HC55171_03 Datasheet, PDF (11/20 Pages) Intersil Corporation – 5 REN Ringing SLIC for ISDN Modem/TA and WLL

HC55171
AC Voltage Gain Design Equations
The HC55171 uses feedback to synthesize the impedance
at the 2-wire tip and ring terminals. This feedback network
defines the AC voltage gains for the SLIC.
The 4-wire to 2-wire voltage gain (V_RX to V_TR) is set by the
feedback loop shown in Figure 7. The feedback loop senses
the loop current through resistors R_S1 and R_S2, sums their
voltage drop and multiplies it by 2 to produce an output voltage
at the V_TX pin equal to +4R_S∆I_L. The V_TX voltage is then fed
into the -IN1 input of the SLIC’s internal op amp. This signal is
multiplied by the ratio R_Z0/R_RF and fed into the tip current
summing node via the OUT1 pin. (Note: the internal V_BAT/2
reference (ring feed amplifier) and the internal +2V reference
(tip feed amplifier) are grounded for the AC analysis.)
The current into the summing node of TF amp is equal to:
I_OUT1
=
–
4_----R_-----S----∆_----I_-L--
R



R^-R----_R^-Z---0F--_{}
(EQ. 8)
Equation 9 is the node equation for the tip amplifier summing
node. The current in the tip feedback resistor (I_R) is given in
Equation 7.
–
I_R
–
4_----R_-----S----∆_----I_-L--
R



R^-R----_RZ^----0F--_{}
+ -^V----^R----^X--
R
=
0
(EQ. 9)
I_R
=
–
4_----R_-----S----∆_----I_-L--
R



R^-R----_R^-Z---0F--_{}
+ -^V----^R----^X--
R
(EQ. 10)
The AC voltage at V_C is then equal to:
V_C = (I_R)(R)
(EQ. 11)
V_C
=
–4
R_S
∆I_L



R^-R----_R^-Z---0F--_{}
+ V_RX
(EQ. 12)
and the AC voltage at V_D is:
V_D
=
4R_S
∆I_L



R^-R----_R^-Z---0F--_{}
– V_RX
(EQ. 13)
The values for R_Z0 and R_RF are selected to match the
impedance requirements on tip and ring, for more
information refer to AN9607 “Impedance Matching Design
Equations for the HC5509 Series of SLICs”. The following
loop current calculations will assume the proper R_Z0 and
R_RF values for matching a 600Ω load.
The loop current (∆I_L) with respect to the feedback network, is
calculated in Equations 14 through 17. Where R_Z0 = 40kΩ ,
R_RF = 40kΩ, R_L = 600Ω, R_P1 = R_P2 = R_S1 = R_S1 = 50Ω.
∆I_L = -_R----_L-----+----_R-----_P----₁----+--^V---_R-^C----_P-–---₂--^V--+--^D---_R-----_S---₁-----+-----_R----_S----₂-
(EQ. 14)
Substituting the expressions for V_C and V_D
∆I_L = _R--²---_L--^×---+--^{}--_R^–----4-_P--^R--₁---^S-+---^∆--_R--^I--^L-_P--^{}--₂-^R-R------+--^R--^Z------_R⁰-^{F-----}-_S---+₁-----+^V----^R-_R---^X-_S---^{}-₂--
(EQ. 15)
Equation 15 simplifies to
∆I_L
=
2_----V_{-----R----X-----–----}4_----0_---0_----∆_---I_--L--
800
(EQ. 16)
Solving for ∆I_L results in
∆I_L
=
-^V----^R----^X--
600
(EQ. 17)
Equation 17 is the loop current with respect to the feedback
network. From this, the 4-wire to 2-wire and the 2-wire to
4-wire AC voltage gains are calculated. Equation 18 shows
the 4-wire to 2-wire AC voltage gain is equal to 1.00 .
A_{4W – 2W}
=
-^V----^T---^R---
V_RX
=
-^∆---^I--^L----⁽--^R----^L----⁾
V_RX
=
-^{V--6-------R0}------⁰--^X------⁽---⁶---⁰---⁰----⁾
V_RX
=
1
(EQ. 18)
Equation 19 shows the 2-wire to 4-wire AC voltage gain is
equal to -0.333.
A_{2W – 4W}
=
V_{-----O----U----T----1-}
V_TR
=
–----4_----R_{---∆-S---I-}∆_-L---I_{(--LR-----L-R}-^R_----)----R--^Z_------⁰_-F-----_{-}
=
–----2_---0_---0_-----^V_-6--------^R₀------₀--^X------(_--1_----)
V_{-----R----X-- ( 600 )}
=
–¹--
3
600
(EQ. 19)
Impedance Matching
The feedback network, described above, is capable of
synthesizing both resistive and complex loads. Matching the
SLIC’s 2-wire impedance to the load is important to
maximize power transfer and maximize the 2-wire return
loss. The 2-wire return loss is a measure of the similarity of
the impedance of a transmission line (tip and ring) and the
impedance at it’s termination. It is a ratio, expressed in
decibels, of the power of the outgoing signal to the power of
the signal reflected back from an impedance discontinuity.
Requirements for Impedance Matching
Impedance matching of the HC55171 application circuit to the
transmission line requires that the impedance be matched to
points “A” and “B” in Figure 7. To do this, the sense and
protection resistors R_P1, R_P2, R_S1 and R_S2 must be
accounted for by the feedback network to make it appear as if
the output of the tip and ring amplifiers are at points “A” and
“B”. The feedback network takes a voltage that is equal to the
voltage drop across the sense resistors and feeds it into the
summing node of the tip amplifier. The effect of this is to
cause the tip feed voltage to become more negative by a
value that is proportional to the voltage drop across the sense
resistors R_P1 and R_S1. At the same time the ring amplifier
becomes more positive by the same amount to account for
resistors R_P2 and R_S2 .
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