Experiment Description and Theory
The element14 Experimenting with Polymer Capacitors Challenge is an opportunity to “experiment, test, breadboard, or just play around with Polymer Capacitors” and then show what was learned. I am grateful to be one of the competitors selected to receive a Polymer Capacitor Kit for my proposal “Deep Dive into ESR”.
In this first post the experiment will be described and the theory behind it explained. In the next post the actual experiments, results and findings will be presented.
Equivalent Series Resistance (ESR) and the actual capacitance of capacitors are among the most important parameters for capacitor performance in a circuit. While an ideal capacitor has no series resistance, ESR exists in all real world capacitors, albeit with very small values in some of the polymer capacitors investigated here. There are other deviations from ideal behavior such as series inductance, parallel resistance, and memory effects (dielectric absorbtion) which we will not be addressing.
Capacitor ESR not only influences circuit behavior when new, but can worsen over time due to age (e.g. drying out of electrolyte in some capacitors), abuse, and overheating. This increases power dissipation which can start a vicious circle of continued performance reduction. Thus, the ability to measure both capacitance and ESR quickly with an instrument like the Peak ESR70 is of value. There is an element14 Cool Tools review of the ESR70 by Michael Wylie here.
An oscilloscope can also be used to measure ESR and provides a visual means of assessing the capacitor. The Peak ESR70 will be used to assess how well the oscilloscope method works.
While the Peak ESR70 can be used with the circuit intact in some cases, there are limitations and it isn’t always appropriate. The experiments performed here will be done on new capacitors outside of a circuit. ESR is typically quoted by manufacturers at around 100 kHz which is where the Peak ESR70 operates, and also what will be used in the oscilloscope method. The reason for this will be explained shortly.
The element14 Kit
The Panasonic polymer capacitors in the element14 kit came nicely packaged in their own compartmentalized box. They are all surface mount. It is nice to have the assortment as it gives a good idea of the size and range of what is available.
My first impression of the Atlas Peak ESR70 is very good. It seems well made and is easy to use.
The experiment seeks to understand ESR and how it differs among different polymer capacitors and from aluminum electrolytic and ceramic capacitors. To do this we will:
- Describe ESR and how it can be measured
- Obtain experimental ESR value for various capacitor types and values
- Obtain experimental capacitance values for various capacitor types and values
- Compare and summarize findings
Capacitance and ESR will each be measured with two different instruments / methods.
Equipment and Materials
- Peak ESR70 ESR meter
- Tenma 72-1020 40,000 count bench multimeter
- 100 MHz oscilloscope
- TI MSP430FR6989 Dev BoardAD9850 DDS Synthesizer
- Panasonic polymer capacitors to be evaluated as listed in the report format section of this blog.
The Panasonic polymer capacitors chosen for the experiment are ones where similarly rated (capacitance and voltage) aluminum electrolytic and ceramic capacitors were readily at hand for comparison.
ESR Measurement Theory
The method for measuring ESR with an oscilloscope is shown in the following diagram:
The square wave generator is modeled as an ideal square wave with a resistor Rout in series. The capacitor is modeled as an ideal capacitor with a resistor R in series. Voltage is measured with an oscilloscope.
In summary, if the frequency of the square wave is in the 100 kHz range an ideal capacitor begins to approximate a short circuit for the values of capacitance we are interested in. However, a real capacitor has some equivalent series resistance (ESR) that will cause a voltage drop across the capacitor which can be observed with an oscilloscope. The method is instructive in that the comparison between ideal and real capacitor behavior can be intuitively grasped from the oscilloscope display.
Consider for a moment an ideal capacitor with capacitance, C and being driven by a sinusoidal wave with frequency, f. Then the reactance is given by the following formula:
Xc = 1 / fC
For a 10 uF capacitor or greater capacitor at a frequency of 100 kHz the reactance will be 1 ohm or less which we will assume can be ignored (an assumption to be tested). The voltage drop observed across the capacitor then is due to non-ideal ESR. Note that we may also see RC time behavior and anomalies due to inductance and transmission line effects. We will watch for these but disregard them in the calculations.
The square wave generator will be modeled as an ideal voltage source with an output resistor. It is necessary to have a known output resistance in order to set up a resistor voltage divider so that the ESR value can be determined. The square wave will be generated by an AD9850 with an added resistor to make the divider. There is a description of the AD9850 module and the microcontroller being used here. Normally a function generator with known output resistance is used and if the proposed method fails a function generator will be obtained.
The ESR can be calculated with the resistor voltage divider equation:
Vr = Vfg (R / (R + Rout))
Where Vr = Measured voltage across capacitor due to ESR (measured)
Vfg = Function generator voltage (measured)
R = ESR
Rout = output resistance on function generator (known)
Rearranging, and solving for ESR we get the equation shown in the diagram.
Vr (R + Rout) = R (Vfg)
Vr (R) + Vr (Rout) = R (Vfg)
Vr (Rout) = R (Vfg – Vr)
R = Vr (Rout) / (Vfg – Vr) formula (1)
The Peak ESR70 will be used to confirm the results from the oscilloscope / function generator experiments. It will also be used to confirm capacitance measurements from a good quality bench multimeter. Tests will be run at room temperature, approximately 20 degrees C. ESR-70 capacitance probes will be calibrated before starting. The function generator square wave (100 kHz, ~3V3) and resistor divider settings will be set before starting. The following procedure will then be followed for each capacitor:
- Measure and record ESR
- Measure and record capacitance
- Measure and record capacitance
- Measure and record open circuit voltage Vfg on oscilloscope
- Put the capacitor being tested in place as shown in the diagram
- Measure and record voltage across capacitor (ESR)
- Look for exponential rise / fall due to RC charge / discharge as shown in diagram and other anomalies. Record with screenshot.
Calculate ESR with formula (1)
Discussion of Error
None of the instruments being used have calibration certificates and all, with the exception of the ESR70, have been in use for more than a year. Some pertinent specifications from the instrument manufacturers are given below.
Testing methods and termination used for ESR measurement with the oscilloscope could introduce error. The ESR model used is relatively simple and inductance / parallel resistance is not accounted for. Accordingly, accuracy and resolution for the oscilloscope method has not been determined.
Screenshots and video will be made as appropriate for the experiment. Results will be recorded in a spreadsheet style tabe with data similar to that listed below for each capacitor evaluated.
Results will then be plotted and summarized as appropriate in written form along conclusions drawn.
A Peek Ahead
Shown below, the Peak ESR70 measuring a 4.7 uF aluminum electrolytic....
The same 4.7 uF aluminum electrolytic being driven with a 100 kHz square wave is now viewed on the oscilloscope. The lower blue trace is the square wave and the upper yellow trace shows the voltage drop across the capacitor (ESR) as indicated by the two white lines drawn in and labelled.
The methodology is still being worked but the calculated ESR is roughly 7 ohms with the oscilloscope method and 5.4 ohms with the Peak ESR70. It probably will not be possible to measure very low ESR with the oscilloscope.
Thanks for the interest - your comments, suggestions and corrections are always appreciated.