ISL5585 Datasheet, PDF (11/22 Pages) Intersil Corporation – 3.3V Ringing SLIC Family for Voice Over Broadband VOB

ISL5585
Complex Impedance Synthesis
Substituting the impedance programming resistor, R_S, with a
complex programming network provides complex
impedance synthesis.
2-WIRE
NETWORK
C₂
PROGRAMMING
NETWORK
C_Parallel
R₁
R₂
R_Series
R_Parallel
FIGURE 5. COMPLEX PROGRAMMING NETWORK
The reference designators in the programming network
match the evaluation board. The component R_S has a
different design equation than the R_S used for resistive
impedance synthesis. The design equations for each
component are provided below.
R_Series = 133.3 × (R₁ – 2(R_P))
R_Parallel = 133.3 × R₂
C_Parallel = C₂ ⁄ 1^· 33.3
(EQ. 22)
(EQ. 23)
(EQ. 24)
Node Equation at ISL5585 AUX input, Figure 4
I_X
=
A_-----U_-----X_--
R
+
-^V----^T---^X--
R
(EQ. 25)
Substituting EQ 17 for VTX with AUX =0 and ∆I_M= -V_2W/Z_L
gives us EQ 26. Note: AUX input is not used.
Substitute EQ 17 into EQ 21
I_X
=
-^V----^T---^X--
R
=
–-^V----^I--^N--
R



R^--R---_I^-S-_N^--_{}
–

V_{-----2-Z--w--L--}3_----0_{- }


R^--R---8^--S--k^{--}
(EQ. 26)
Loop Equation at ISL5585 feed amplifiers and load.
(EQ. 27)
I_XR - V_TR + I_XR = 0
Substitute EQ 26 into EQ 27
V_TR
=
–
2
V
I
N



R^--R---_I^-S-_N^--_{}
+



2_----V_{----Z-2---wL----}3_---0_{--}


R_{-8----kS--}
(EQ. 28)
Substitute Equation 19 for R_S/8k in Equation 28.
V_TR
=
–
2
V_IN



R^--R---_I^-S-_N^--_{}
+



2_----V_{----Z-2---wL----}3_---0_{--}


-¹---³---³---^.-₈-³--_k-³----^Z----^O---_
(EQ. 29)
Simplifying
V_TR
=
–
2V_I
N



R^--R---_I^-S-_N^--_{}
+



V_{---Z--2--L-w--}
(
Z_O
)
(EQ. 30)
Loop Equation at Tip/Ring interface
(EQ. 31)
V_2W -I_M2R_P + V_TR = 0
Substitute Equation 30 into Equation 31 and combine terms
V_2W
Z_{----L-----+-----}Z_{----O-----+-----}2_---R_-----P--
Z_L
=
2V_I
N
--^R----^S---
R_IN
(EQ. 32)
where:
V_IN = The input voltage at the -IN pinthrough resistor R_IN.
AUX = Auxiliary input of SLIC. Not used for AC gains.
V_SA = An internal node voltage that is a function of the loop
current and the output of the Sense Amplifier.
I_X = Internal current in the SLIC that is the difference between
the input receive current and the feedback current.
I_M = The AC metallic current.
R_P = A protection resistor (typical 49.9Ω).
R_S = An external resistor/network for matching the line
impedance.
V_TR = The tip to ring voltage at the output pins of the SLIC.
V_2W = The tip to ring voltage including the voltage across the
protection resistors.
Z_L = The line impedance.
Z_O = The source impedance of the device.
4-Wire to 2-Wire Gain
4-wire to 2-wire gain across the ISL5585 is equal to the V_2W
divided by the input voltage V_IN, reference Figure 4. The
receive gain is calculated using Equation 32.
Equation 33 expresses the receive gain (V_IN to V_2W) in
terms of network impedances. From Equation 21, the value
of R_S was set to match the line impedance (Z_L) to the
ISL5585 plus the protection resistors (Z₀ + 2R_P). This
results in a 4-wire to 2-wire gain equal to R_S/R_IN, as shown
in EQ. 33.
G_4-2
=
V_{-----2---W---}
V_IN
=

2

R^--R---_I^-S-_N^--_{}
Z^----_L^-----+-----Z^---Z-_O^---L---+^------2^---_R^----_P^--
=
2 -_Z---_L---^Z--+--^L---_Z----_L-
=
--^R----^S---
R_IN
(EQ. 33)
2-Wire to 4-Wire Gain
The 2-wire to 4-wire gain is equal to V_TX/E_G with V_IN = 0,
reference Figure 4.
Loop Equation
–E_G + Z_LI_M + 2R_PI_M – V_TR = 0
(EQ. 34)
From Equation 30 with V_IN = 0
V_TR
=
Z_----O-----V_{----2----W---}
Z_L
(EQ. 35)
Substituting Equation 35 into Equation 34 and simplify.
E_G
=
–V_2W
Z_{----L-----+-----}2_----R_{----P-----+-----}Z_----O--
Z_L
(EQ. 36)
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