AD538
150
100
10
FOR THE FREQUENCY RANGE OF 10Hz
TO 100kHz THE TOTAL RMS OUTPUT
100
NOISE, e , FOR A GIVEN BANDWIDTH
o
Bw, IS CALCULATED e = e Bw
o
n
V
V
V
= 10V
X
Y
Z
V
= 0.01V
10
X
= 5V +5V SIN t VOLTS
= 0V
1
1.0
0.1
V
= 10V
X
0.10
0.01
0.01
0.1
1
10
100
1k
10k
100k
1M
DC OUTPUT VOLTAGE – Volts
INPUT FREQUENCY – Hz
Figure 7. VY Feedthrough vs. Frequency
Figure 8. 1 kHz Output Noise Spectral Density vs. DC Output
Voltage
Under normal operation, the log-ratio output will be directly
connected to a second functional block at input C, the antilog
subsection. This section performs the antilog according to the
transfer function:
1
2
3
4
5
6
7
8
9
18
17
16
15
14
13
12
11
10
I
A
D
Z
LOG
25k⍀
RATIO
V
Z
B
+10V
+2V
I
X
⎛
⎞
q
kT
VO = VY e ⎜⎝VC
⎟
⎠
V
X
25k⍀
100⍀
100⍀
As with the log-ratio circuit included in the AD538, the user
may use the antilog subsection by itself. When both subsections
are combined, the output at B is tied to C, the transfer function
of the AD538 computational unit is:
SIGNAL
GND
INTERNAL
VOLTAGE
PWR
GND
+V
S
S
REFERENCE
AD538
–V
C
OUTPUT
⎡
⎤
⎥
⎛
⎞ ⎛
⎞
⎛
⎞
kT
q
q
kT
VZ
V
X
ln
VO = VY e ⎢⎣⎢⎜⎝
⎥⎦ ;VB = VC
⎟ ⎜
⎠ ⎝
⎟
⎠
⎜
⎝
⎟
⎠
25k⍀
V
I
Y
O
ANTILOG
which reduces to:
I
V
LOG
Y
25k⍀
⎛
⎜
⎞
V
Z
V
O
= V
Y
⎟
V
X
Figure 9. Functional Block Diagram
⎝
⎠
Finally, by increasing the gain, or attenuating the output of the
log ratio subsection via resistor programming, it is possible to
raise the quantity VZ/VX to the mth power. Without external
programming, m is unity. Thus the overall AD538 transfer
function equals:
FUNCTIONAL DESCRIPTION
As shown in Figures 9 and 10, the VZ and VX inputs connect
directly to the AD538’s input log ratio amplifiers. This subsec-
tion provides an output voltage proportional to the natural log
of input voltage VZ, minus the natural log of input voltage VX.
The output of the log ratio subsection at B can be expressed by
the transfer function:
m
⎛
⎞
VZ
VO = VY
⎜
⎟
V
⎝
⎠
X
⎛
⎞
kT
q
VZ
V
VB
=
ln
⎜
⎟
where 0.2 < m < 5.
⎝
⎠
X
When the AD538 is used as an analog divider, the VY input can
be used to multiply the ratio VZ /VX by a convenient scale factor.
The actual multiplication by the VY input signal is accomplished
by adding the log of the VY input signal to the signal at C, which
is already in the log domain.
where k = 1.3806 × 10–23 J/K,
q = 1.60219 × 10–19 C,
T is in Kelvins.
The log ratio configuration may be used alone, if correctly tem-
perature compensated and scaled to the desired output level
(see Applications section).
REV. C
REV. D
–6–
ROCHESTER [ Rochester Electronics ]
