15
FN4924.2
November 3, 2004
Note that in Figure 13, VTR is referenced on the line side of the
protection resistors.
On the 2-wire side, solving for IL in terms of VIN gives
Equation 49. Equations 50 and 51 show the relationship of
VIN to the outputs of the Sense Amplifier (VSA) and the
Feedback Amplifier (VZ0) respectively.
Simplifying Equation 51 in terms of Z0 gives the following
equation.
The resulting differential output voltage VTX4W, is shown in
Equation 53.
Note that the gain from VZ0 to the differential output is outside
the impedance synthesis loop and will have no effect on the
SLIC’s programmed impedance.
Substituting Equation 53 into Equation 52 and rearranging
terms gives the gain from the 2-wire source (VIN) to the
differential output of the Transmit Amplifier.
If the combination of the protection resistors and the
programmed impedance of the SLIC are equal to ZL the
voltage VTR will be 1/2 VIN. The 2-wire to 4-wire gain is
defined by Equation 55.
4-WIRE TO 4-WIRE GAIN
The 4-Wire to 4-Wire gain is defined in Equation 56 and is
illustrated in Figure 14.The first term is identical to
Equation 48.
The second term is derived in a similar manner as the 2-wire
to 4-wire gain starting with Equation 57.
Moving around the loop from the 2-wire side to the 4-wire
output we solve for VSA and VZO.
The relationship between VZ0 and the 4-wire output is
shown in Equation 53. Substituting Equation 59 into
Equation 53 yields Equation 60, the second term in Equation
56.
FIGURE 12. SCHEMATIC FOR 4-WIRE TO 2-WIRE GAIN DERIVATION
Irx4w
TIP
RING
-IN
VZO
200K
+
-
+
-
+
-
1:1
20
3R
4R
3R
8K
RS
CFB
TA
VSA
IL
Vtr
+
-
VRXM
VRXP
VRX4W
1.4R
R
1.4R
V2W
RP
VFB
ZL
VRX
+
-
200K
Iz0
+ -
+
-
IL
VIN
ZL Z
+
0
2RP
+
--------------------------------------
=
(EQ. 49)
VSA
VIN
ZL Z
+
0
2RP
+
--------------------------------------
–
220
×
3
4
---
×
=
(EQ. 50)
VZ0
VIN
ZL Z
+
0
2RP
+
--------------------------------------
–
220
×
3
4
---
×
RS
8K
------------
×
=
(EQ. 51)
VZ0
VIN
ZL Z
+
0
2RP
+
--------------------------------------
–
Z0
2
------
×
=
(EQ. 52)
VTX4W
VTXP VTXM VZ0
V
–
(
–
Z0
) 2V
Z0
=
–
=
(EQ. 53)
VTX4W
VIN
--------------------
Z0
ZL Z
+
0
2RP
+
--------------------------------------
–
=
(EQ. 54)
VTX4W
VTR
--------------------
2Z0
ZL Z
+
0
2RP
+
--------------------------------------
–
=
(EQ. 55)
VTX4W
VRX4W
--------------------
V2W
VRX4W
--------------------
VTX4W
V2W
--------------------
×
=
(EQ. 56)
V2W
IL ZL
×
=
(EQ. 57)
VSA
I
– L220
×
3
4
---
×
V2W
ZL
------------ 40 3
4
---
×
=
(EQ. 58)
VZ0
V2W
ZL
------------
RS
8K
------------
×
40
3
4
---
×
V2W
ZL
------------
Z0
2
------
×
==
(EQ. 59)
VTX4W
V2W
--------------------
Z0
ZL
------
=
(EQ. 60)
ISL5586