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capacitance coefficients matter

Where capacitance coefficients matter

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Where capacitance coefficients matter

Bonnie Baker
- WEBENCH Design Center

Feb 05 2014 17:53 PM

Comments 0

One thing to watch out for in choosing a capacitor for any circuit is
distortion. This type of distortion occurs, if the capacitor is in the signal
path. Figure 1 shows a few typical circuits that contain capacitors in the
signal path.

Figure 1. The first stage of a sixth-order bandpass filter
(a) and an amplifier driving an R/C pair to an ADC (b).

Figure 1a shows the first stage of a Sallen-Key, bandpass filter. In this
circuit two key capacitors are exposed to the signal going through the filter.
Figure 1b shows an amplifier, using an R/C pair to drive a SAR-ADC. The
capacitor, CF, is fully exposed to the incoming signal before it
reaches the ADC.

This distortion occurs due to the normal capacitor voltage-dependant
characteristic. In other words, the capacitance changes with the voltage and
frequency applied.

An equation that describes this change in one region of the voltage curve
is:

C = C0
( 1 + bVCAP),

where

C0 is the nominal capacitance,

VCAP is the
voltage across the capacitance,

b is the voltage
coefficient of the capacitor.

Figure 2 plots a typical curve of this effect across a capacitor.

Figure 2. Capacitor voltage coefficient

The input or output charge on a capacitor travels through adjacent
impedances, creating a voltage drop error. Since the charging current from a
capacitor is voltage dependant, it creates a non-linear error. For a sine wave,
this error contains harmonics.

The capacitor voltage coefficient characteristic can be more pronounced in
semiconductor process technologies. Since the ADC input (Figure 1b) has an
internal input R/C, this distortion-producing phenomena also occurs at the
converter’s input.

The input signal frequency across a capacitor also can impact the accuracy of
your conversion. The capacitance value introduces distortion, which also changes
with frequency (Figure 3).

Figure 3. Capacitor THD+N versus Frequency

This graph shows the characteristics
of several capacitor technologies and their total harmonic distortion plus noise
(SINAD) versus frequency performance. The lowest line on this chart is taken
using a C08 capacitor. The line above the C0G capacitor data shows the system
measurement. The other lines on this chart are from ceramic caps with different
dielectrics: Z5U, Y5V, and X7R. Note that these types of capacitors introduce
significant non-linearity and signal distortion over frequency.

Not shown on this chart is the ceramic NPO-type capacitor. The NPO type
capacitor closely matches the C0G performance. It is critical that you select
the right capacitor type for C1 and C2 (Figure 1a) and
CF (Figure 1b). You will find that a higher quality external
capacitor (CF) will not degrade the ADC’s AC specifications. The
larger voltage coefficient of the smaller internal ADC capacitor
(CSH) will be dwarfed by the lower voltage coefficient of the larger
external capacitor.

Signal distortion can come in many forms, but the capacitors in the circuit
signal path may be the last thing that you think about if you encounter this
type of problem. Do you have any war stories when it comes to distortion? Please
share! Meanwhile, for more information check out these references:

“How the
Voltage Reference Affects your Performance: Part 1,” Baker, Oljaca, Analog
Applications Journal (SLYT331), Texas Instruments, 2Q 2009

“How the
Voltage Reference Affects your Performance: Part 2,” Baker, Oljaca, Analog
Applications Journal (SLYT 339), Texas Instruments, 3Q 2009

“How the
voltage reference affects ADC performance, Part 3,” Baker, Oljaca, Analog
Applications Journal (SLYT 355), Texas Instruments, 4Q 2009

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Precision
DAC (=<10MSPS), Precision
ADC (<=10MSPS), Integrated
Precision ADC and DAC, Precision
DAC with 4 to 20mA current output

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