AD640
(see Figure 20). For the AD640, VX is calibrated to exactly
1 mV. The slope of the line is directly proportional to VY. Base
10 logarithms are used in this context to simplify the relation-
ship to decibel values. For VIN = 10 VX, the logarithm has a
value of 1, so the output voltage is VY. At VIN = 100 VX, the
output is 2 VY, and so on. VY can therefore be viewed either as
the Slope Voltage or as the Volts per Decade Factor.
When the attenuator is not used, the PTAT variation in VX
will result in the intercept being temperature dependent. Near
300K (27°C) it will vary by 20 LOG (301/300) dB/°C, about
0.03 dB/°C. Unless corrected, the whole output function would
drift up or down by this amount with changes in temperature. In
the AD640 a temperature compensating current IYLOG(T/TO)
is added to the output. This effectively maintains a constant
intercept VXO. This correction is active in the default state (Pin
8 open circuited). When using the attenuator, Pin 8 should be
grounded, which disables the compensation current. The drift
term needs to be compensated only once; when the outputs of
two AD540s are summed, Pin 8 should be grounded on at least
one of the two devices (both if the attenuator is used).
IDEAL
V LOG (V /V )
Y
IN
X
ACTUAL
2V
V
Y
SLOPE = V
Y
Y
Conversion Range
Practical logarithmic converters have an upper and lower limit
on the input, beyond which errors increase rapidly. The upper
limit occurs when the first stage in the chain is driven into limit-
ing. Above this, no further increase in the output can occur and
the transfer function flattens off. The lower limit arises because
a finite number of stages provide finite gain, and therefore at
low signal levels the system becomes a simple linear amplifier.
0
INPUT ON
LOG SCALE
ACTUAL
V
= V
V
= 10V
V
= 100V
IN
X
IN
X
IN X
IDEAL
Figure 20. Basic DC Transfer Function of the AD640
Note that this lower limit is not determined by the intercept
voltage, VX; it can occur either above or below VX, depending
on the design. When using two AD640s in cascade, input offset
voltage and wideband noise are the major limitations to low
level accuracy. Offset can be eliminated in various ways. Noise
can only be reduced by lowering the system bandwidth, using a
filter between the two devices.
The AD640 conforms to Equation (1) except that its two out-
puts are in the form of currents, rather than voltages:
I
OUT = IY LOG (VIN/VX)
Equation (2)
IY the Slope Current, is 1 mA. The current output can readily be
converted to a voltage with a slope of 1 V/decade, for example,
using one of the 1 kΩ resistors provided for this purpose, in
conjunction with an op amp, as shown in Figure 21.
EFFECT OF WAVEFORM ON INTERCEPT
R2
1mA PER
DECADE
The absolute value response of the AD640 allows inputs of
either polarity to be accepted. Thus, the logarithmic output in
response to an amplitude-symmetric square wave is a steady
value. For a sinusoidal input the fluctuating output current will
usually be low-pass filtered to extract the baseband signal. The
unfiltered output is at twice the carrier frequency, simplifying the
design of this filter when the video bandwidth must be maxi-
mized. The averaged output depends on waveform in a roughly
analogous way to waveform dependence of rms value. The effect
is to change the apparent intercept voltage. The intercept volt-
age appears to be doubled for a sinusoidal input, that is, the
averaged output in response to a sine wave of amplitude (not rms
value) of 20 mV would be the same as for a dc or square wave
input of 10 mV. Other waveforms will result in different inter-
cept factors. An amplitude-symmetric-rectangular waveform
has the same intercept as a dc input, while the average of a
baseband unipolar pulse can be determined by multiplying the
response to a dc input of the same amplitude by the duty cycle.
It is important to understand that in responding to pulsed RF
signals it is the waveform of the carrier (usually sinusoidal) not
the modulation envelope, that determines the effective intercept
voltage. Table I shows the effective intercept and resulting deci-
bel offset for commonly occurring waveforms. The input wave-
form does not affect the slope of the transfer function. Figure 22
shows the absolute deviation from the ideal response of cascaded
AD640s for three common waveforms at input levels from
–80 dBV to –10 dBV. The measured sine wave and triwave
responses are 6 dB and 8.7 dB, respectively, below the square
wave response—in agreement with theory.
R1
48.7⍀
AD844
C1
330pF
OUTPUT VOLTAGE
1V PER DECADE
FOR R2 = 1k⍀
100mV PER dB
for R2 = 2k⍀
15
14
13
12
11
SIG
+OUT
LOG LOG +V
OUT COM
S
AD640
SIG
–V
ITC BL2 –OUT
S
6
10
7
9
8
Figure 21. Using an External Op Amp to Convert the
AD640 Output Current to a Buffered Voltage Output
Intercept Stabilization
Internally, the intercept voltage is a fraction of the thermal volt-
age kT/q, that is, VX = VXOT/TO, where VXO is the value of VX
at a reference temperature TO. So the uncorrected transfer
function has the form
I
OUT = IY LOG (VIN TO/VXOT)
Equation (3)
Now, if the amplitude of the signal input VIN could somehow be
rendered PTAT, the intercept would be stable with tempera-
ture, since the temperature dependence in both the numerator
and denominator of the logarithmic argument would cancel.
This is what is actually achieved by interposing the on-chip
attenuator, which has the necessary temperature dependence to
cause the input to the first stage to vary in proportion to abso-
lute temperature. The end limits of the dynamic range are now
totally independent of temperature. Consequently, this is the
preferred method of intercept stabilization for applications
where the input signal is sufficiently large.
REV. C
–9–
ADI [ ADI ]
