HC55120_06 Datasheet, PDF (18/36 Pages) Intersil Corporation – Low Power Universal SLIC Family

HC55120, HC55121, HC55130, HC55140, HC55142, HC55143, HC55150
V_TR = The tip to ring voltage including the voltage across the
protection resistors.
Z_L = The line impedance.
Z_TR = The input impedance of the SLIC including the
protection resistors.
(AC) 4-Wire to 2-Wire Gain
The 4-wire to 2-wire gain is equal to V_TR/V_RX.
From Equation 21 and the relationship Z_T = 200(Z_TR-2R_P).
G_4-2
=
-^V----^T---^R--
V_RX
=
-2
----------^Z----^L-----------
Z_L + Z_TR
=
–2
--------------------^Z----^L----------------------
Z_L
+
⎛
⎝
--^Z----^T---
200
+
2R_{P⎠⎞}
(EQ. 22)
Notice that the phase of the 4-wire to 2-wire signal is 180°out
of phase with the input signal.
TIP ^{+ IM -}
-
Z_TR
R_P
I_{M ZL}
-
V_TR ⁺
-
V_TX´
+
+
E_G
-
- ^IM +
RING ^RP
I_X
-
+
500K
R_S R_INT
-
+
20Ω 20Ω
UniSLIC14
500K
I_X I_X
500K
A=1
-
V_TX
+
PTG
R_{S RINT}
+
20Ω
+
I_X
20Ω
-
-
500K
1/80K
5
Z_T = 200 (Z_TR - 2R_P)
I_X
500K
500K
V_RX
V_A = I_M(Z_TR-2R_P)
2
+
V_TX
-
+
V_RX
-
FIGURE 17. SIMPLIFIED AC TRANSMISSION CIRCUIT
(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
Loop Equation
–E_G + Z_LI_M + 2R_PI_M – V_TX′ = 0
(EQ. 23)
From Equation 18 with V_RX = 0
V_TX′ = – I_M(Z_TR – 2R_P)
(EQ. 24)
Substituting Equation 24 into Equation 23 and simplifying.
E_G = I_M(Z_L + Z_TR)
(EQ. 25)
By design, VTX = -VTX´, therefore
G_2-4
=
V_-----T---X--
E_G
=
I_--M-----(_---Z_{----T---R-----–-----}2_---R_-----P----)
I_M(Z_L + Z_TR)
=
(_---(Z_{--Z--T--L-R---+---–--Z--}2_--T--R_--R--P--)--)
(EQ. 26)
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.
V_TR
=
⎛
⎜
⎝
Z^----_T^---Z-_R^{---T--+--R---}Z^----_L^- _{⎠⎟⎞}
E_G
(EQ. 27)
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).
G_2-4
=
-^V----^T---^X--
V_TR
=
Z_{----T----R------}-_-----2_---R_-----P--
Z_TR
(EQ. 28)
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.
V_TX′ = –V_TX = –2V_RX + I_M(Z_TR – 2R_P)
(EQ. 29)
Substituting -V_TR/Z_L into Equation 29 for I_M results in
Equation 30.
V_TX
=
– 2 V _RX
–
V_{-----T---R-----}(_--Z_{----T---R------–----}2_----R_----P----)_-
Z_L
(EQ. 30)
18
FN4659.13
June 1, 2006