AUTO AUDIO BOOST CAPACITORS AND PROBLEMS IN THE DETERMINATION OF THE ACTUAL CAPACITANCE VALUE

Ronald R. Stiffler1

1Senior Scientist, Stiffler Scientific, Humble, Texas, USA DrStiffler@embarqmail.com

Abstract—In this paper I present the test results and test methods used in an effort to confirm vendor specified capacitance values on three capacitors with an advertised purpose of providing power boost to large high power auto audio sound systems. My testing procedures consisted of two different methods for measuring the discharge curve of the capacitors under test.

I. Introduction During the course of an energy research project I required a number of large capacity capacitors in the range of 2-3 Farad with a minimum voltage rating of twelve volts. In order to utilize current super capacitors I would have been required to connect together a combination of series and parallel units to provide the capacity and voltage required. Rather than do this for the initial phase of my work I purchased from two different vendors a number of similar units often referred to as ‘Digital Power Capacitors’. The capacitors I purchased are among a line of products sold and referred to under different titles such as; Boost Capacitor, Power Capacitor, Stiffening Capacitor TM [1] and Car Audio Capacitors [2]. My first three capacitors were labeled as being the same value in capacity and physically appeared similar but were different in weight and color. See Appendix Initially in my research work no effort was made to confirm the actual capacity of the units as my margin of error in the research allowed for a deviation 10-15% in the capacity value. Problems surfaced midway in the research project when calculations for energy stored in the capacitors did not match the energy that could be drawn from them after charging. The energy of the capacitors in the research project and the testing results presented in this paper were calculated with the following equation. Eq: 1 Uc = ½(CV2) where Uc is in Joules. My research project required the capacitors be discharged into a linear carbon resistance and the following formula was used to determine dissipated energy.

Eq: 2

Ur = I2RL where I is the current through the load resistance Rd. Ur was actually derived from Σ (I2*Rd*T) where T is the time interval in seconds of the measurement period, providing the sum of total Joules. In order to calculate the actual capacity from test results I used the generally accepted method of using the time constant with a known resistance [8]. I therefore used the following equation rearranged for this purpose. Eq: 3

t = RC as C = t/R where C is the calculated capacitance, R is the discharge resistance in ohms and t is the time in seconds [8].

I researched various papers covering both regular multi-layer and super capacitors. One particular paper was ‘Electrochemical Supercapacitor Time Domain Analysis by Means of Multi-Channel Measurement System [4]’ and ‘Cap-XX, Application Note AN1005 [5] along with Illinois Capacitor, Inc. [6] One particular paper of note was by ‘Richard Clark’, titled ‘A2546 Fusing Stiffening Capacitors TM [1,7] where the capacitors being described are not really of the current super capacitor construction, rather a conventional build from multiplayer foils. What I was able to determine was that t=RC (Eq: 3) [8], should apply to these capacitors, including the newer super capacitors and without doubt to a conventional configuration as described by ‘Richard Clark’ [7]. With this information I wrote a special computer program, Fig: 1, to control all aspects of the testing, thereby removing manual timing or calculation errors.

II. The Test Setup Two different test configurations were used, both using ‘Capacitor Inspector’ Fig: 1, the software program specifically written for the controlling computer CC and performing control and logging. (See Test Setup 1 & 2) The CC program controlled all switching, monitoring and calculations during teach testing procedure.

Test Setup 1:

Acronyms used in this paper referring to both test setups 1 & 2 are;

CC Controlling Computer, controls switching, monitoring, logging and calculations.

PS Computer Controlled Digital Power supply. DM Computer Controlled Digital Multi-meter (Volt meter). Rd Computer Controlled Digital Electronic Load Rc Carbon resistor of a value equal to Rd. CUT Capacitor Under Test, each capacitor identified by CUTn.

Test Setup 2: The second testing configuration uses a DSO in place of the DMM in order to see the actual capacitor discharge curve.

Each capacitor tested was assigned an identifier and these identifiers were CUT1, CUT2 and CUT3. See Appendix The following image is from the control screen of the ‘Capacitor Inspector’ program written specifically for testing the CUT’s.

Fig: 1

III. Test Procedure Each capacitor was tested multiple times both for numerical results as obtained from the control software CC shown in Fig: 1, followed by discharge cycles into load Rd while monitoring with a DSO capturing the discharge curve. Each capacitor tested was fully discharged before each test by shorting it terminals with a heavy gauge wire for a period of fifteen minutes. All three CUT’s were put through three cycles of charge and discharge to obtain the data shown in Fig: 2. The final tests ran each capacitor again through three charge and discharge cycles while under the control of the control software and monitored with the DSO.

IV. Test Results

The Table shown in Fig: 2, indicates the results for each of the three CUT’s. Each of the three capacitors was physically marked as being 3.0 Farads in value. Fig: 2 Each CUT shown with (3) Charge/Discharge cycles

Device CUT t = Seconds Charge Cc = t/Rc Discharge Cd = t/Rd ∆∆∆∆C

1 7 0.642F 11 1.009F +0.367F

7 0.642F 11 1.009F +0.367F

7 0.642F 11 1.009F +0.367F

2 7 0.642F 11 1.009F +0.367F

7 0.642F 10 0.917F +0.275F

7 0.642F 10 0.917F +0.275F

3 4 0.367F 6 0.550F +0.183F

5 0.459F 6 0.550F +0.060F 5 0.459F

6 0.550F +0.060F No effort was made to calculate or measure the capacitors ESR (Electrical Series Resistance) because the data was so far from the manufactures specified values that the ESR would not have significantly change the test results. It should be noted that the same load Rd was used for the entire series of tests and was of an accuracy of 0.15%. The load resistor used in the tests involving the control program CC was 10.9 ohms, while the loads used in the DSO measurements were 5 and 10 ohms respectively. In the measurement of the discharge curves with the DSO the capacitors were fully charged and allowed to top off for 5 minutes before the discharge. I performed the discharge tests with the DSO and measured the results to the 36.8% of Vc (stabilized charge voltage of the capacitor) point as seen in the following images taken from the DSO during the tests.

Fig: 3

Fig: 4

You can see in Fig: 3 the discharge curve of CUT1 into a 10-ohm load returned a calculated capacity of 0.900 Farad. Looking back to the table in Fig: 2 where the discharge was measured with the CC we can see that CUT1 for the three indicated tests was determined to be 1.009 Farad and Fig: 3 shows it as 0.900 Farad. In addition looking at Fig: 4 along with Fig: 3 and the table from Fig: 2 we can see that the real capacity of the capacitor must be between 0.876 Farads and 1.009 Farads.

This can be confirmed by looking at a curve taken from CUT2 when discharged into 10 ohms. The DSO curve is shown in the following image. Fig: 5

Again looking back to Fig: 2, we see that CUT2 ranged from 0.917 Farad to 1.009 Farad and the DSO shows 0.958 Farads. Therefore I feel that the real capacity ranges between 0.917 Farad to 1.009 Farad. Again I would accept the DSO results as closer to accurate than the CC, merely because the CC is capturing data at one second intervals as opposed to the real time view of the DSO.

V. Conclusions Being fully confident in the measurement techniques and procedures I can only arrive at one result and that is that the capacitors in question are for whatever reason mislabeled and do not offer or present the capacity indicated. I make no claim or offer no opinion as to how or why this may be, but I do stand by the results and the three capacitors used in the testing do not meet by even a small margin the values advertised. I contacted ‘Pyramid Car Audio’ [3] both by initial email and by a follow-up telephone conversation with a gentleman presented as the technical representative for the company and was not able to resolve the issue of the results I obtained in this paper. I requested the test procedures used by the manufacture, but they were not forth coming.

References

[1] Stiffening Capacitor is a trademark of Autosound 2000, Inc. [2] Car Audio Capacitor Installation by CarAudio, www.caraudiohelp.com [3] Pyramid Car Audio, 1600 63rd. Street, Brooklyn N.Y. 11204. www.pyramidcaraudio.com [4] ‘Electrochemical Supercapacitor Time Domain Analysis by Means of Multi-Channel Measurement System, by Valeriy Martynyuk, Denis Markaryshkin and Juliy Boyko and can be found at, http://www.imeko.org/publications/tc4-2007/IMEKO-TC4-2007-009.pdf [5] Cap-XX. Application Note AN1005 revision 2.1 http://www.cap-xx.com/resources/app_notes/AN1005%20Simple%20Supercapacitor%20Measurement%202-1.pdf [6] Illinois Capacitor, Inc., Lincolnwood, IL. http://www.illinoiscapacitor.com/uploads/papers_application/72B4ADF9DAD74E4CB7293DE6F4B62427.pdf [7] A2546 Fusing Stiffening Capacitors by Richard Clark. http://www.monstercable.com/mpc/stable/tech/A2546_Fusing_Stiffening_Capacitors.pdf [8] Rowan University, ‘Charging and Discharging a capacitor’. http://www.rowan.edu/colleges/lasold/physicsandastronomy/LabManual/labs/Capacitor.pdf

Appendix

CUT1 and CUT2 were both labeled - Royal Blue, CAP300DBL, 3.0 Farad, Digital Power Capacitor with the name Pyramid written vertically on the left side of the label. Each capacitor had a weight of 1.24kg.

CUT3 was a large Silver colored capacitor labeled - Royal Blue, CAP300DBL, 3.0 Farad, Digital Power Capacitor with the name Pyramid written vertically on the left side of the label. Underneath the ‘CAP300DBL’ was an internet site listed of www.pyramidcaraudio.com . This larger Silver capacitor weighed in at 1.97kg.