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RS-485: Transmitting Full-Duplex Data over Single Twisted-Pair Cable Application Note
1.5
Deriving the R
From the differential 4-to-2 wire conversion network in
Figure
10. Recall that V
and the driver outputs (see also
prevent the local driver output (V
receiver input resistance (R
specified in the datasheet.
R
R
IN
D
Figure 9. 2-to-4 Wire Conversion
The differential receiver input voltage of Node 1, V
V
=
V
AB1
Bus
Multiplying out then gives:
V
=
V
AB1
Bus
To arrive at an equation that includes the R
R
×R
:
D
IN
V
V
=
AB1
Bus
As both fractions have the same denominators, combine both voltage terms onto one denominator:
V
Bus
-------------------------------------------------------------- -
V
=
AB1
1
+
Now substitute V
using
Bus
V
OD1
---------------------------------------------------------------------------------------------------------
V
=
AB1
After collecting terms, there are two separate voltage terms, one for V
V
OD1
--------------------------------------------------------------------------------------- -
(EQ. 6)
V
=
AB1
R15AN0009EU0100 Rev.1.00
Mar 4, 2022
/R
Ratio of the 4-to-2 Wire Conversion
B
D
is inverted to -V
OD1
OD1
4-to-2 Wire
Conversion). To determine the R
) from appearing at the local receiver input (V
OD1
) as it presents a common-mode load to the voltage divider output. R
IN
R
B
V
Bus
R
B
R
IN
R
R
D
D
-V
OD
R
R
D
IN
------------------------------------- - V
–
OD1
R
+
R
R
B
D
IN
R
R
D
IN
------------------------------------------------------------------ - V
R
R
+
R
R
+
R
B
IN
D
IN
B
/R
B
1
---------------------------------------------------------- - V
1
+
R
R
+
R
R
B
D
B
IN
–
V
R
R
OD1
B
D
R
R
+
R
R
B
D
B
IN
Equation 4
(V
= V
Bus
k
+
V
k
–
V
OD2
OD1
1
R
R
R
R
+
+
B
D
B
IN
k R
–
R
+
V
B
D
OD2
1
+
R
R
+
R
R
B
D
B
IN
Figure
9, construct its single-ended representation in
by the connections of the R
Figure 10. Single-Ended Representation
, therefore, becomes:
AB1
R
R
B
IN
------------------------------------- -
R
+
R
R
D
B
IN
R
B
------------------------------------------------------------------ -
–
OD1
R
R
R
+
R
D
B
IN
, divide the numerators and denominators of both fractions by
D
R
R
B
D
---------------------------------------------------------- -
–
OD1
1
+
R
R
+
R
B
D
× k + V
× k) and get:
OD1
OD2
R
R
B
D
k
resistors between the receiver inputs
D
/R
ratio that is necessary to
B
D
) you must also include the
AB1
R
R
V
D
AB1
-V
OD1
R
IN
R
IN
R
+
R
R
D
IN
B
D
R
B
IN
and another for V
OD1
is commonly
IN
B
V
Bus
:
OD2
Page 5
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