Sources of Nonlinearity
Capacitors and resistors both exhibit a phenomenon called
voltage coefficient, in which a change in voltage across
the component changes its physical characteristics and
hence its value, to some degree. For example, a particular
1.00kΩ resistor with no voltage across it becomes a
1.01kΩ resistor when 10V is applied. That effect varies
enormously according to the component's type, construction,
and (for capacitors) chemistry. Voltage-coefficient
information is sometimes available from the manufacturer
as a graph, showing the percent change in capacitance vs.
the percent of rated voltage.
The voltage coefficient of modern film resistors is very
good, and usually below the level that is readily
measured in the lab. Capacitors, on the other hand, can
limit performance as a consequence of several departures
from the ideal:
- Voltage coefficient: Described previously.
- Dielectric absorption (DA): A memory-like effect in
which a discharged capacitor retains some of the charge
previously stored on it.
- Equivalent series resistance (ESR): This can be
frequency dependent, and can limit power output when
series-coupling capacitors drive the low impedance of a
headphone or speaker.
- Microphony: Some capacitors have a marked piezoelectric
effect, in which physical stress and flexure of
the capacitor generates a voltage across the terminals.
- Poor tolerance: For most large-valued capacitors
(several µF and higher), accuracy is not tightly
specified. Resistors, on the other hand, are readily and
inexpensively specified for a tolerance of 1% or 2%.
The following discussion outlines a test method consisting
of a simple test circuit and readily available audio test
equipment that can quantify the undesired effects of
capacitors in the audio signal path. The intent is not to
pass judgement on particular sizes, voltage ratings, and
case types, but to alert readers to the phenomena, show
representative results, and offer a test method that allows
meaningful comparisons and conclusions.
Nonlinear AC effects are easily found in capacitors. The
frequency response of analog audio (necessarily restricted)
dictates that most circuit blocks include highpass, lowpass,
or bandpass filter circuits, and that the nonlinearities of
such filters can have real and measurable effects.
Consider a simple, highpass RC filter (Figure 1
frequencies well above its -3dB cutoff, the capacitor's
impedance is low with respect to that of the resistor. The
application of a high-frequency AC signal develops very
little voltage across the capacitor, so any change due to the
voltage coefficient should be minimal. Signal current
flowing through the capacitor, however, generates a corresponding
voltage across the capacitor's ESR. Any
nonlinear component of that ESR sums in at the appropriate
level and can degrade THD.
Figure 1. Simple highpass RC filter.
At and near the -3dB cut-off point, however, impedances
of the capacitor and resistor are of the same order. The
result is a significant AC voltage across the capacitor at a
point in the response that imposes only minor attenuation
on the input signal. Thus, any voltage-coefficient effects
tend to peak around that point.
By focusing on THD at the -3dB cutoff, this test highlights
nonideal behavior-primarily that due to the
voltage coefficient. The test circuit is based on a highpass
filter with -3dB cutoff at 1kHz and an audio analyzer
(Audio Precision System One) that looks for any degradation
of THD+N while various capacitors of differing
construction, chemistry, and type are substituted. A 1µF
capacitor value was chosen because it offers a wide choice
of capacitor types for testing. It is loaded with a 150Ω
resistor to form a headphone filter with nominal 1kHz
cutoff. Note that the capacitor under test has no DC bias
across it. Input and output have the same DC potential.
Polyester Capacitor and Reference Baseline
A plot of THD+N vs. frequency in Figure 2
limit of resolution in the test setup, and also the minimal
effects of a 25V through-hole polyester capacitor not
typically used in portable designs. Little, if any, THD
degradation due to voltage coefficient is apparent. Note
that the polyester capacitor allows THD to rise below
1kHz, but the output signal is actually falling with a
frequency below 1kHz, thereby reducing the ratio of
signal-to-noise (plus distortion) registered by the analyzer.
The key region is at and above 1kHz, where the polyester
capacitor performs well—only slightly worse than the
Figure 2. THD+N vs. frequency for a 1kHz highpass passive filter with polyester capacitor, compared to a reference measurement.
Tantalum capacitors are often found in portable devices,
usually for blocking DC voltage to a headphone and especially
if more than a few µF are required. Another plot of
THD+N vs. frequency in Figure 3
compares three variations
of a popular SM tantalum capacitor with a traditional,
through-hole "dipped" tantalum capacitor readily
available in the lab. The capacitors again have 1µF values;
only their physical dimensions (case size) and voltage
ratings differ. See Table 1
. No DC bias was applied to the
capacitors during this test.
Figure 3. Comparison of THD+N vs. frequency for various tantalum capacitors in a 1kHz highpass passive filter.
Table 1. Comparison of SM tantalum
capacitors tested in Figure 3.
||Case Size L x W (mm)
||Voltage Rating (V)
||A (3.2 x 1.6)
||B (3.5 x 2.8)
||C (6.0 x 3.2)
Ceramic capacitors are often used for AC-coupling
between audio stages, and in bass-boost and filtering
circuits. Various dielectric types are available, as Figure
illustrates, based on the components listed in Table 2.
Figure 4. Comparison of THD+N vs. frequency for various ceramic capacitors in a 1kHz highpass passive filter.
Table 2. SM ceramic capacitors tested in
||Voltage Rating (V)
Figure 4 also depicts the performance of a through-hole
ceramic capacitor selected from a random assortment of
lab components. The worst result is just 0.2% THD at
the -3dB point for the X5R dielectric. To put it in
perspective, that performance equates to distortion at the
-54dB level. The THD for most 16-bit audio DACs and
CODECs, with respect to full scale, is at least an order of
magnitude better than this. Note that C0G dielectrics can
exhibit very low voltage coefficients, but at this time
their capacitance ranges are restricted to values near
0.047µF and below. These tests were based on 1µF
capacitors, so C0G types were not included.
How to Avoid Capacitor Voltage-Coefficient
shows a line-input topology whose novel AC-coupling
configuration allows a much lower valued input
capacitor than that of a traditional configuration. The input
capacitor in this example (C1) is 0.047µF, which can be
specified as a ceramic with C0G dielectric in a 1206 case
size—a configuration that minimizes the THD contribution
from voltage-coefficient effects. DC feedback for the
op amp (which should be a device with low input-bias
current, such as the MAX4490) is provided by the two
100kΩ resistors. The effect of the DC-feedback path at
audio frequencies is attenuated by C2 and R5, so the
majority of the feedback is from R1 and R2 through C1.
With the values shown, the -3dB point is set at 5Hz.
Figure 5. This novel line-input stage reduces degradation due to voltage-coefficient effects. Including the traditional AC-coupling capacitor inside the amplifier's error path lowers the value of that capacitor, and enables the use of C0G capacitors in portable designs.
This type of compound feedback ultimately has a first-order
LF rolloff, but can be tuned for a 2nd-order response
around the highpass cutoff frequency. Consequently, pay
careful attention to overshoot and peaking when adjusting
the component values from those shown in Figure 5.
Values in the example approximate a maximally flat
highpass function. This circuit principle can easily be
adapted to quasidifferential (ground-sensing) and fully
differential input stages.
Figure 6. Frequency response for the circuit in Figure 5 shows a smooth rolloff below 10Hz with the -3dB point at 5Hz. The ultimate rolloff rate with decreasing frequency is 20dB/decade.
The stereo headphone driver IC shown in Figure 7
(MAX4410) features an innovative technology called
DirectDrive®, in which the output bias, powered from a
single positive supply, is set at 0V to allow direct DC-coupling
to the headphones. Several advantages follow:
Figure 7. In this typical application circuit for the MAX4410 stereo headphone driver, setting CIN to 10µF restricts any voltage-coefficient effects to subaudible frequencies. Large-valued coupling capacitors at the output are not necessary.
- Large DC-blocking capacitors (100µF–470µF, typ) are
eliminated, which removes a significant THD contribution
based on voltage coefficients.
- The lower -3dB cutoff, now defined by the input
capacitor and input resistor, is around 1.6Hz with the
values shown in Figure 7, but a -3dB point of 1.6Hz in
standard AC-coupled headphone drivers for 16Ω headphones
requires about 6200µF. In addition, the low-frequency
response is no longer load dependent.
- Eliminating the large-case capacitors saves a significant
amount of PCB area. Such capacitors are
expensive when compared with the 1µF and 2.2µF
ceramic compacitors required by MAX4410 charge-pump
- To enable the outputs to sink and source load current
with a ground-referenced load, the chip generates an
internal negative supply for the amplifier. Because that
supply (PVSS) is an inverted version of the positive
supply (VDD), the available voltage swing at the output
(almost 2VDD) is twice that of a traditional single-supply,
AC-coupled headphone driver.
In this example, it has been a relatively simple matter to
minimize the voltage-coefficient effect of input capacitors
on audio bandwidth by oversizing those capacitors. Given
a 10kΩ input resistor, choose a 10µF ceramic for CIN
. That combination places the -3dB point at 1.6Hz, so the
worst effects due to voltage-coefficient nonlinearity are at
least an order of magnitude below the lowest audible
frequencies being reproduced.
Regarding larger valued capacitors, Figure 8
two types of 100µF capacitors used with a 16Ω resistor in forming a passive highpass filter. At the 100Hz, -3dB
frequency, both types contribute significant THD due to
the capacitors' voltage coefficient. The 100µF tantalum
contribution to THD+N is 0.2% at the -3dB cutoff, which
is equal to the worst-performing ceramic device in Figure
4. Eliminating those devices from the audio path using
Maxim's DirectDrive components, or similar techniques,
improves the audio quality significantly and notably at
low frequencies. In Figure 8, a MAX4410 is used to
derive the reference plot (limit of measurement).
Figure 8. THD+N vs. frequency for large-valued, 100µF capacitors driving a 16Ω load. Both types (tantalum and aluminum electrolytic) contribute heavily to THD at the nominal -3dB point of 100Hz. No such output-coupling capacitors are required with Maxim's DirectDrive headphone amplifiers.
Passive components can add real, measurable degradation
to an analog audio path. Those effects can be easily
examined and assessed using standard audio test
equipment. Of the capacitor types tested, aluminum-electrolytic
and polyester capacitors give the lowest THD.
X5R ceramics give the poorest THD.
When choosing active components, take care to minimize
the number of AC-coupling capacitors in analog audio
stages. For example, use differential signal paths or
DirectDrive components for headphone feeds (e.g.,
MAX4410). When possible, design audio circuitry with
low capacitance values in which C0G or PPS dielectrics
can be used. To reduce voltage-coefficient effects in AC-coupled
audio stages, restrict potential problems to the
subaudio frequencies by lowering the -3dB point much
more than necessary, by 10x, for example.