AD606
REV. B
–4–
INPUT LEVEL CONVENTIONS
RF logarithmic amplifiers usually have their input specified in
“dBm,” meaning “decibels with respect to 1 mW.” Unfortu-
nately, this is not precise for several reasons.
1. Log amps respond not to power but to voltage. In this re-
spect, it would be less ambiguous to use “dBV” (decibels
referred to 1 V) as the input metric. Also, power is dependent
on the rms (root mean-square) value of the signal, while log
amps are not inherently rms responding.
2. The response of a demodulating log amp depends on the
waveform. Convention assumes that the input is sinusoidal.
However, the AD606 is capable of accurately handling any
input waveform, including ac voltages, pulses and square
waves, Gaussian noise, and so on. See the AD640 data sheet,
which covers the effect of waveform on logarithmic intercept,
for more information.
3. The impedance in which the specified power is measured is
not always stated. In the log amp context it is invariably
assumed to be 50 Ω. Thus, 0 dBm means “1 mW rms in 50 Ω,”
and corresponds to an rms voltage of
(1 mW × 50 Ω),
or
224 mV.
Popular convention requires the use of dBm to simplify the
comparison of log amp specifications. Unless otherwise stated,
sinusoidal inputs expressed as dBm in 50 Ω are used to specify
the performance of the AD606 throughout this data sheet. We
will also show the corresponding rms voltages where it helps to
clarify the specification. Noise levels will likewise be given in
dBm; the response to Gaussian noise is 0.5 dB higher than for a
sinusoidal input of the same rms value.
Note that dynamic range, being a simple ratio, is always speci-
fied simply as “dB”, and the slope of the logarithmic transfer
function is correctly specified as “mV/dB,” NOT as “mV/dBm.”
LOGARITHMIC SLOPE AND INTERCEPT
A generalized logarithmic amplifier having an input voltage V
IN
and output voltage V
LOG
must satisfy a transfer function of the
form
VV VV
LOG Y IN X
= log ( / )
10
where, in the case of the AD606, the voltage V
IN
is the differ-
ence between the voltages on pins INHI and INLO, and the
voltage V
LOG
is that measured at the output pin VLOG. V
Y
and
V
X
are fixed voltages that determine the slope and intercept of
the logarithmic amplifier, respectively. These parameters are
inherent in the design of a particular logarithmic amplifier,
although may be adjustable, as in the AD606. When V
IN
= V
X
,
the logarithmic argument is one, hence the logarithm is zero. V
X
is, therefore, called the logarithmic intercept voltage because the
output voltage V
LOG
crosses zero for this input. The slope volt-
age V
Y
is can also be interpreted as the “volts per decade” when
using base-10 logarithms as shown here.
Note carefully that V
LOG
and VLOG in the above paragraph
(and elsewhere in this data sheet) are different. The first is a
voltage; the second is a pin designation.
This equation suggests that the input V
IN
is a dc quantity, and,
if V
X
is positive, that V
IN
must likewise be positive, since the
logarithm of a negative number has no simple meaning. In fact,
in the AD606, the response is independent of the sign of V
IN
because of the particular way in which the circuit is built. This
is part of the demodulating nature of the amplifier, which
results in an alternating input voltage being transformed into a
quasi-dc (rectified and filtered) output voltage.
The single supply nature of the AD606 results in common-mode
level of the inputs INHI and INLO being at about +2.5 V (us-
ing the recommended +5 V supply). In normal ac operation,
this bias level is developed internally and the input signal is
coupled in through dc blocking capacitors. Any residual dc
offset voltage in the first stage limits the logarithmic accuracy for
small inputs. In ac operation, this offset is automatically and
continuously nulled via a feedback path from the last stage, pro-
vided that the pins INHI and INLO are not shorted together, as
would be the case if transformer coupling were used for the signal.
While any logarithmic amplifier must eventually conform to the
basic equation shown above, which, with appropriate elabora-
tion, can also fully account for the effect of the signal waveform
on the effective intercept,
1
it is more convenient in RF applica-
tions to use a simpler expression. This simplification results
from first, assuming that the input is always sinusoidal, and
second, using a decibel representation for the input level. The
standard representation of RF levels is (incorrectly, in a log amp
context) in terms of power, specifically, decibels above 1 milli-
watt (dBm) with a presumed impedance level of 50 Ω. That
being the case, we can rewrite the transfer function as
VVPP
LOG Y IN X
= ( –)
where it must be understood that P
IN
means the sinusoidal input
power level in a 50 Ω system, expressed in dBm, and P
X
is the
intercept, also expressed in dBm. In this case, P
IN
and P
X
are
simple, dimensionless numbers. (P
X
is sometimes called the
“logarithmic offset,” for reasons which are obvious from the
above equation.) V
Y
is still defined as the logarithmic slope,
usually specified as so many millivolts per decibel, or mV/dB.
In the case of the AD606, the slope voltage, V
Y
, is nominally
750 mV when operating at V
POS
= 5 V. This can also be ex-
pressed as 37.5 mV/dB or 750 mV/decade; thus, the 80 dB
range equates to 3 V. Figure 1 shows the transfer function of the
AD606. The slope is closely proportional to V
POS
, and can more
generally be stated as V
Y
= 0.15 × V
POS.
Thus, in those applica-
tions where the scaling must be independent of supply voltage,
this must be stabilized to the required accuracy. In applications
where the output is applied to an A/D converter, the reference
VLOG – Volts DC
INPUT SIGNAL – dBm
4
0
+20
1
0.5
–80–100
2
1.5
2.5
3
3.5
0–20–40–60
SLOPE = 37.5mV/dB
INTERCEPT
AT –88.33dBm
Figure 1. Nominal Transfer Function
1
See, for example, the AD640 data sheet, which is published in Section 3 of
the Special Linear Reference Manual or Section 9.3 of the 1992 Amplifier
Applications Guide.
