Using FFT Analysis Function of LTspice® to Measure Effective Capacitor Ripple Current

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Figure 1

   

Abstract

This article provides power supply designers with a practical methodology for measuring the effective ripple current of aluminum electrolytic capacitors (Al-Ecaps) within switch-mode power supplies, which is an important factor to estimate capacitor lifetime. By leveraging LTspice to process real-world data, this method allows for the accurate calculation of effective ripple current—the primary driver of internal heating and capacitor degradation. This approach uses an oscilloscope-captured dataset converted into a piecewise linear (PWL) source, enabling an automated fast Fourier transform (FFT) analysis to account for frequency-dependent acceleration factors. With this workflow, verifying the effective ripple current and resulting internal temperature rise of the capacitor can be achieved without the use of expensive equipment or relying on oversimplified approximations.

Introduction

Robustness in power supply design is based on predictable, long-term service life. For conventional switch-mode power supplies (SMPS), this reliability is most often dictated by the characteristics of an aluminum electrolytic capacitor (Al-Ecap).¹ Unlike other types of capacitors,^2,3 this type utilizes a liquid electrolyte that is subject to diffusion and evaporation, making it the primary life-limiting component and the determinant factor for a system’s operational longevity.^1,4

For an Al-Ecap, the estimated lifetime (L_X) is modeled as a product of the rated life specified by the manufacturer and a set of acceleration factors that account for electrical and thermal properties specific to the application. The generalized multiplicative formula is expressed as:

where L₀ is the rated life or capacitor’s designed lifetime, K_T is the thermal acceleration factor, K_V is the voltage acceleration factor, and K_R is the ripple current acceleration factor.^4,5 Equation 1 can then vary depending on the capacitor manufacturer; an example is shown in Equation 2.⁶

where L_X and L_O are in terms of hours, K_T is the ambient temperature acceleration factor, T_O is the upper limit of the category temperature range in °C, T_X is the actual ambient temperature in °C, ΔT_O is the rise of internal temperature due to the rated ripple current in °C, Δ_T is the rise of internal temperature due to actual ripple current in °C, and A is the acceleration factor of temperature rise due to the ripple current.

What Is Ripple Current?

Ripple current (I_R) refers to current that flows through the capacitor, typically generated during the charging and discharging cycles in filtering applications. The internal heating generated by this current is a quadratic function of the current and the component’s equivalent series resistance (ESR), as shown in Equation 3. This power dissipation generates heat, leading to an internal temperature rise (ΔT).⁶

Since an SMPS consists of main power frequency and switching frequency elements, the internal power loss of the capacitor seen in Equation 3 can then be translated to Equation 4, where I_f1, I_f2, and I_fn are the ripple current (A rms) at frequency f₁ to f_n, F_fn is the frequency compensation factor (frequency multiplier), and f_o is the reference frequency of the ripple current.⁶

With Equation 4 and Equation 5, the ripple current at any frequency can be converted into its rms value at the reference frequency (I_f0) using Equation 6.⁶

Furthermore, an approximate value of ripple current-caused internal temperature rise (ΔT) can be calculated using Equation 4 where I_X is the operating ripple current (A rms) flowing in the capacitor, I_O is the rated ripple current (A rms) frequency compensated, at the upper limit of the category temperature range. Such output from Equation 7 can then be used as input for Equation 2 to calculate the estimated capacitor lifetime in hours.⁶

Using LTspice to Measure a Capacitor’s Ripple Current

In power factor correction converters, the aluminum electrolytic capacitors at the output are subjected to low‑frequency ripple currents of around 100Hz or 120Hz from rectification, as well as high‑frequency ripple currents produced by the converter’s switching operation. Fast Fourier transform (FFT) analysis provides the rms ripple current for each spectral component. By applying the frequency correction coefficient and summing these rms values, the net effective ripple current can be calculated using Equation 6.

To demonstrate how to use LTspice to measure a capacitor’s ripple current, the DC2104A evaluation board was used. This demo board is an offline, boundary‑conduction‑mode (BCM), power factor correction (PFC) boost converter based on the LT8312. It delivers a single 400V, 150W constant‑voltage output, making it suitable for applications that need a regulated input bus.

To start, short lead extensions need to be added to the capacitor so the current probe can be connected, as shown in Figure 1. With the circuit running at input and output conditions where it will give the highest expected ripple current, the oscilloscope view needs to be adjusted so the time window contains as much as possible of an integral multiple of the waveform period, as shown in Figure 2. For ripple current waveform, the low-frequency components contribute more significantly to the capacitor’s internal heating than the high-frequency ones. For this reason, when performing an FFT, a time window that is equal to an integer multiple of the lowest frequency component must be used; for this example, 120Hz (100Hz) was used.

Next, export the captured ripple current waveform from the oscilloscope into a CSV file form. To ensure that LTspice can properly recognize the oscilloscope’s exported CSV data, the dataset must match the formatting illustrated in Figure 3. The process involves opening the CSV file in a text editor, removing the header row, and converting all comma delimiters to spaces.

After editing the format of the data, create a new schematic in LTspice and copy the configuration shown in Figure 4a. This schematic consists of a piecewise linear (PWL) voltage source connected to a 1Ω resistive load. Assign the edited CSV file to the PWL voltage source as illustrated in Figure 4b and perform a transient simulation with a duration that matches the time span of the data captured from the oscilloscope. It is important to use the latest version of LTspice before running the simulation. After this, probe the current in the resistor to obtain the ripple current as shown in Figure 5.

For accurate FFT analysis, the input waveform must be continuous and repetitive. If the waveform displayed on the oscilloscope or LTspice has discontinuities at its edges, performing FFT on such data can lead to significant errors compared to the true value. To address this, a window function is applied to smooth the discontinuities and make the waveform appear continuous.⁷ However, in LTspice, the waveform can be zoomed to remove low-frequency discontinuities. This is achieved by adjusting the time axis to display an integral multiple of the waveform period, which in this case is 120Hz (100Hz). To do this, right-click the time axis and modify the leftmost, tick, and rightmost values accordingly. As an example in Figure 5, the leftmost value is 1.2ms and the rightmost value is 76ms.

As shown in Figure 6a, with the waveform window active, navigate to View then FFT from the menu bar. This action generates the FFT to use the data from the current zoom extent selected and shown in Figure 6b. Right-click the y-axis to select linear representation and right-click the x-axis to edit the range from 10Hz to 1MHz to obtain the frequency domain of the ripple current as shown in Figure 7.

From the menu bar, choose File > Export Data as Text to generate a CSV file containing the FFT results. The data can be exported in either rectangular or polar format. The key requirement is to obtain the magnitude for each frequency (column D) using Equation 8 and then sort the values from highest to lowest (column F) as shown in Figure 8.

where the Iripple(Re) is the real component and Iripple(Im) is the imaginary component of the exported current ripple data in rectangular form.

The frequency correction coefficient from the capacitor’s data sheet (column E) is required to calculate the ripple current for the base frequency. Use the ripple current frequency obtained from the data (column A) to determine the capacitor’s frequency correction coefficient to be used. Then, use Equation 6 to compute for the effective ripple current of the capacitor.

In a boundary conduction mode PFC converter, the switching frequency varies, so it is important to sum as many frequency components as possible to closely approximate the actual ripple current, similar with the example considered in this article. However, in continuous conduction mode PFC converters where the switching frequency is fixed, the process can be simplified by selecting few ripple current peaks at the switching frequency and its harmonics. The calculated effective ripple current for the first 1000 highest peak points is 0.76A rms. The estimated internal temperature rise (ΔT) can then be calculated using Equation 7 where capacitor-rated specifications such as ripple current rating (I_O) and its corresponding internal temperature rise (ΔT_O) will come from the manufacturer’s data.

Conclusion

LTspice simulation offers an efficient and reliable way to estimate the effective ripple current in aluminum electrolytic capacitors in power supply designs. Furthermore, the output provides a clear spectral component of each frequency, which, when combined with the data sheet-derived frequency correction coefficient, allows for an accurate calculation of capacitor internal temperature rise and lifetime.

References

1. Martin. “MTBF – Is It A Prediction of a Power Supply’s Operating Life?” TDK Lambda, February 2020.
2. Bryan A. Borres, Ino L. Ardiente, Jahres R. Satur, Flordeliza Valiente, and Jesus Martinez. “Design Optimization of a Two-Phase Interleaved Transition Mode Boost Converter for Power Factor Correction.” 2019 IEEE 11th International Conference on Humanoid, Nanotechnology, Information Technology, Communication and Control, Environment, and Management (HNICEM), April 2020.
3. Tianyu Chen, Sen Li, and Babak Fahimi. “Analysis of DC-Link Voltage Ripple in Voltage Source Inverters Without Electrolytic Capacitor.” IECON 2018 – 44th Annual Conference of the IEEE Industrial Electronics Society, December 2018.
4. Marcantonio Catelani, Lorenzo Ciani, Roberto Singuaroli, and Andrea Mannucci. “Electrolytic Capacitor Lifetime Prediction In Ground Mobile Applications.” 13th IMEKO TC10 Workshop on Technical Diagnostics, June 2014.
5. "Lifetime Estimation of Capacitors.” AIC tech Inc.
6. "Lifetime of Aluminum Electrolytic Capacitors.” Nippon Chemi-Con Corporation.
7. "How to Measure Ripple Current Using the FFT Analysis Function.” Nippon Chemi-Con Corporation
8. "Snap-in Aluminum Electrolytic Capacitors." Rubycon.

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