Introduction

Ideal capacitors can be defined with the following simple equation:

In this design challenge I will explore parasitic elements of polymer capacitors that are not modeled by the previous equation, in particular I will explore how temperature affects the capacitance and leakage current, and the dielectric absorption of 3 types of polymer capacitors.

Experimental methods

I received 17 different polymer capacitors, from them I selected 3 different types, of "roughly" similar capacitances:

Type: Polymer aluminum electrolytic capacitor (Polymer Al-e-cap)

Name: EEFCD0J100R - Polymer Aluminium Electrolytic Capacitor, 10 µF, 6.3 V, 2917 [7343 Metric], SP-Cap CD Series

Link: https://www.newark.com/panasonic/eefcd0j100r/cap-alu-elec-polymer-10uf-6-3v/dp/62W7346

Type: Polymer tantalum electrolytic capacitor (Polymer Ta-e-cap)

Name: 12TPG33M - Tantalum Polymer Capacitor, 33 µF, 12.5 V, POSCAP TPG Series, ± 20%, B, 0.07 ohm

Link: https://www.newark.com/panasonic/12tpg33m/cap-33uf-12-5v-tant-polymer/dp/78AC7775

Type: Hybrid polymer capacitor (Hybrid polymer Al-e-cap)

Name: EEH-ZA1H100R - Hybrid Aluminium Electrolytic Capacitor, Hybrid Polymer, 10 µF, 50 V, ZA Series, ± 20%

Link: https://www.newark.com/panasonic/eeh-za1h100r/aluminum-electrolytic-capacitor/dp/91T4889

I soldered cables into the capacitors and then waterproofed them with hot glue. The quality of the waterproofing was tested by checking if the DMM measured a capacitance changed after immersion into water (oil would have been much better but water was what I had at hand). As the Keithley DMM6500 measures the capacitance by measuring the voltage slope while supplying a constant current to the capacitor, a parallel resistor (water making contact to both terminals) would have the effect of making the DMM display a higher capacitance. The hot glue waterproofing appeared to work well as in none of the 3 capacitors I noticed any increase of the measured capacitance after immersion.

I used a hotplate magnetic stirrer to heat water of a recipient and avoid a temperature gradient buildup (as water is stirred through a coupled magnet).

Temperature was measured with a thermistor and a NI MyDAQ, which is an inexpensive DAQ that comes with a built-in DMM. Capacitance, current and voltage where measured concurrently with a Keithley DMM6500.

To convert the measured resistance into temperature, I used the Steinhart–Hart equation:

Where:

T is the temperature in °C

R the resistance in Ohms

A,B,C are the Steinhart–Hart coefficients, which depend on the thermistor

A, B and C coefficients were computed out of a table that shows the correspondence between resistance and temperature of the thermistor.

Data acquisition was done with a small Python program that I wrote:

import visa
import nidaqmx
import time
import numpy


# 'i' = current, 'C' = capacitance, 'v' = voltage
mode = 'v'


# Print message with timestamp
def log(s):
    print('[%.1f] %s' % ((time.time() - t0) / 60., s))


# Compute temperature (°C) from thermistor resistance
def steinhartHart(r):
    a = 1.027628774E-3
    b = 2.393890857E-4
    c = 1.555947964E-7

    logR = numpy.log(r)

    return 1. / (a + b * logR + c * (logR ** 3.)) - 273.15


# Time of the beginning of the execution
t0 = time.time()

# Connect to the instrument, set the timeout and clear the buffer
keithley = visa.ResourceManager().open_resource('TCPIP0::192.168.0.30::inst0::INSTR')
keithley.timeout = 30000
keithley.clear()

# Setup the instrument with the specified sampling rate, digitizing time, and current range. Then create the "currentDigitizer" script.
keithley.write('reset()')

if mode == 'i':
    keithley.write('dmm.measure.func = dmm.FUNC_DC_CURRENT')
    keithley.write('dmm.measure.nplc = 2')
    keithley.write('dmm.measure.filter.enable = dmm.ON')
    keithley.write('dmm.measure.filter.count = 100')

if mode == 'C':
    keithley.write('dmm.measure.func = dmm.FUNC_CAPACITANCE')
    keithley.write('dmm.measure.filter.enable = dmm.ON')
    keithley.write('dmm.measure.filter.count = 20')

if mode == 'v':
    keithley.write('dmm.measure.func = dmm.FUNC_DC_VOLTAGE')
    keithley.write('dmm.measure.inputimpedance = dmm.IMPEDANCE_AUTO')
    keithley.write('dmm.measure.nplc = 1')
    keithley.write('dmm.measure.filter.enable = dmm.ON')
    keithley.write('dmm.measure.filter.count = 5')

# Setup MyDAQ
with nidaqmx.Task() as task:
    task.ai_channels.add_ai_resistance_chan('myDAQ1/dmm', min_val = 1000., max_val = 30000., current_excit_source = nidaqmx.constants.ExcitationSource.INTERNAL)

    i = 0
    l = []

    # Main loop
    while True:
        if mode == 'i' or mode == 'C':
            temperatureT = time.time() - t0
            resistance = numpy.array(task.read(10, timeout = 10)).mean()
            temperature = steinhartHart(resistance)

            log('Temperature: %.2f °C' % temperature)
    
        valueT = time.time() - t0
        value = float(keithley.query('print(dmm.measure.read())'))

        if mode == 'i':
            log('Current: %.2f nA' % (value * 1E9))

        if mode == 'C':
            log('Capacitance: %.4f uF' % (value * 1E6))

        if mode == 'v':
            log('Voltage: %.3f mV' % (value * 1E3))
        
        if mode == 'i' or mode == 'C':
            l.append([temperatureT, temperature, valueT, value])

        if mode == 'v':
            l.append([valueT, value])

        i = (i + 1) % 50

        if i == 0:
            log('Saving data...')
            numpy.save('data.npy', numpy.array(l))