manufacturer (and ideally the same production batch) to ensure the capacitance vs. frequency curves match perfectly.
3. Symmetrical PCB Layout:At high frequencies (100kHz+), stray capacitance to ground can disturb the voltage balance.

• Ensure the PCB traces and copper pours around the series capacitors are symmetrical.
• Avoid placing one capacitor in the string very close to a grounded heatsink while the other is floating, as this creates parasitic capacitive coupling that can unbalance the voltage.

Summary Checklist

Feature	Guideline
Series Connection?	Yes, highly recommended for high-voltage withstand.
Balancing Resistors?	No, do not use them. They are ineffective for AC and cause loss.
Capacitor Type	C0G/NP0 MLCC (Best density) or MKP Film (High robustness).
Tolerance	Must be ±5% or better.
Derating	Leave at least 20-30% voltage margin. If the theoretical split is 600V each, use 800V or 1000V rated caps.

[小聪同学]

Let me state the conclusion first:

• Theoretically, MKP film capacitors or MLCCs (especially C0G/NP0) can be connected in series in the LLC resonant position to increase the equivalent voltage rating.
• But “can” does not equal “recommended”:
  • Series connection of MLCCs brings issues of mechanical stress, reliability, layout, and additional losses. In high-power LLC, it’s generally preferred to directly select a high-voltage C0G/MKP resonant capacitor rather than stacking many small capacitors in series.
  • If series connection is indeed used, especially for capacitors with relatively large leakage current like MKP, paralleling balancing resistors across each capacitor is a common and reasonable practice. For capacitors with extremely low loss and extremely low leakage current like C0G/NP0, the role and necessity of balancing resistors are somewhat weaker, but they can still be used as a safety measure, just with larger resistance values to reduce losses.

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Let’s expand on several key points below.

1. First, Look at the Operating Conditions of LLC Resonant Capacitors: High Voltage + High Frequency + High Current

The resonant capacitor C_r in LLC operates in a series resonant circuit, characterized by:

• It withstands “AC voltage,” not pure DC bias;
• Voltage peaks often approach or reach the swing of the half-bridge midpoint voltage (for example, with a 400 V bus, the midpoint swings approximately 0–400 V, and the AC peak on the resonant capacitor is related to this magnitude);
• The resonant capacitor carries high-frequency, high-current (tens of kHz to hundreds of kHz, several A to tens of A), so the following are required:
  • Equivalent Series Resistance ESR (losses),
  • current ripple capability,
  • frequency characteristics (stable capacitance value, low loss angle)
    are all relatively high.

Therefore, LLC resonant capacitors are generally selected as:

• C0G/NP0 MLCCs: extremely stable capacitance, minimal losses, suitable for resonant capacitors. Many manufacturers have high-voltage C0G resonant capacitor solutions for LLC/DCDC/OBC.
• Or dedicated MKP film resonant capacitors: high voltage rating, strong current capability, widely used in power electronics.

2. Series Connection Can Increase Equivalent Voltage Rating, But What Are the Issues in LLC?

From the principle of capacitor series connection:

• N identical capacitors C in series, equivalent capacitance is C/N;
• Under ideal conditions, each capacitor shares 1/N of the total voltage, so the “equivalent voltage rating” can be stacked.

But when placed in the specific position of the “LLC resonant tank,” the following must be considered:

1. Frequency and Losses Will Change

• After series connection, equivalent capacitance decreases. To maintain the same resonant frequency, the individual capacitor value needs to be made larger;
• Series connection introduces additional connection resistance and inductance, potentially increasing ESR and parasitic parameters, affecting resonant characteristics and efficiency.

2. Voltage Imbalance Caused by Leakage Current / Insulation Resistance Differences

• In reality, the leakage current (or insulation resistance) of each capacitor cannot be completely identical;
• Under the operating condition of “DC + AC” superposition, the DC bias component will be distributed according to the insulation resistance of each capacitor, potentially causing some capacitor to withstand high voltage for a long time, accelerating aging and increasing the risk of breakdown.
• This is exactly the problem that “adding parallel balancing resistors in series” aims to solve (discussed separately later).

3. Special Attention for MLCCs: Mechanical Stress and Reliability

• Large-size high-voltage MLCCs (such as 1812, 2220, 2225 packages) are very sensitive to PCB deformation and thermal expansion;
• LLC is often high-power with significant heating and thermal cycling. Multiple MLCCs connected in series and placed on the board are more prone to cracks due to stress, leading to short circuits or failure;
• Many manufacturers’ application guides emphasize: high-voltage ceramic capacitors require special attention to mechanical mounting, soldering profile, and PCB layout to avoid cracking.

4. Increased Layout and Loop Inductance

• The LLC resonant circuit is very sensitive to parasitic inductance;
• Series connection means an additional set of traces and solder joints, making the loop longer and increasing parasitic inductance, which may affect ZVS conditions and EMI.

Therefore:

• In engineering practice, the more common approach for LLC resonant capacitors is: select a single high-voltage C0G or MKP capacitor that already meets the voltage rating and capacitance requirements, rather than stacking many small capacitors in series to achieve the voltage rating.
• Series connection is more like an “emergency measure” or “compromise solution” when suitable high-voltage capacitors cannot be purchased.

3. Should Balancing/Voltage-Sharing Resistors Be Added?

1. In Principle: What Problem Does Parallel Balancing Resistor Solve?

When capacitors are connected in series, if the insulation resistance/leakage current of each capacitor is inconsistent:

• DC bias voltage will be distributed according to the proportion of insulation resistance, rather than ideally according to the proportion of capacitance;
• Capacitors with large leakage current will have lower voltage division, while capacitors with small leakage current will bear higher voltage;
• In severe cases, some capacitor will operate long-term near or above its rated voltage, reducing lifespan or even causing breakdown.

Therefore, the common practice in power electronics is: parallel a resistor R_b across each series capacitor, much larger than the normal load impedance but much smaller than the capacitor’s own insulation resistance, thereby “forcing” the DC voltage to be distributed according to the resistance value. As long as R_b is properly selected, it can ensure roughly balanced DC voltage across each capacitor.

Typical experience is:

• The current flowing through the balancing resistor should be much larger than the capacitor leakage current, for example, 5~10 times or even higher;
• This way, the actual voltage division error can be controlled within about ±10%.

2. Necessity Varies Slightly for Different Capacitor Types

• MKP and other film capacitors:

  • Leakage current is relatively large. Although insulation resistance is also high, it’s not as extreme as C0G;
  • When used with high DC bus voltage and in series, it’s generally “recommended” or even “mandatory” to add balancing resistors to ensure long-term safe operation.

• High-voltage C0G/NP0 MLCCs:

  • Extremely high insulation resistance, minimal losses, equivalent to an almost perfect capacitor;
  • In the resonant position, it mainly withstands AC voltage. If DC bias is not large, the problem of DC bias imbalance caused by “leakage current differences” is actually not serious;
  • However, due to the device’s own weak leakage current and batch differences, many engineers still add larger-value balancing resistors as “insurance” when the DC bus is high and the number of series capacitors is large.

Overall Engineering Recommendations:

• If you are using MKP film resonant capacitors, in series:

  • “Strongly recommended” to parallel balancing resistors across each capacitor;
  • The resistance and power rating of balancing resistors must be carefully calculated based on DC bus voltage and capacitor specifications (a simple estimation method is provided later).

• If you are using C0G/NP0 MLCCs:

  • If DC bias is very small (for example, the resonant capacitor mainly sees AC, and bus voltage is completely transferred through transformer coupling, etc.), and the number of series capacitors is not large, balancing resistors can be omitted;
  • If bus voltage is high, number of series capacitors is large, and there is obvious DC bias in the design, adding a “relatively large-value” balancing resistor will be more reliable, but weigh the additional losses and heating it brings.

4. How to Select Balancing Resistors? (Simple Engineering Estimation)

Here is a common approach applicable to MKP film capacitors. MLCCs can follow a similar approach but with appropriately larger resistance values.

1) Resistance Selection Approach

• Goal: The current I_R in the balancing resistor should be much larger than the maximum leakage current difference ΔI_leak of the capacitor.
• Many references and manufacturer experience recommend I_R ≥ (5~10)·ΔI_leak, which can control voltage division deviation within about ±10%.
• If the capacitor datasheet provides typical leakage current or insulation resistance, it’s best to calculate according to the datasheet. When no data is available, you can estimate the order of magnitude of leakage current using the following empirical formula (using aluminum electrolytic as example): I_leak ≈ k·C·U. Film and C0G leakage currents are often much smaller.

A commonly used “empirical rule” in engineering (for electrolytic capacitors, but the approach can be referenced) is:

• Assume about 0.5–0.7 μA leakage current per μF of capacitance at rated voltage (at high temperature), estimate ΔI_leak accordingly, and take 5~10 times that as I_R.
• For MKP/C0G, leakage current is much smaller than electrolytic, so under the same conditions, R_b can be made larger.

Estimation Steps Example (for illustration only):

1. Determine the long-term maximum DC voltage U_dc across each capacitor;
2. Estimate leakage current I_leak based on capacitor type and specifications (best to check datasheet);
3. Take I_R ≈ (5~10)·I_leak;
4. Balancing resistor R_b ≈ U_dc / I_R.

2) Power Estimation

• Voltage across balancing resistor ≈ U_dc (approximate);
• Power of each resistor P_R ≈ U_dc² / R_b;
• When selecting actual components, leave sufficient margin. It’s recommended to select resistor power rating at 2~3 times the calculated power.

3) Additional Losses from Resistors in LLC’s High-Frequency Operation

On LLC resonant capacitors:

• The capacitor terminals mainly have high-frequency AC;
• The parallel balancing resistor will also have additional AC losses under high-frequency AC: P_ac ≈ U_ac_rms² / R_b.
• Since LLC has high efficiency requirements, if R_b is too small, it will significantly increase losses;
• Therefore, R_b should be made as large as possible without affecting the balancing effect to reduce losses.

Common engineering practice is:

• Under the premise of meeting “balancing error requirements,” select a larger R_b as much as possible. Typical range may be several hundred kΩ to several MΩ, specifically calculated based on voltage and capacitor type;
• Simultaneously use precision resistors with low temperature coefficient and high temperature resistance (such as metal film resistors) to ensure long-term stability.

5. A Simple Flowchart to Clarify the Decision Logic

Below is a flowchart summarizing: how to consider selecting resonant capacitors in LLC and whether to connect them in series and whether to add balancing resistors.

flowchart LR
  A[Determine LLC Specifications<br/>Frequency, Power, Resonant Capacitor Cr Value] --> B[Calculate Maximum Voltage Peak on Resonant Capacitor<br/>and Possible DC Bias]
  B --> C{Can a Single High-Voltage C0G or MKP<br/>Meeting Voltage Rating and Capacitance be Purchased?}
  C -- Yes --> D[Prioritize Single Capacitor<br/>Avoid Series Connection]
  C -- No --> E{Must Series Connect?}
  E -- Yes --> F{Capacitor Type?}
  F -- MKP Film --> G[Recommended Series Connection<br/>Parallel Balancing Resistor Across Each Capacitor<br/>R_b Estimated at 5~10 Times Leakage Current<br/>Considering Losses and Heating]
  F -- C0G/NP0 MLCC --> H[Series Connection Possible<br/>No Balancing Needed for Small DC Bias and Few in Number<br/>Recommended for Large DC Bias or Many in Number<br/>R_b Can Be Larger Than for MKP]
  D --> I[Pay Attention to Layout and Loop Inductance<br/>Verify Resonant Parameters and Efficiency]
  G --> I
  H --> I

6. Some Additional Practical Suggestions (More Engineering-Oriented)

• Try to use “dedicated resonant capacitor” devices:

  • Manufacturers generally provide capacitor series specifically for LLC/CLLC resonant use, marking current ripple capability, loss angle, frequency characteristics, etc.
  • Selecting such dedicated capacitors is more reliable than stacking a bunch of ordinary capacitors in series by yourself.

• If connecting MLCCs in series, pay attention to mechanical stress:

  • Try to avoid placing large-size high-voltage MLCCs near board edges or mounting holes that are prone to deformation;
  • Avoid excessive screw fastening and external force bending of the board;
  • Strictly follow the manufacturer’s recommended soldering temperature profile to reduce cracks caused by thermal shock.

• Simulation and actual measurement verification:

  • In simulation software, model the series capacitors, ESR, balancing resistors, and trace inductance to see if there is obvious deviation in resonant frequency and gain curves;
  • On the prototype, actually measure the voltage waveforms across each series capacitor to confirm they are indeed within safe range without obvious imbalance.

• Protection design:

  • LLC generally has overvoltage, overcurrent, and overtemperature protection;
  • If using a series capacitor scheme, consider adding some additional “stress monitoring” for capacitors, such as case temperature, abnormal whistling detection, etc.

7. Direct Answers to Your Three Questions

1. “In high-power LLC circuits, can MKP film or MLCC resonant capacitors be used in series?”

• Theoretically and in engineering, they “can” be connected in series. Many literature sources also introduce the theory of multi-capacitor series connection and balancing resistor calculation methods.
• But in high-power LLC, the priority recommendation is: directly select a single high-voltage C0G/NP0 MLCC or MKP film resonant capacitor with sufficient voltage rating, rather than relying on multiple capacitors in series to achieve the voltage rating.

2. “If the voltage rating is insufficient at high frequency, can these capacitors be connected in series?”

• It can be used as a remedial measure to increase equivalent voltage rating through series connection;
• But special attention must be paid to:
  • Capacitance value will decrease, requiring redesign of resonant parameters;
  • Increased parasitic parameters may affect efficiency and ZVS conditions;
  • For MLCCs, mechanical stress, layout, and reliability risks increase significantly.

3. “If possible, should voltage-dividing resistors be added?”

• For MKP film capacitor series connection, it is strongly recommended to parallel balancing resistors across each capacitor to balance DC bias voltage and improve long-term reliability.
• For C0G/NP0 MLCCs:
  • If DC bias is not large and series quantity is not many, they can be omitted;
  • If DC bias is large or series quantity is many, it’s recommended to add a larger-value balancing resistor as insurance, but weigh the additional losses and heating it brings.
    The resistance value of balancing resistors is usually selected based on “current flowing through being much larger than capacitor leakage current difference,” generally in the range of several hundred kΩ to several MΩ, specifically estimated based on voltage and capacitor specifications.

If convenient, you can post your current LLC parameters (bus voltage, power, switching frequency, planned capacitor model and specifications), and I can help you calculate: whether series connection is worthwhile, how many are recommended if series-connected, and what balancing resistor value would be appropriate.

[9527]

Series Connection of Resonant Capacitors in High-Power LLC Circuits

Can resonant capacitors be used in series?

Yes, resonant capacitors can be connected in series in high-power LLC circuits when voltage rating requirements exceed what a single capacitor can provide, but with important considerations that differ between capacitor types:

For MKP Film Capacitors:

• Series connection is common and practical in resonant applications
• These capacitors maintain stable characteristics at high frequencies
• They offer good self-healing properties and predictable behavior
• Most manufacturers explicitly support series configurations for film capacitors in resonant applications

For MLCC Capacitors:

• Series connection is less recommended for high-power LLC applications because:
  • Voltage coefficient effect (capacitance changes with applied voltage)
  • Limited high-voltage/high-capacitance options
  • Risk of mechanical stress and microphonic effects
  • Better practice is to use parallel MLCCs with adequate voltage rating

Are voltage-dividing resistors necessary?

For high-frequency LLC applications (typically 50kHz-1MHz+), traditional DC balancing resistors are generally not recommended because:

• They would introduce significant power losses at high frequencies
• They would reduce the Q factor of the resonant tank, lowering efficiency
• Their impedance behavior at switching frequencies makes them ineffective for AC voltage balancing

Practical approaches for series-connected resonant capacitors:

1. For MKP film capacitors:

• Use tightly matched capacitors from the same manufacturing batch (±5% tolerance or better)
• Apply proper voltage derating (typically 20-30%)
• For critical applications, consider small-value high-frequency balancing networks instead of simple resistors
• Many high-power designs successfully use series MKP capacitors without balancing components when properly matched

2. Alternative solutions:

• Select single capacitors rated for the full voltage (preferred approach)
• Use parallel capacitors to handle current requirements rather than series for voltage
• Consider specialized high-voltage resonant capacitors designed specifically for LLC applications

For extremely high-power applications (>1kW), many engineers prefer to redesign the resonant tank parameters to work with available single-component solutions rather than implementing series connections.