THAT2252 Datasheet, PDF (4/10 Pages) List of Unclassifed Manufacturers – IC RMS-Level Detector

Page 4
THAT 2252 RMS-Level Detector
Computing the Mean
In the classic mathematical definition of rms
value, the time integral of the square of the signal
must be evaluated over infinite time. Obviously, for
a practical measurement, only a finite time is
available, which leads to the question of how to
weight events occuring at various times. Tradi-
tionally, the simplest and most meaningful weight-
ing is exponential in time, giving highest weight to
the most recent history, and exponentially less
weight to increasingly older events. This weighting
corresponds to convolution in time with the famil-
-t
iar exponential weighting function, e ^t .
To accomplish this weighting, Pin 6 is normally
connected to a capacitor and a negative current
source. (Refer to the Typical Application Circuit in
Figure 4. In this circuit, CT is the capacitor and RT
together with V- form the current source.) This
current source establishes a quiescent dc bias
current, IT, through Q6. Over time, the capacitor
charges to 1 VBE below Vlog (the potential at the
output of OA2).
The instantaneous emitter current in Q6 is propor-
tional to the antilog of its VBE, which is the differ-
ence between Q6’s base voltage and the voltage at
pin 6. The potential at the base of Q6 represents
the log of the square of the input current, while
the emitter of Q6 is held at ac ground via the ca-
pacitor. Since Q6’s emitter current is proportional
to the antilog of its VBE, the current in Q6 is pro-
portional to the square of the instantaneous input
current.
Note that this antilogging only takes place for dy-
namic signals. For a dc input, the output of OA2
represents the square of the input current. After
charging, the external timing capacitor voltage
again approaches one diode drop below Vlog. The
exact value of the diode drop will be determined by
SYM
50k
V+
V-
1u
24k
47k
20
Rb
560k
V+
1k
10u
428
1
SYM IBIAS V+
IN 2252 OUT
7
V- GND CAP
53 6
OUT
IN
Cin
20u
Rin
10k
RT
CT
2M2
10u
V-
Rf 22M
Figure 4. Typical Application Circuit (±15V)
the bias current IT. However, for sudden increases
in the input current Iin, the current available to
charge the capacitor CT is proportional to the
square of the short-term increase in input current.
The “dynamic” antilogging causes the capacitor
voltage to represent the log of the mean of the
square of the input current.
Time Constants
Another way of looking at this situation is to con-
sider the action of Q6 and CT as a first-order filter
in the log domain. Q6 and CT establish a single
pole at a frequency determined by a) the imped-
ance of Q6 at the bias current I_T and b) the value
of C_T. The time constant t is given below.
t
=
C_T
V_T
I_T
=
C_T
0.0259
I_T
,
at
300°
Kelvin.
The result is that the voltage at pin 6 represents
the average (or mean) of the square of the input
signal, averaged over the time constant t. The av-
eraging corresponds to convolution with the time
weighting of a simple RC circuit. Mathematically,
this is as follows:
ò ^V
6
a
1n^{æèçç}
1
T²
T
0
I
i²n^e
-t
t
dt
öø÷÷
,
where
T
is
the
time
at
which the average level is computed. Note that
æç
èç
-t
e^t
öø÷÷
represents
the
exponential
time
weighting
imposed by the log-domain filter.
How fast the 2252 acquires a signal (the “attack”),
and how fast it returns to rest following a signal
(the “release”), are locked in relationship to each
other by the nature of the exponential
time-weighting imposed by this log-domain filter.
Separate attack and release adjustments are not
possible within the constraint of rms response.
The time response for typical values of IT and CT
(the circuit of Figure4 ) is shown in Figure 5,
which shows the 2252’s response to a 100 ms,
1 kHz tone burst at ~+10 dBV followed by
~500 ms of 1 kHz at ~–30 dBV. The top trace is
the input tone burst (at 10 V/div), the bottom trace
is the output at 50 mV/div. The time scale is
50 ms/div.
The shape of the attack and release waveforms is
determined by the interaction of the exponential
response of the log-domain filter with the
log-representation of the signal. The straight-line
decay follows from the fact that the natural release
of the exponential time weighting is a decaying ex-
ponential in the linear world. This maps to a
straight line in the log representation. The attack
in the photo appears exponential, but actually fol-
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