THAT2252 THAT, THAT2252 Datasheet - Page 4

• Manufacturer Part Number: THAT2252
• Description: IC RMS-Level Detector
• Manufacturer: THAT

Page 4
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-
iar exponential weighting function, e
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, C
together with V- form the current source.) This
current source
current, I
charges to 1 V
output of OA2).
The instantaneous emitter current in Q6 is propor-
tional to the antilog of its V
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 V
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 V
exact value of the diode drop will be determined by
SYM
50k
V+
IN
Figure 4. Typical Application Circuit ( 15V)
T
20u
, through Q6. Over time, the capacitor
Cin
BE
V-
24k
47k
20
establishes a quiescent dc bias
10k
Rin
below V
THAT Corporation; 45 Sumner Street; Milford, Massachusetts 01757-1656; USA
1u
BE
Tel: [phone]; Fax: [phone]; Web: www.thatcorp.com
, the current in Q6 is pro-
1
T
log
560k
SYM
IN
5
V-
is the capacitor and R
4
BE
V-
Rb
2252
(the potential at the
2M2
, which is the differ-
GND
3
2
IBIAS
R
T
6
8
Rf
CAP
OUT
V+
22M
7
t
.
1k
10u
10u
C
T
log
V+
OUT
. The
T
the bias current I
in the input current I
charge the capacitor C
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 C
in the log domain. Q6 and C
pole at a frequency determined by a) the imped-
ance of Q6 at the bias current I
of C
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 . The av-
eraging corresponds to convolution with the time
weighting of a simple RC circuit. Mathematically,
this is as follows:
V
which the average level is computed. Note that
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
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 I
(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
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-
e
6
t
T
. The time constant
1
n
represents the exponential time weighting
C
C
by
T
T
1
T
2
V
I
0 0259
of
T
T
.
I
T
0
the
T
I e dt
in
2
the
, at 300° Kelvin.
T
. However, for sudden increases
t
nature
log-domain
THAT 2252 RMS-Level Detector
in
, where T is the time at
, the current available to
T
is given below.
is proportional to the
T
of
as a first-order filter
T
T
establish a single
the
filter
and b) the value
exponential
with
T
and C
the
T