ISL5586 Datasheet, PDF (14/20 Pages) Intersil Corporation – Low Power Ringing SLIC for Home Gateways

ISL5586
Impedance and Gain Derivations
The feedback mechanism for monitoring the AC portion of
the loop current consists of two amplifiers, the sense
amplifier (SA) and the transmit amplifier (TA). The AC
feedback signal is used for impedance synthesis. A detailed
model of the AC feed back loop is provided below
Impedance Programming Resistor Derivation
The gain of the transmit amplifier, set by R_S , determines the
programmed resistance of the SLIC. For complex line
terminations R_S is replaced with a complex network Z_S
(Figure 1). The capacitor C_FB blocks the DC component of
the loop current. Figure 11 illustrates the impedance
synthesis loop. Note that the ground symbols shown in
Figures 11 through 14 represent AC grounds, not
necessarily actual DC potentials.
The receiver block provides a single-ended to differential
conversion with a voltage gain of 2. The voltage at Tip and
Ring due to the feedback from V_ZO is shown in Equation 35.
VTR = –2 × V_ZO
(EQ. 35)
The Feedback amplifier (TA) provides the programmable
gain required for impedance synthesis to the Receiver block.
The output voltage (V_ZO) is a function of the Sense Amplifier
output voltage and the gain of the feedback amplifier, which
can be substituted for V_ZO.
VTR
=
–2
×
V_S
A
×


8^---R-K^----S-Ω^{---}
(EQ. 36)
The sense amplifier shown in Figure 11 is configured as a 4
input differential amplifier with a gain of 3/4. The output
voltage, V_SA , is a function of the voltage across the Tip and
Ring sense resistors (20Ω each) which can also be
expressed in terms of loop current.
V_SA = –2 × 20 × IL × (3 ⁄ 4 )
(EQ. 37)
Substituting Equation 37 into Equation 35 and rearranging
terms yields Z₀, the SLIC’s synthesized 2-wire impedance.
Rearranging and solving for R_S , Equation 39 shows the
relationship between the impedance programming resistor
and the programmed impedance.
Z₀ = -^V---_I-^T-_L--^R-- = 4 × 20 × IL × ³⁴-- × ₈---^R-_K----^s-_Ω--- = 60 × ₈---^R-_K----^s-_Ω---
(EQ. 38)
R_S = 133.3 × Z₀
(EQ. 39)
4-WIRE TO 2-WIRE GAIN
The 4-wire to 2-wire gain is defined as the gain from the
differential receive input to the 2-wire load Z_L. The gain is a
function of the terminating impedance, synthesized
impedance and protection resistors and is illustrated in
Figure 12. The input current to the receiver block Irx4w
comes from the difference of the V_RX input current and the
V_ZO feedback current. This current is fed to the Tip and Ring
amplifiers and yields the relationship shown in Equation 40.
V_TR = –2 × (V_rx – V_ZO)
(EQ. 40)
The voltage V_ZO, is a function of the sense amplifier output
voltage V_SA.
V_Z0 = –V_SA × ₈---^R-_K----^S-_Ω---
(EQ. 41)
V_SA can be expressed in terms of loop current as shown in
Equation 42.
V_SA = –IL × 2 × 20 × ³⁴--
(EQ. 42)
Substituting Equation 42 into Equation 41 gives Equation 43.
V_Z0 = –IL × 2 × 20 × ³⁴-- × ₈---^R-_K----^S-_Ω---
(EQ. 43)
The V_Z0 term in Equation 40 can now be replaced by
Equation 43 yielding Equation 44.
V_TR
=
– 2 × V_rx – 2_IL × 2 × 20 × ³⁴--_
×


8^---R-K^---S--Ω^{---}
(EQ. 44)
A loop equation can be derived for the 2-wire side that
replaces V_TR as shown in the equation below.
V_2W + IL × 2R_p
=
– 2V_rx
– IL_ 4 × 20 × ³⁴--_
×


8^---R-K^----S-Ω^{---}
(EQ. 45)
Expressing IL in terms of V_2W/Z_L, rearranging, and solving
for V_2W yields the relationship between the 2-wire voltage
and the output of the Receive amplifier.
V_2W
=
–2V_rx
×



Z^----_L^-----+-----Z^--Z--₀^--L--+-----2^----R^----_P^--_{}
(EQ. 46)
The differential voice input is configured for a gain of 1.4.
The relationship between V_RX and the voice input is shown
in Equation 47. Substituting for V_RX, the 4-2-Wire gain is
shown in Equation 48. Note that the differential voice input is
outside the impedance synthesis loop, so the gain of the
receive amplifier has no effect on the SLIC’s impedance.
V_rx = 1.4 × (V_RXP – V_RXM ) = 1.4 × V_RX4W
(EQ. 47)
V^-----V_R^----2X---W-₄^---_W^---
=
–2.8



Z^-----_O^------+^-----2^--Z--R^--L---_P^-----+^------Z^----_L^-_{}
(EQ. 48)
When the combination of the device source impedance and
the protection resistors equal the terminating impedance, the
receive gain equals 2.92dB and is inverted with respect to
the 4-wire input.
2-WIRE TO 4-WIRE GAIN
The 2-wire to 4-wire gain (G₂₄) is defined as the gain from the
Tip and Ring terminals (V_TR) to the V_TX differential output.
4-14