Online Indirect Measurement of ESR and Capacity for PHM of Capacitors

Daniel Astigarraga Electronics & Communications Dept.

CEITdastigarraga@ceit.es

Fernando Arizti Electronics & Communications Dept.

CEIT Fernando@ceit.es

Federico Martín Ibañez Electronics & Communications Dept.

CEITfmibanez@ceit.es

Ainhoa Galarza Electronics & Communications Dept.

CEIT agalarza@ceit.es

Abstract—this paper shows a system to measure the Equivalent Series Resistance (ESR) and Capacitance (C) of capacitors. This system provides a cost effective solution for Prognostic Health Monitoring (PHM) of capacitors used in fully electric vehicles (FEV) and medium-power switching supplies. The system is based on a Hartley resonant topology formed by two inductors and a variable capacitor. This circuit is able to measure Metalized Thin Film Capacitors (MTFC) as well as electrolytic capacitors. The paper analyzes the circuit and compares the results of simulations and experiments.

Keywords—capacitor; ESR; PHM; Hartley Oscillator;

I. INTRODUCTION

Power converters have become an essential subsystem of several applications. Failures of these converters lead to increase losses, abrupt stoppage, long maintenance time and increased costs. In applications where system reliability must be guaranteed, the remaining useful life (RUL) prediction and failure detection of components has become an issue of major interest. In order to implement PHM systems, accurate, reliable and low cost variables are required [2].

The development of PWM switching power supplies has led to their application in several industries such as railway, aerospace and automotive [1]. These power converters require the use of a capacitor in the DC Bus line. This capacitor reduces the voltage ripple produced by switching process. However, capacitors has been reported the first cause of failure in power converters [1, 2, 3]. The introduction of FEVs has raised concerns on reliability issues regarding the electronic components.

Automotive industry is specially affected by systems failure due to their high impact on customer’s image. A sudden breakdown on a system must be avoided; therefore system high reliability is necessary. The extreme vibration, shock, thermal and humidity conditions affect the components

degradation reducing their life time. Early failure detection or prediction reduces costs and improves customer’s feeling.

Historically, electrolytic capacitors have been used in switching power converters, however, manufacturers are moving to MTFC. These are thought to have longer life time than electrolytic capacitors [4].

The largely used equivalent series circuit of capacitors is:

Fig. 1: Capacitor equivalent series circuit

Where, R is the ESR of the capacitor, L is the equivalent series inductance and r is the equivalent parallel resistance. Previous researches have studied the degradation process of electrolytic capacitors and MTFC capacitors. Most of them report the use of thermal, humidity and electrical actions to develop accelerated aging tests [3, 4, 5, and 6]. Electrolyte dry-out is the main reason of electrolytic capacitors degradation [3]. MTFC degradation is mainly caused by the so-called clearing process [4].

Degradation processes prove the increase of the ESR and the decrease of capacitance for both types of capacitors [3, 4, 5 and 6]. In this article, thermal accelerated process has been applied to analyze the degradation of electrolytic capacitors (model: KEMET ALS30 300 uF). The parameters of components have been measured with a FLUKE PM6306 LCR meter. Fig. 2 and 3 presents the evolution of capacitance and ESR within 1320h at 145ºC respectively.

As a result, the ESR and the capacitance variables are demonstrated as appropriate failure precursor for capacitors. However, a common LCR measurement device costs around 10000€, which is not an affordable for an online PHM system

in transport application. This paper shows a low cost circuit to assess the ESR and the capacitance of capacitors where online measurements are required. The circuit is based on a Hartley oscillator [12]. The simplified schematic is shown in Fig. 4.

102 103 104 105 1060

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1x 10-3

frequency (Hz)

Cap

acity

val

ue (F

)

Capacity Decrease with Degradation0 h24 h168 h264 h432 h528 h696 h960 h1104 h1320 h

Fig. 2: capacitance degradation

102 103 104 105 1060

0.1

0.2

0.3

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0.5

0.6

0.7

frequency (Hz)

ESR

val

ue (O

hm)

ESR Increase with Degradation0 h24 h168 h264 h432 h528 h696 h960 h1104 h1320 h

Fig. 3: ESR degradation

Fig. 4: Hartley oscillator

II. CIRCUIT ANALYSIS First, The Hartley oscillator is based on the resonance of an

LC tank formed by L1, L2 and C1. The frequency and amplitude of the output wave highly depends on the values of the LC tank. However, the influence of the parasitic elements is also very noticeable and will be studied in this research.

Ideally, if the components were lossless, the tank would always oscillate. However, given the influence of the parasitic elements, it is necessary to supply energy to the tank. This energy supply is sustained by an operational amplifier that provides enough gain to compensate the losses of the parasitic elements. The current supplied is mainly controlled through a resistor R0. The tank output voltage, Vout (see Fig. 4) will be inversely proportional to the losses as will be demonstrated through the simulations and the experiments; therefore, an increase of the ESR value will mean a decrease of Vout. A capacitance change of the capacitor will mean a change in the oscillation frequency. Both changes can be easily detected using an analog to digital converter and a microcontroller.

The capacitance of the capacitors under study depends on the application. However, the circuit has been proved to work well for a wide range of capacitance (from 20 uF to 2000 uF). The resonance of the circuit is obtained for low values of inductors, thus, the size of the circuit is kept small. Unfortunately, the circuit parameters need to be tuned for each capacitor.

Now, we analyze the circuit in Fig. 4. The gain of the circuit is A= -R2/R1.

Let’s assume Z0 is: (sombrear en el circuito)

CjLjLjZ 1

210

Therefore, VIN is:

OUTOUTIN AVKAVRZ

ZV 1

00

0

VIN can be put as function of VOUT:

ININCL

LOUT VKV

ZZZ

V 22

2

As a result, the following expression could be written:

ININ VAKKV 21

Therefore, the circuit will be capable of sustaining the oscillations as long as AK1K2=1. Where AK1K2 is defined in (5).

12212

0

22

1

221 11111

1

LLCLLjR

CLRRKAK

As AK1K2 should be a real value, the imaginary part should be zero. So, the resonance frequency can be obtained:

210 2

1LLC

f

And the real part determines the minimum gain to sustain the oscillation:

11

2

1

2

LL

RR

It must be taken into account that the parasitic elements of the components have not been considered in this analysis. Eq. (6) describes the dependence with the C of the resonance frequency. The dependence with ESR of the output voltage is not analyzed here because of the mathematical complexity.

III. SIMULATIONS Previous to the circuit testing, several simulations were

developed in order to assess the circuit behavior. The simulation software is ICAP4 from Intusoft. The real circuit parameters were introduced in the model. The selected operational amplifier is OPA541.

The parasitic elements considered in this analysis are the ESR of the capacitor and of the inductors. Although the value of the ESR of the inductors might be higher than the one of the capacitor, they will remain constant in time, thus their influence will be considered as an offset. The simulations were tuned using an MTFC EPCOS B25655J4307K - 300uF. In Table I the considered values of the components are shown.

TABLE I SIMULATION COMPONENTS VALUES

Name Value UnitCapacity 300 uF

ESR (Typical) 0.002 Ohm

L1 L2 47 uH

ESR of L 0.070 Ohm

Gain(R2/R1) 500k/10k Ohm

R0 5 Ohm At a supply voltage of ±12V

Fig. 5: Simulation Circuit schematic

The simulation for the values shown in Table I gives the waveforms in Fig. 6.

a)

b)

c)Fig. 6: Simulated output waveforms: a) Current in the tank; b) OPAMP output

voltage; c) Tank output voltage (Vout) The results of the different simulations can be seen in Table

II. The characteristic parameters are the frequency, the peak to peak current value and the output voltage of the tank (Vout).

TABLE II RESULTS OF SIMULATIONS

Simulation 1 2 3 4

Capacitance 300 uF 300uF 300uF 280 uF

ESR 0.002 0.01 0.05 0.002

f0 800 Hz 800 Hz 775 Hz 862 Hz

Ipk-pk 3.64 A 3.43 A 2.685 A 3.82 A

VOUT pk-pk 1.23 V 1.17 V 923.19 mV 1.34 V

The simulations have proved the following statements: An increase of the ESR decreases the output voltage,

keeping the frequency almost constant (simulations 1, 2, 3).

A small decrease in capacity increases the oscillation frequency and the output voltage (simulation 4).

Once the gain is tuned, that value is enough to sustain the oscillation for the ESR variation range.

The values of the parasitic elements of the inductors remain constant, thus, their influence in Vout behaves as an offset. However, it is observed that inductors with high values of ESR will reduce the output voltage, and so the sensibility of the circuit in capacitor ESR variation.

Finally, the simulation results also show (Fig. 9) that the relationship between the output voltage and the ESR is not completely linear, but it could be easily approximated and tuned.

IV. RESULTSThe prototype is shown in Fig. 5. The oscillator circuit

consists on the MTFC, two inductors and the OPA541 operational amplifiers (Top-left corner). The power resistors are rated for 10W. A voltage adequation circuit is also built with OPA445 amplifiers in order to range the output voltage

(Bottom-right corner). Two different set of experiments has been carried out. One set for a new MTFC, and another one for a semi-degraded MTFC of the same type (Fig. 5). The semi-degraded capacitor has been aged for 888h at a constant temperature of 145ºC. The ESR value of the semi-degraded capacitor has not changed after the degradation process compared to a new capacitor, but its capacity has decreased. Therefore, for a given capacitor the ESR value has been artificially increased. Three copper wires of 8.6cm, 17cm and 26cm length with equivalent series resistances of 70m ,108m and 150m respectively, has been used to increase the ESR. The gain is fixed in x60 and R0 in 5 Ohm.

The results obtained for each capacitor are shown in the following tables:

TABLE III RESULTS OF EXPERIMENTS ON NEW MTFC

Experiment 1 2 3 4

Capacity 303 uF 303uF 303uF 303 uF

ESR 0.006 0.07 0.108 0.150

f0 833 Hz 800 Hz 790 Hz 781 Hz

Ipk-pk 3.49 A 2.67 A 2.23 A 1.92 A

VOUT pk-pk 1.10 V 850 mV 710 mV 590 mV

TABLE IV RESULTS OF EXPERIMENTS ON SEMI-DEGRADED MTFC

Experiment 1 2 3 4

Capacity 292 uF 292uF 292uF 292 uF

ESR 0.006 0.07 0.108 0.150

f0 850 Hz 820 Hz 806 Hz 794 Hz

Ipk-pk 3.55 A 2.67 A 2.26 A 1.97 A

VOUT pk-pk 1.15 V 880 mV 730 mV 630 mV

The waveforms of the measured signals on the oscilloscope for experiment number 1 of TABLE III can be seen on Fig. 8. The red line is the current in the tank; the yellow line is the input voltage to the tank from the OPA445 and the green line is the output voltage of the tank (VOUT).

Fig. 8: Experiment waveforms

It can be seen that the output waveforms of the circuit are very close to the ones predicted by the simulations. It must be highlighted the low standard deviation of the measurements, therefore a high measurement repeatability. This means the circuit is stable and it is possible to rely on the measurements. Finally, an important issue is the tank output voltage variation with the ESR. As it can be seen in Fig. 9, it is an almost linear variation, therefore easy to predict and even to be introduced in a prognostic algorithm.

Finally, it has been proved that the output voltage of the tank is a measurable unit and it is a good indicator of the ESR value of the capacitor.

0

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1

1.2

1.4

0 0.05 0.1 0.15 0.2

Vout

(V)

ESR value (Ohm)

ESRvs Tank Vout

ESR vs Tank_VoutExperiments

ESR vs Tank_VoutSimulations

Fig. 9: Relationship between Vout in simulations and experiments

Fig. 10: The two MTFC

Fig. 11: Prototype

V. CONCLUSIONS Knowing that the ESR and the capacitance are precursor

parameters of capacitors degradation, a cost effective solution has been given in order to convert them into measurable quantities. The advantages of this design can be clearly seen. The PCB size could be minimized and it has a small number of components.

In conclusion, this design can be used in portable applications where size and cost are the main issue. Together with a reliable prognostic algorithm the capacitor could be replaced before a faulty event occurs, saving costs and increasing the overall reliability of the system.

AcknowledgmentThe research leading to these results has received funding

from the European Community’s Framework Programme (FP7/2007-2013) under grant agreement n° 314609. The authors are grateful for the support and contributions from other members of the HEMIS project consortium, from CEIT (Spain), IDIADA (Spain), Jema (Spain), MIRA (UK), Politecnico di Milano (Italy), VTT (Finland), and York EMC Services (UK). Further information can be found on the project website (www.hemis-eu.org)

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