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.
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.
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:
- the relative permittivity of the dielectric εr (εo is the permittivity of free space),
- the area of the electrodes “A,” and
- 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. See Figure 3.
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. (See Figure 4.)
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.
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!
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…
 Investment Profile, Acacia Research Corporation (February 2013).
 SMD Aluminum Solid Capacitors with Conductive Polymer, Vishay OS-CON, Document Number 90021, Aug 28, 2012.
 Application Notes for Tantalum Capacitors, Kemet Electronics Corporation, Greenville, S.C.
 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.
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