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4-17
(AC) 2-Wire to 4-Wire Gain
The 2-wire to 4-wire gain is equal to V
TX
/E
G
with V
RX
= 0
From Equation 18 with V
RX
= 0
V
TX
′
Substituting Equation 24 into Equation 23 and simplifying.
By design, VTX = -VTX′, therefore
V
G
A more useful form of the equation is rewritten in terms of
V
TX
/V
TR
. A voltage divider equation is written to convert
from E
G
to V
TR
as shown in Equation 27.
Z
TR
Rearranging Equation 27 in terms of E
G
, and substituting
into Equation 26 results in an equation for 2-wire to 4-wire
gain that’s a function of the synthesized input impedance of
the SLIC (Z
TR
) and the protection resistors (R
P
).
Notice that the phase of the 2-wire to 4-wire signal is in
phase with the input signal.
(AC) 4-Wire to 4-Wire Gain
The 4-wire to 4-wire gain is equal to V
TX
/V
RX
, E
G
= 0.
From Equation 18.
Substituting -V
TR
/Z
L
into Equation 29 for I
M
results in
Equation 30.
Substituting Equation 21 for V
TR
in Equation 30 and
simplifying results in Equation 31.
(AC) 2-Wire Impedance
The AC 2-wire impedance (Z
TR
) is the impedance looking
into the SLIC, including the fuse resistors. The formula to
calculate the proper Z
T
for matching the 2-wire impedance is
shown in Equation 32.
Equation 32 can now be used to match the SLIC’s
impedance to any known line impedance (Z
TR
).
V
TX
V
RX
TIP
RING
Z
TR
V
TR
E
G
-
V
TX
′
I
M
V
TX
UniSLIC14
R
P
R
P
+
-
+
-
+
-
+
V
RX
+
-
I
M
Z
L
FIGURE 17. SIMPLIFIED AC TRANSMISSION CIRCUIT
+
500K
R
S
+
-
500K
R
S
Z
T
500K
500K
500K
500K
PTG
+
-
I
X
V
A
= I
M
(Z
TR
-2R
P
)
2
I
X
I
X
+
-
I
X
+
-
5
+
-
+
-
I
M
+
-
20
20
1/80K
= 200 (Z
TR
- 2R
P
)
A = 1
I
X
I
R
INT
20
R
INT
20
E
–
G
Z
L
I
M
2R
P
I
M
V
TX
′
–
+
+
0
=
Loop Equation
(EQ. 23)
I
M
Z
TR
2R
P
–
(
)
–
=
(EQ. 24)
E
G
I
M
Z
L
Z
TR
+
(
)
=
(EQ. 25)
G
2-4
=
----------
=
I
Z
M
L
2R
TR
–
(
)
)
-------------------+
Z
L
2R
TR
–
(
-------------+
)
)
=
(EQ. 26)
V
TR
=
L
-------------+
E
G
(EQ. 27)
G
2-4
=
V
TR
----------
=
Z
- 2R
P
TR
-----------------------------
(EQ. 28)
V
TX
′
V
–
TX
2
–
V
RX
I
M
Z
TR
2R
P
–
(
)
+
=
=
(EQ. 29)
V
TX
2
–
V
RX
V
Z
---------------------------------------------
2R
–
(
)
L
–
=
(EQ. 30)
G
4
4
–
V
RX
-----------
2
–
Z
+ 2R
P
L
TR
-------+
=
=
(EQ. 31)
Z
T
200
Z
TR
2R
P
–
(
)
=
(EQ. 32)
HC55120, HC55121, HC55130, HC55131, HC55140, HC55141, HC55142, HC55143, HC55150, HC55151