AD8307-EB Analog Devices Inc, AD8307-EB Datasheet - Page 9

• Manufacturer Part Number: AD8307-EB
• Manufacturer: Analog Devices Inc

Specifications of AD8307-EB

• Lead Free Status / Rohs Status: Not Compliant

LOG AMP THEORY
Logarithmic amplifiers perform a more complex operation than
that of classical linear amplifiers, and their circuitry is significantly
different. A good grasp of what log amps do and how they work
can prevent many pitfalls in their application. The essential purpose
of a log amp is not to amplify, though amplification is utilized to
achieve the function. Rather, it is to compress a signal of wide
dynamic range to its decibel equivalent. It is thus a measurement
device. A better term may be logarithmic converter, because its
basic function is the conversion of a signal from one domain of
representation to another via a precise nonlinear transformation.
Logarithmic compression leads to situations that can be confusing
or paradoxical. For example, a voltage offset added to the output
of a log amp is equivalent to a gain increase ahead of its input.
In the usual case where all the variables are voltages, and regardless
of the particular structure, the relationship between the variables
can be expressed as
where:
V
V
(in which case V
V
V
All log amps implicitly require two references, in this example,
V
lute accuracy of a log amp cannot be any better than the accuracy
of its scaling references. Equation 1 is mathematically incomplete
in representing the behavior of a demodulating log amp, such
as the AD8307, where V
basic principles are unaffected, and this can be safely used as the
starting point in the analyses of log amp scaling.
Figure 21 shows the input/output relationship of an ideal log amp,
conforming to Equation 1. The horizontal scale is logarithmic and
spans a wide dynamic range, shown in Figure 21 as over 120 dB, or
six decades. The output passes through zero (the log intercept)
at the unique value V
inputs below the intercept. In the ideal case, the straight line
OUT
Y
IN
X
X
is the slope voltage; the logarithm is usually taken to base 10
is the intercept voltage.
and V
is the input voltage.
V
V
is the output voltage.
OUT
OUT
V
–2V
V
OUT
5V
4V
3V
2V
= 0
IN
V
–40dBc
Y
Y
Y
Y
Y
Y
Y
= 10
, which determine the scaling of the circuit. The abso-
=
V
–2
Y
V
X
log
Y
LOWER INTERCEPT
Figure 21. Ideal Log Amp Function
is also the volts per decade).
(
V
IN
V
IN
IN
0dBc
= V
/
IN
= V
V
X
has an alternating sign. However, the
X
X
)
and ideally becomes negative for
V
IN
+40dBc
V
SHIFT
= 10
2
V
X
V
IN
+80dBc
= 10
4
V
LOG V
X
IN
Rev. D | Page 9 of 24
(1)
describing V
directions. The dotted line shows that the effect of adding an
offset voltage, V
voltage, V
the gain (or signal level) ahead of the log amp by the factor,
V
an offset of 150 mV added to the output appears to lower the
intercept by two-tenths of a decade, or 6 dB. Adding an offset to
the output is thus indistinguishable from applying an input level
that is 6 dB higher.
The log amp function described by Equation 1 differs from that
of a linear amplifier in that the incremental gain δV
very strong function of the instantaneous value of V
apparent by calculating the derivative. For the case where the
logarithmic base is δ,
That is, the incremental gain is inversely proportional to the
instantaneous value of the input voltage. This remains true
for any logarithmic base, which is chosen as 10 for all decibel
related purposes. It follows that a perfect log amp is required to
have infinite gain under classical small signal (zero amplitude)
conditions. Less ideally, this result indicates that whatever
means are used to implement a log amp, accurate response
under small signal conditions (that is, at the lower end of the
dynamic range) demands the provision of a very high gain
bandwidth product. A further consequence of this high gain is
that in the absence of an input signal, even very small amounts
of thermal noise at the input of a log amp cause a finite output
for zero input. This results in the response line curving away
from the ideal shown in Figure 21 toward a finite baseline,
which can be either above or below the intercept. Note that the
value given for this intercept can be an extrapolated value, in
which case the output cannot cross zero, or even reach it, as is
the case for the AD8307.
While Equation 1 is fundamentally correct, a simpler formula is
appropriate for specifying the calibration attributes of a log amp
like the AD8307, which demodulates a sine wave input.
where:
V
RSSI) output.
V
between 15 mV/dB and 30 mV/dB).
P
reference power level.
P
the same reference level.
The most widely used reference in RF systems is decibels above
1 mW in 50 Ω, written dBm. Note that the quantity (P
IN
0
OUT
SLOPE
SHIFT
is the logarithmic intercept, expressed in decibels relative to
is the input power, expressed in decibels relative to some
V
is the demodulated and filtered baseband (video or
δ
/V
δ
is the logarithmic slope, now expressed in V/dB (typically
OUT
V
V
Y
OUT
IN
. For example, if V
X
= V
. Exactly the same alteration can be achieved by raising
OUT
=
SLOPE
V
SHIFT
V
for all values of V
IN
Y
(P
, to the output is to lower the effective intercept
IN
– P
0
)
Y
is 500 mV per decade (25 mV/dB),
IN
continues indefinitely in both
OUT
AD8307
IN
, as is
IN
/δV
– P
IN
0
) is
is a
(2)
(3)