THEORY OF OPERATION
The AD8309 is an advanced IF signal processing IC, intended
for use in high performance receivers, combining two key func-
tions. First, it provides a large voltage gain combined with pro-
gressive compression, through which an IF signal of high dynamic
range is converted into a square-wave (that is, hard limited)
output, from which frequency and phase information modulated
on this input can be recovered by subsequent signal processing.
For this purpose, the noise level referred to the input must be
very low, since it determines the
detection threshold
for the receiver.
Further, it is often important that the group delay in this ampli-
fier be essentially independent of the signal level, to minimize
the risk of amplitude-to-phase conversion. Finally, it is also desir-
able that the amplitude of the limited output be well defined and
temperature stable. In the AD8309, this amplitude can be con-
trolled by the user, or even completely shut off, providing greater
flexibility.
The second function is to provide a demodulated (baseband)
output proportional to the decibel value of the signal input,
which may be used to measure the signal strength. This output,
which typically runs from a value close to the ground level to a
few volts above ground, is called the
Received Signal Strength
Indication,
or RSSI. The provision of this function requires the
use of a logarithmic amplifier (log amp). For this output to be
suitable for measuring signal strength, it is important that its
scaling attributes
are well controlled.
These are the logarithmic
slope,
specified in mV/dB, and the
intercept,
often specified as an equivalent power level at the
amplifier input, although a log amp is inherently a voltage-
responding device. (See further discussion, below). Also
important is the
law conformance,
that is, how well the RSSI
approximates an ideal function. Many low quality log amps
provide only an approximate solution, resulting in large errors in
law conformance and scaling. All Analog Devices log amps are
designed with close attention to matters affecting accuracy of
the overall function.
In the AD8309, these two basic signal-processing functions are
combined to provide the necessary voltage gain with progressive
compression and hard limiting, and the determination of the
logarithmic magnitude of the input (RSSI). This combination is
called a log limiting amplifier. A good grasp of how this product
works will avoid many pitfalls in their application.
Log-Amp Fundamentals
references.
Note that (1) is mathematically incomplete in rep-
resenting the behavior of a
demodulating
log amp such as the
IN
has an alternating sign. However, the basic
principles are unaffected.
Figure 19 shows the input/output relationship of an ideal log
amp, conforming to Equation (1). The horizontal scale is loga-
rithmic, and spans a very wide dynamic range, shown here as
over 120 dB, that is, six decades of voltage or twelve decades of
input-referred power. The output passes through zero (the
“log-intercept”) at the unique value V
IN
= V
X
and becomes
negative for inputs below the intercept. In the ideal case, the
straight line describing V
OUT
for all values of V
IN
would con-
tinue indefinitely in both directions. The dotted line shows that
the effect of adding an offset voltage V
SHIFT
to the output is to
lower the effective intercept voltage V
X
.
V
OUT
5V
Y
4V
Y
V
SHIFT
3V
Y
2V
Y
V
Y
LOG V
IN
V
OUT
= 0
V
IN
= 10
–2
V
X
–40dBc
V
IN
= V
X
0dBc
V
IN
= 10
2
V
X
+40dBc
V
IN
= 10
4
V
X
+80dBc
LOWER INTERCEPT
–2V
Y
Figure 19. Ideal Log Amp Function
Exactly the same modification could be achieved raising the gain
(or signal level) ahead of the log amp by the factor V
SHIFT
/V
Y
.
For example, if V
Y
is 400 mV/decade (that is, 20 mV/dB, as for
the AD8309), an offset of 120 mV added to the output will
appear 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 (1) differs from that of a
linear amplifier in that the incremental gain DV
OUT
/DV
IN
is a
very strong function of the instantaneous value of V
IN
, as is
apparent by calculating the derivative. For the case where the
logarithmic base is
e,
it is easy to show that
The essential purpose of a logarithmic amplifier is to reduce a
signal of wide dynamic range to its decibel equivalent. It is thus
primarily a
measurement device.
The logarithmic representation
leads to situations that may be confusing or even paradoxical.
For example, a voltage
offset
added to the RSSI output of a log
amp is equivalent to a
gain
increase ahead of its input.
When all the variables expressed as voltages, then, regardless of
the particular structure, the output can be expressed as
V
OUT
=
V
Y
log (V
IN
/V
X
)
(1)
where
V
Y
is the “slope voltage.”
V
IN
is the input voltage, and
V
X
is the “intercept voltage.” The logarithm is usually to base-10,
which is appropriate to a decibel-calibrated device, in which
case V
Y
is also the “volts-per-decade.” It will be apparent from
(1) that a log amp requires two references, here V
X
and V
Y
, that
determine the
scaling
of the circuit. The absolute accuracy of a
log amp cannot be any better than the accuracy of its
scaling
REV. B
–7–
∆
V
OUT
V
Y
=
∆
V
IN
V
IN
(2)
That is, the incremental gain of a log amp is inversely propor-
tional to the instantaneous value of the input voltage. This re-
mains true for any logarithmic base. A “perfect” log amp would
be required to have infinite gain under classical “small-signal”
(zero-amplitude) conditions. This demonstrates that, whatever
means might be used to implement a log amp, accurate HF
response under small signal conditions (that is, at the lower end
of the full dynamic range) demands the provision of a
very high
gain-bandwidth product.
A wideband log amp must therefore use
many cascaded gain cells each of low gain but high bandwidth.
For the AD8309, the gain-bandwidth (–10 dB) product is
52,500 GHz.
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