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LTC1968IMS8#TRPBF

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10
LTC1968
1968f
Because this peak has energy (proportional to voltage
squared) that is 16 times (4
2
) the energy of the RMS value,
the peak is necessarily present for at most 6.25% (1/16)
of the time.
The LTC1968 performs very well with crest factors of 4 or
less and will respond with reduced accuracy to signals
with higher crest factors. The high performance with crest
factors less than 4 is directly attributable to the high
linearity throughout the LTC1968.
DESIGN COOKBOOK
The LTC1968 RMS-to-DC converter makes it easy to
implement a rather quirky function. For many applications
all that will be needed is a single capacitor for averaging,
appropriate selection of the I/O connections and power
supply bypassing. Of course, the LTC1968 also requires
power. A wide variety of power supply configurations are
shown in the Typical Applications section towards the end
of this data sheet.
Capacitor Value Selection
The RMS or root-mean-squared value of a signal,
the root
of the mean of the square
, cannot be computed without
some averaging to obtain the
mean
function. The LTC1968
true RMS-to-DC converter utilizes a single capacitor on
the output to do the low frequency averaging required for
RMS-to-DC conversion. To give an accurate measure of a
dynamic waveform, the averaging must take place over a
sufficiently long interval to average, rather than track, the
lowest frequency signals of interest. For a single averaging
capacitor, the accuracy at low frequencies is depicted in
Figure 6.
Figure 6 depicts the so-called “DC error” that results at a
given combination of input frequency and filter capacitor
values
2
. It is appropriate for most applications, in which
the output is fed to a circuit with an inherently band-limited
frequency response, such as a dual slope/integrating A/D
converter, a ∆Σ A/D converter or even a mechanical analog
meter.
However, if the output is examined on an oscilloscope with
a very low frequency input, the incomplete averaging will
be seen, and this ripple will be larger than the error
depicted in Figure 6. Such an output is depicted in
Figure 7. The ripple is at twice the frequency of the input
APPLICATIO S I FOR ATIO
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Figure 6. DC Error vs Input Frequency
Figure 7. Output Ripple Exceeds DC Error
TIME
OUTPUT
1968 F07
DC
ERROR
(0.05%)
IDEAL
OUTPUT
DC
AVERAGE
OF ACTUAL
OUTPUT
PEAK
RIPPLE
(5%)
ACTUAL OUTPUT
WITH RIPPLE
f = 2 × f
INPUT
PEAK
ERROR =
DC ERROR +
PEAK RIPPLE
(5.05%)
2
This frequency-dependent error is in additon to the static errors that affect all readings and are
therefore easy to trim or calibrate out. The “Error Analyses” section to follow discusses the effect
of static error terms.
INPUT FREQUENCY (Hz)
1
–2.0
DC ERROR (%)
–1.6
–1.2
–0.8
–0.4
10 100
1968 F06
0
–1.8
–1.4
–1.0
–0.6
–0.2
C = 0.22µFC = 0.47µFC = 1µF
C = 10µF
C = 2.2µF
C = 22µF
C = 47µF
C = 4.7µF
11
LTC1968
1968f
APPLICATIO S I FOR ATIO
WUUU
because of the computation of the square of the input. The
typical values shown, 5% peak ripple with 0.05% DC error,
occur with C
AVE
= 10µF and f
INPUT
= 6Hz.
If the application calls for the output of the LTC1968 to feed
a sampling or Nyquist A/D converter (or other circuitry
that will not average out this double frequency ripple) a
larger averaging capacitor can be used. This trade-off is
depicted in Figure 8. The peak ripple error can also be
reduced by additional lowpass filtering after the LTC1968,
but the simplest solution is to use a larger averaging
capacitor.
A 10µF capacitor is a good choice for many applications.
The peak error at 50Hz/60Hz will be <1% and the DC error
will be <0.1% with frequencies of 10Hz or more.
Note that both Figure 6 and Figure 8 assume AC-coupled
waveforms with a crest factor less than 2, such as sine
waves or triangle waves. For higher crest factors and/or
AC + DC waveforms, a larger C
AVE
will generally be
required. See “Crest Factor and AC + DC Waveforms.”
Capacitor Type Selection
The LTC1968 can operate with many types of capacitors.
The various types offer a wide array of sizes, tolerances,
parasitics, package styles and costs.
Ceramic chip capacitors offer low cost and small size, but
are not recommended for critical applications. The value
stability over voltage and temperature is poor with many
types of ceramic dielectrics. This will not cause an RMS-
to-DC accuracy problem except at low frequencies, where
it can aggravate the effects discussed in the previous
section. If a ceramic capacitor is used, it may be neces-
sary to use a much higher nominal value in order to
assure the low frequency accuracy desired.
Another parasitic of ceramic capacitors is leakage, which
is again dependent on voltage and particularly tempera-
ture. If the leakage is a constant current leak, the I • R drop
of the leak multiplied by the output impedance of the
LTC1968 will create a constant offset of the output voltage.
If the leak is Ohmic, the resistor divider formed with the
LTC1968 output impedance will cause a gain error. For
<0.1% gain accuracy degradation, the parallel impedance
of the capacitor leakage will need to be >1000 times the
LTC1968 output impedance. Accuracy at this level can be
hard to achieve with a ceramic capacitor, particularly with
a large value of capacitance and at high temperature.
For critical applications, a film capacitor, such as metal-
ized polyester, will be a much better choice. Although
more expensive, and larger for a given value, the value
stability and low leakage make metal-film capacitors a
trouble-free choice.
With any type of capacitor, the self-resonance of the
capacitor can be an issue with the switched capacitor
LTC1968. If the self-resonant frequency of the averaging
capacitor is 1MHz or less, a second smaller capacitor
should be added in parallel to reduce the impedance seen
by the LTC1968 output stage at high frequencies. A
capacitor 100 times smaller than the averaging capacitor
will typically be small enough to be a low cost ceramic with
a high quality dielectric such as X7R or NPO/COG.
Figure 8. Peak Error vs Input Frequency with One Cap Averaging
INPUT FREQUENCY (Hz)
1
–1.2
PEAK ERROR (%)
–1.0
–0.8
–0.6
–0.4
10 100 1000
1968 F08
–1.4
–1.6
–1.8
–2.0
–0.2
0
C = 220µF
C = 100µF C = 47µF C = 22µF C = 10µF C = 4.7µF C = 2.2µF C =1µF
12
LTC1968
1968f
Input Connections
The LTC1968 input is differential and DC coupled. The
LTC1968 responds to the RMS value of the differential
voltage between Pin 2 and Pin 3, including the DC portion
of that difference. However, there is no DC-coupled path
from the inputs to ground. Therefore, at least one of the two
inputs must be connected with a DC-return path to ground.
Both inputs must be connected to something. If either
input is left floating, a zero volt output will result.
For single-ended DC-coupled applications, simply con-
nect one of the two inputs (they are interchangeable) to
the signal, and the other to ground. This will work well for
dual supply configurations, but for single supply con-
figurations it will only work well for unipolar input sig-
nals. The LTC1968 input voltage range is from rail-to-rail,
and when the input is driven above V
+
or below GND the
gain and offset errors will increase substantially after just
a few hundred millivolts of overdrive. Fortunately, most
single supply circuits measuring a DC-coupled RMS
value will include some reference voltage other than
ground, and the second LTC1968 input can be connected
to that point.
For single-ended AC-coupled applications, Figure 9 shows
three alternate topologies. The first one, shown in Figure
9a uses a coupling capacitor to one input while the other
is grounded. This will remove the DC voltage difference from
the input to the LTC1968, and it will therefore not be part
of the resulting output voltage. Again, this connection will
APPLICATIO S I FOR ATIO
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work well with dual supply configurations, but in single
supply configurations it will be necessary to raise the volt-
age on the grounded input to assure that the signal at the
active input stays within the range of 0V to V
+
. If there is
already a suitable voltage reference available, connect the
second input to that point. If not, a midsupply voltage can
be created with two resistors as shown in Figure 9b.
Finally, if the input voltage is known to be between 0V and
V
+
, it can be AC coupled by using the configuration shown
in Figure 9c. Whereas the DC return path was provided
through Pin 3 in Figures 9a and 9b, in this case, the return
path is provided on Pin 2, through the input signal volt-
ages. The switched capacitor action between the two input
pins of the LTC1968 will cause the voltage on the coupling
capacitor connected to the second input to follow the DC
average of the input voltage.
For differential input applications, connect the two inputs to
the differential signal. If AC coupling is desired, one of the
two inputs can be connected through a series capacitor.
In all of these connections, to choose the input coupling
capacitor, C
C
, calculate the low frequency coupling time
constant desired, and divide by the LTC1968 differential
input impedance. Because the LTC1968 input impedance
is about 100 times its output impedance, this capacitor is
typically much smaller than the output averaging capaci-
tor. Its requirements are also much less stringent, and a
ceramic chip capacitor will usually suffice.
Figure 9. Single-Ended AC-Coupled Input Connection Alternatives
+
–
LTC1968
GND
V
+
V
+
V
+
V
–
(9a)
C
C
IN1
V
IN
IN2
2
3
LTC1968
(9b)
C
C
R1
10k
R2
10k
0.1µF
IN1
V
IN
V
+
IN2
2
3
LTC1968
(9c)
C
C
IN1
V
IN
1968 F09
V
DC
IN2
2
3
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LTC1968IMS8#TRPBF

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Manufacturer:
Analog Devices Inc.
Description:
Power Management Specialized - PMIC Prec Wide B&width, RMS-to-DC Conv
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