19
LTC1968
1968f
waveform dynamics and the type of filtering used. The
above method is conservative for some cases and about
right for others.
The LTC1968 works well with signals whose crest factor
is 4 or less. At higher crest factors, the internal ∆Σ
modulator will saturate, and results will vary depending on
the exact frequency, shape and (to a lesser extent) ampli-
tude of the input waveform. The output voltage could be
higher or lower than the actual RMS of the input signal.
The ∆Σ modulator may also saturate when signals with
crest factors less than 4 are used with insufficient averag-
ing. This will only occur when the output droops to less
than 1/4 of the input voltage peak. For instance, a DC-
coupled pulse train with a crest factor of 4 has a duty cycle
of 6.25% and a 1V
PEAK
input is 250mV
RMS
. If this input is
50Hz, repeating every 20ms, and C
AVE
= 10µF, the output
will droop during the inactive 93.75% of the waveform.
This droop is calculated as:
V
V
e
MIN
RMS
INACTIVE TIME
=
2
1–
2 Z C
OUT AVE
For the LTC1968, whose output impedance (Z
OUT
) is
12.5k, this droop works out to –3.6%, so the output
would be reduced to 241mV at the end of the inactive
portion of the input. When the input signal again climbs to
1V
PEAK
, the peak/output ratio is 4.15.
With C
AVE
= 100µF, the droop is only –0.37% to 249.1mV
and the peak/output ratio is just 4.015, which the LTC1968
has enough margin to handle without error.
For crest factors less than 3.5, the selection of C
AVE
as
previously described should be sufficient to avoid this
droop and modulator saturation effect. But with crest
factors above 3.5, the droop should also be checked for
each design.
Error Analyses
Once the RMS-to-DC conversion circuit is working, it is
time to take a step back and do an analysis of the accuracy
of that conversion. The LTC1968 specifications include
three basic static error terms, V
OOS
, V
IOS
and GAIN. The
output offset is an error that simply adds to (or subtracts
APPLICATIO S I FOR ATIO
WUUU
from) the voltage at the output. The conversion gain of the
LTC1968 is nominally 1.000 V
DCOUT
/V
RMSIN
and the gain
error reflects the extent to which this conversion gain is
not perfectly unity. Both of these affect the results in a
fairly obvious way.
Input offset on the other hand, despite its conceptual
simplicity, effects the output in a nonobvious way. As its
name implies, it is a constant error voltage that adds
directly with the input. And it is the sum of the input and
V
IOS
that is RMS converted.
This means that the effect of V
IOS
is warped by the
nonlinear RMS conversion. With 0.4mV (typ) V
IOS
, and a
200mV
RMS
AC input, the RMS calculation will add the DC
and AC terms in an RMS fashion and the effect is
negligible:
V
OUT
= (200mV AC)
2
+ (0.4mV DC)
2
= 200.0004mV
= 200mV + 2ppm
But with 10× less AC input, the error caused by V
IOS
is
100× larger:
V
OUT
= (20mV AC)
2
+ (0.4mV DC)
2
= 20.004mV
= 20mV + 200ppm
This phenomena, although small, is one source of the
LTC1968’s residual nonlinearity.
On the other hand, if the input is DC coupled, the input
offset voltage adds directly. With +200mV and a +0.4mV
V
IOS
, a 200.4mV output will result, an error of 0.2% or
2000ppm. With DC inputs, the error caused by V
IOS
can be
positive or negative depending if the two have the same or
opposing polarity.
The total conversion error with a sine wave input using the
typical values of the LTC1968 static errors is computed as
follows:
V
OUT
= ((500mV AC)
2
+ (0.4mV DC)
2
) • 1.001 + 0.2mV
= 500.700mV
= 500mV + 0.140%
V
OUT
= ((50mV AC)
2
+ (0.4mV DC)
2
) • 1.001 + 0.2mV
= 50.252mV
= 50mV + 0.503%
20
LTC1968
1968f
V
OUT
= ((5mV AC)
2
+ (0.4mV DC)
2
) • 1.001 + 0.2mV
= 5.221mV
= 5mV + 4.42%
As can be seen, the gain term dominates with large inputs,
while the offset terms become significant with smaller
inputs. In fact, 5mV is the minimum RMS level needed to
keep the LTC1968 calculation core functioning normally,
so this represents the worst-case of usable input levels.
Using the worst-case values of the LTC1968 static errors,
the total conversion error is:
V
OUT
= ( (500mV AC)
2
+ (1.5mV DC)
2
) • 1.003 + 0.75mV
= 502.25mV
= 500mV + 0.45%
V
OUT
= ((50mV AC)
2
+ (1.5mV DC)
2
) • 1.003 + 0.75mV
= 50.923mV
= 50mV + 1.85%
V
OUT
= ((5mV AC)
2
+ (1.5mV DC)
2
) • 1.003 + 0.75mV
= 5.986mV
= 5mV + 19.7%
These static error terms are in addition to dynamic error
terms that depend on the input signal. See the Design
Cookbook for a discussion of the DC conversion error with
low frequency AC inputs. The LTC1968 bandwidth limita-
tions cause additional errors with high frequency inputs.
Another dynamic error is due to crest factor. The LTC1968
performance versus crest factor is shown in the Typical
Performance Characteristics.
Output Errors Versus Frequency
As mentioned in the design cookbook, the LTC1968 per-
forms very well with low frequency and very low frequency
inputs, provided a large enough averaging capacitor is used.
However, the LTC1968 will have additional dynamic errors
as the input frequency is increased. The LTC1968 is de-
signed for high accuracy RMS-to-DC conversion of sig-
nals up to 100kHz. However, the switched capacitor cir-
cuitry samples the inputs at a modest 2MHz nominal. The
response versus frequency is depicted in the Typical Per-
formance Characteristics titled Input Signal Bandwidth.
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Although there is a pattern to the response versus fre-
quency that repeats every sample frequency, the errors
are not overwhelming. This is because LTC1968 RMS
calculation is inherently wideband, operating properly with
minimal oversampling, or even undersampling, using sev-
eral proprietary techniques to exploit the fact that the RMS
value of an aliased signal is the same as the RMS value of
the original signal. However, a fundamental feature of the
∆Σ modulator is that sample estimation noise is shaped
such that minimal noise occurs with input frequencies
much less than the sampling frequency, but such noise
peaks when input frequency reaches half the sampling
frequency. Fortunately the LTC1968 output averaging fil-
ter greatly reduces this error, but the RMS-to-DC topology
frequency shifts the noise to low (baseband) frequencies.
See Output Noise vs Input Frequency in the Typical Perfor-
mance Characteristics.
Input Impedance
The LTC1968 true RMS-to-DC converter utilizes a 0.8pF
capacitor to sample the input at a nominal 2MHz sample
frequency. This accounts for the 1.2M input impedance.
See Figure 20 for the equivalent analog input circuit. Note
however, that the 1.2M input impedance does not di-
rectly affect the input sampling accuracy. For instance, if
a 15.5k source resistance is used to drive the LTC1968, the
sampling action of the input stage will drag down the
voltage seen at the input pins with small spikes at every
sample clock edge as the sample capacitor is connected to
be charged. The time constant of this combination is
small, 0.8pF • 15.5k = 12.5ns, and during the 125ns
period devoted to sampling, ten time constants elapse.
Figure 20. LTC1968 Equivalent Analog Input Circuit
IN1
V
DD
V
DD
V
SS
V
SS
R
SW
(TYP)
2k
C
EQ
0.8pF
(TYP)
C
EQ
0.8pF
(TYP)
I
IN1
IN2
I
IN2
1968 F20
R
SW
(TYP)
2k
IIN
VV
R
IIN
VV
R
RM
AVG
IN IN
EQ
AVG
IN IN
EQ
EQ
1
2
1.2
12
21
()
=
()
=
=
21
LTC1968
1968f
APPLICATIO S I FOR ATIO
WUUU
This allows each sample to settle to within 46ppm and it is
these samples that are used to compute the RMS value.
This is a much higher accuracy than the LTC1968 conver-
sion limits, and far better than the accuracy computed via
the simplistic resistive divider model:
Output Impedance
The LTC1968 output impedance during operation is simi-
larly due to a switched capacitor action. In this case, 20pF
of on-chip capacitance operating at 2MHz translates into
25k. The closed-loop RMS-to-DC calculation cuts that in
half to the nominal 12.5k specified.
In order to create a DC result, a large averaging capacitor
is required. Capacitive loading and time constants are not
an issue on the output.
However, resistive loading is an issue and the 10M
impedance of a DMM or 10× scope probe will drag the
output down by –0.125% typ.
During shutdown, the switching action is halted and a
fixed 12.5k resistor shunts V
OUT
to OUT RTN so that C
AVE
is discharged.
Interfacing with an ADC
The LTC1968 output impedance and the RMS averaging
ripple need to be considered when using an analog-to-
digital converter (ADC) to digitize the LTC1968 RMS
result.
The simplest configuration is to connect the LTC1968
directly to the input of a type 7106/7136 ADC as shown in
Figure 21a. These devices are designed specifically for
DVM/DPM use and include display drivers for a 3 1/2 digit
LCD segmented display. Using a dual-slope conversion,
the input is sampled over a long integration window, which
results in rejection of line frequency ripple when integra-
tion time is an integer number of line cycles. Finally, these
parts have an input impedance in the G range, with
specified input leakage of 10pA to 20pA. Such a leakage,
combined with the LTC1968 output impedance, results in
less than 1µV of additional output offset voltage.
Another type of ADC that has inherent rejection of RMS
averaging ripple is an oversampling ∆Σ ADC such as the
LTC2420. Its input impedance is 6.5M, but only when it
is sampling. Since this occurs only half the time at most,
if it directly loads the LTC1968, a gain error of –0.08% to
–0.11% results. In fact, the LTC2420 DC input current is
VV
R
RR
V
M
V
IN SOURCE
IN
IN SOURCE
SOURCE
SOURCE
=
+
=
=
1.2
125–. %
Mk+1.2 15.5
This resistive divider calculation does give the correct
model of what voltage is seen at the input terminals by a
parallel load averaged over a several clock cycles, which is
what a large shunt capacitor will do—average the current
spikes over several clock cycles.
When high source impedances are used, care must be taken
to minimize shunt capacitance at the LTC1968 input so as
not to increase the settling time. Shunt capacitance of just
0.8pF will double the input settling time constant and the
error in the above example grows from 46ppm to 0.67%
(6700ppm). As a consequence, it is important to
not
try to
filter the input with large input capacitances unless driven
by a low impedance. Keep time constant <<125ns.
When the LTC1968 is driven by op amp outputs, whose
low DC impedance can be compromised by sharp capaci-
tive load switching, a small series resistor may be added.
A 1k resistor will easily settle with the 0.8pF input sampling
capacitor to within 1ppm.
These are important points to consider both during design
and debug. During lab debug, and even production testing,
a high value series resistor to any test point is advisable.

LTC1968IMS8#TRPBF

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