# Plug That leak: Look out for Capacitor Leakage!

Recently, a customer came to the Precision Amplifier Forum here in the TI E2E Community with some confusing circuit behavior.

His circuit used an op amp to amplify the output of a microphone at very low frequencies. He used a large (47 μF) AC coupling capacitor and a high input resistance (100 kΩ) to achieve a low corner frequency for his measurements.

Unfortunately, a significant amount of DC offset was appearing at the output of the op amp — almost a volt! What could cause this?

One of my favorite quotes is by Danish physicist Niels Bohr: “An expert is a person who has made all the mistakes that can be made in a very narrow field.” I don't consider myself an expert yet, but this is one mistake that I have made.

Figure 1

A customer circuit from the Precision Amplifier Forum on the TI E2E Community
that exhibits a large offset at the output of the op amp.

Looking at the customer's schematic in Figure 1, the value of capacitor C1 provides an important clue to the source of this offset. Large capacitors, especially electrolytic and tantalum types, can have significant leakage currents. This causes a voltage to develop on the input resistor R2, which the op amp would amplify.

To understand where leakage current comes from, let's take a look at the basic structure of a capacitor.

Figure 2

A basic capacitor structure with two electrode plates of
area “A” separated by distance “d.”

The capacitor in Figure 2 consists of two electrode plates separated by some insulating material, shown in blue. The capacitance, C, of this structure is given by the equation:

The capacitance depends on:

1. the relative permittivity of the dielectric εro is the permittivity of free space),
2. the area of the electrodes “A,” and
3. the distance they are separated “d.”

This structure will also have a resistance:

The resistance, R, is determined by the resistivity of the dielectric material “ρ” as well as the area of the electrodes and the distance they are separated. Unfortunately there is no perfectly insulating dielectric material. Even Teflon has a finite resistivity of 1•1023 to 1•1025 (Ω-m).

R is referred to as the “insulation resistance” and is in parallel with the capacitance. Factors that increase capacitance will also tend to decrease the insulation resistance. To illustrate this trend, I plotted the values of insulation resistance versus capacitance for several 10 V rated electrolytic capacitors.[1] See Figure 3.

Figure 3

Capacitor insulation resistance tends to decrease for
larger capacitors of equal voltage rating.

The insulation resistance of a capacitor is normally specified at the capacitor's rated voltage, but it is not the same for all applied voltages.

As a result, the leakage current through a capacitor varies greatly with applied voltage.[2] (See Figure 4.)

Figure 4

DC leakage is highly dependent on the applied voltage.

Generally, at 40 percent of the rated voltage, the leakage current will fall to one tenth its rated value, as shown in Figure 4. Therefore, one could increase the capacitor voltage rating to reduce leakage currents or switch to ultra-low leakage type electrolytics.[3]

I normally use polypropylene film capacitors for low leakage coupling applications. If I needed really low leakage I could borrow the vacuum capacitor (Figure 5) from my colleague Thomas Kuehl's office, although a 47 μF vacuum capacitor would be huge!

Figure 5

A 50 pF, 20 kV vacuum capacitor.

When debugging a circuit, it's often the components that aren't on the schematic, like the insulation resistance of a coupling capacitor, that cause problems. Assuming a passive component will behave in an ideal way is just one of many mistakes I've learned from on my quest to become an expert. I wonder what my next mistake will be…

References:

[1] Investment Profile, Acacia Research Corporation (February 2013).

[2] SMD Aluminum Solid Capacitors with Conductive Polymer, Vishay OS-CON, Document Number 90021, Aug 28, 2012.

[3] Application Notes for Tantalum Capacitors, Kemet Electronics Corporation, Greenville, S.C.

[4] Williams, Tim, The Circuit Designers Companion, Elsevier ltd., Burlington MA, © 2005.

About the author: John Caldwell is an applications engineer in the Precision Linear group at Texas Instruments, where he supports operational amplifiers and industrial linear devices He specializes in precision circuit design for sensors, low-noise design and measurement, and electromagnetic interference issues. John received his MSEE and BSEE from Virginia Tech with a research focus on biomedical electronics and instrumentation.

Related posts:

## 17 comments on “Plug That leak: Look out for Capacitor Leakage!”

1. eafpres
October 17, 2013

I realize that using simulation on such a circuit might seem overkill, but that would have shown the leakage right away.  As simulation gets more cost effective, eventually even garage tinkerers will be able to model circuits.  I would guess some model parameters were available for the cap in question.

2. samicksha
October 18, 2013

I recommend polyster compared to Polypropylene, although till an extent advantage remains same that film capacitor internal construction is direct contact to the electrodes on both ends of the winding, thus keeping in mind design behaves like a large number of individual capacitors connected in parallel, thus reducing the internal ohmic losses .

3. jcaldwell
October 18, 2013

Eafpres, this raises an interesting chicken-and-egg dilemma. Many engineers simulate with ideal capacitors because they haven't had an experience such as this one to warn them otherwise. So a simulation would only show this behavior if the engineer knew to model the capacitor leakage instead of just using an ideal capacitor. Yes a simulation would show this, if you already knew about capacitor leakage and included it in your simulation.

4. Davidled
October 18, 2013

I-V relationship for capacitor would be available in the semiconductor or other engineering tool as electronic is moving from one point to other point. Equivalent circuit would be designed based on this relationship.

5. samicksha
October 19, 2013

I am not sure if ideal capacitors really keep presence but, an ideal capacitor would not dissipate any power rather they store it, they dissipate a small amount of power whenever current flows through them, due to ohmic losses.

6. Vishal Prajapati
October 20, 2013

I never knew the relation with applied voltage and leackage current. I mean ya it is apparent from ohm's law that as voltage increases the current through dielectric will increase. But I didn't know it is so drametic that at 40% of the rated voltage it reduces to 10th part.

Second question, does every simulation model integrate this type of non linear leackage current vs. applied voltage?

7. Hughston
October 21, 2013

The designer should have never used such a large value of capacitor for an audio design. He may have been worried about the microphonic effect of ceramic capacitors but he could have still used an X7R in most cases.  He put the cuttoff frequency way too low. You cannot hear frequencies that low even if you're an elephant. The low frequency cutoff for audio is 20 Hz and for voice systems about 300 Hz.  Voice systems can sound better with higher cutoff frequencies because the low frequencies make the voice sound too bassy in a lot of systems.

8. jcaldwell
October 21, 2013

Hughston,

Thank you for your comment. This actually was not for an audio system, at least not in the standard 20Hz to 20kHz sense. Microphones are really only a tranducer that converts changes in air pressure to an electrical signal, most commonly for audio uses, but occasionally otherwise. In this case, the customer was attempting to use this microphone to measure extremely low frequency changes in air pressure.

9. Hughston
October 21, 2013

I have seen electret mics used that way before. It was used to detect a door opening via pressure changes for a security system. I would try a larger electret transducer for that application. When people use electret mics for audio, they often don't realize the mic can pick up some very low frequencies if you don't filter them out. I saw hoses on a TV program used as part of a sensor system for picking up low frequency vocalizations of elephants.  That was the reason for the elephant reference.  But this brings up a relevant point. Limit your bandwidth or else you will saturate your amplifiers with unwanted low frequency noise. If you saturate your amplifier with low frequency signals, then that's all you'll hear.

10. Guru of Grounding
October 23, 2013

Anyone who's actually experimented with capacitors (do engineering students do that kind of thing any more?) is very familiar with the rather high leakage currents of electrolytic capacitors … reading a data sheet completely will help a lot, too. Since the “film” (actually aluminum oxide) actually forms with applied voltage, leakage is also a function of how long voltage has been applied … it will reduce considerably over minutes or hours. Also the reason that any long-stored (years) equipment should be powered up slowly because the leakage current may be high enough to overheat the capacitor and make the (wet) electrolytic paste steam and the capacitor explode (ever wonder why there are either little rubber plugs or criss-cross indentations in the aluminum can?).  Anyway, the solution for this circuit is to choose an op-amp with extremely low bias current (FET input, for example), raise the value of R2 to perhaps 10 Megohm, and use a plastic film capacitor of 0.47 uF to get the same time constant (-3 dB frequency). That being said, electret mics have their own low cutoff frequency due to the internal capacitance between the electret film and the internal FET (the “output” terminal is simply the drain of that FET).  While I'm here, someone offered that the cutoff frequency for audio should be set at 20 Hz. I would disagree with that! If you care about phase distortion (properly measured as deviation from linear phase) at low audio frequencies (so a kick drum still sounds like a kick drum after passing through a signal chain), you should set the cutoff frequency to about 0.5 to 1.0 Hz. These phase distortions are cumulative and no amount of “aligning them” will reduce the problem. While cascades of low-pass filters can be aligned to some extent (as a multi-pole Bessel filter, for example) to flatten high-frequency phase deviation, there is no counterpart at low frequencies (i.e., no Bessel high-pass filter). Extended LF response at each stage is the only cure (short of a FIR filter if the chain uses DSP). – Bill Whitlock, Jensen Transformers, AES Life Fellow & IEEE Life Senior

11. jcaldwell
October 24, 2013

Hi Bill,

Thanks for your comment. I really enjoyed your article on high-performance balanced audio interfaces. The solution you propose is eventually what I convinced the customer to do, he was already using a JFET input op amp (TL082) so increasing the input resistance to allow for smaller capacitors of different dielectric types was not a problem.

You bring up a good point about experimentation. Many of the comments here have stated “couldn't you just simulate this?”. Well, yes, if you took the time to build a capacitor model which includes the leakage characteristics. But many people just plop down the standard capcitor model in SPICE, and when it doesn't work in real life: blame the op amp!

After all, a resistor is a resistor, a capacitor is a capacitor, an inductor is an inductor right?! 😉

12. DynaMho
October 25, 2013

Ideally, a coupling device would not store a charge, it would only transfer a signal.

The problem I see in this circuit is the capacitor needs a discharge path which would reduce leakage and improve the response time. Also, without a discharge path, the input impedance of this circuit can vary drastically depending on the input signal.  I would try placing a 1M trim pot across the mic and trim it to the lowest possible value.

13. WKetel
October 26, 2013

I wish that folks would abandon that concept that only a narrow bandwidth is neeeded for speech. In some communication systems it may make some sense to reduce the bandwidth a lot, but the result is unpleasant to hear and quite unnatural sounding. It is used a bit in amateur radio with speech processing and while it may provide better understanding of speech in high noise conditions, it is not enjoyable to hear.

The simplest way to reduce capacitor leakage is to have the same voltage on both sides of the capacitor. But that is seldom an option.

14. yalanand
October 27, 2013

In current digital circuits, utmost capacitors are used to even the power amount and lessen circuit noise. When capacitors are used for frequency generation or pulse width modulation they commonly have a flexible resistor or crystal to set the control. When capacitors are used to de bounce a switch or hold open a transistor, the exact clench time is frequently not critical.

15. Hughston
October 28, 2013

The opposite can actually be true. A telephone does sound natural and the frequency response is shaped to reduce the low frequency by the telephone. If the response was flat, it would sound unnatural.  Perhaps the reason for that depends on the frequency response for the rest of the system. You could add more high frequency bandwidth and it would not hurt anything or sound unnatural. At low frequencies you hear the difference.

Some microphones are designed to be close talking and some are not. In a phone or aircraft system, the microphones are close talking.  In a noisy environment you have to get close to the microphone. A singer does not get very close to the microphone in most circumstances because it increases the low frequencies. But they will get close if they want to make their voice sound lower.

Many speech systems will be in a noisy environment; especially today where the person can be talking from a football stadium, a moving car with the top down or a Hong Kong street. Or they are trying to hear in that environment. The weak links in the quality of that system are not the S/N of the converters but the acoustics and noise at each end. Extra bandwidth does not help; it just adds to the noise.

On the microphone side, the system can use noise reduction with signal processing, microphone arrays and automatic gain control.  On the receive side you can make the response louder or shape it for the environment. For example, in a cell phone, the earpiece does not fit well to the ear and that affects the low frequency response into the ear. What a cellphone does is assume a leaky seal to the ear and boost the low frequency to compensate. I don't think it helps much. In the old telephones, the earcup fit well against the ear and that gave good low frequency reception.

16. RedDerek
November 6, 2013

@Samicksha – I agree that a film cap would have been a much better choice in the application. Film caps do have low dissipation and they have other advantages. However, they do not have the capacitance volume as an electrolytic or tantalum. Film caps are also good for applications where low drift is required. Another option would be to use a glass cap.

17. samicksha
November 8, 2013

Yes RedDrek, one of the plus here is direct contact to the electrodes on both ends of the winding, this keeps all current paths to the entire electrode very short.

This site uses Akismet to reduce spam. Learn how your comment data is processed.