TA0313 Datasheet, PDF (7/9 Pages) STMicroelectronics – STMicroelectronics Solutions for ADSL Line Interfaces

STMicroelectronics Solutions for ADSL Line Interfaces
TA0313
As Vo° equals Vo without loading, the gain in this case becomes:
G = -^V----^o----⁽--ⁿ---_V-^o----^li--^o---^a----^d----⁾ = -1----+-----1--2---^R---R--_–----1----2--_{RR----------+23-------}^{RR----------23----}
The gain for the loaded system will be:
Equation 1
GL = ^V-----^o----⁽--^w-----ⁱ-_V-^t--^h-_i---^l--^o---^a----^d----⁾ = ^{12-- 1-----+-----1-2---R}----^R--_–----1----2--_{RR----------+23-------}^{RR----------23----}
As shown in Figure 9, this system is an ideal generator, with a synthesized impedance equal to the
internal impedance of the system. Therefore, the output voltage becomes:
Equation 2
Vo = (ViG) – (RoIout)
with Ro the synthesized impedance and Iout the output current. On the other hand Vo can be expressed
as:
Equation 3
Vo
=
Vi_1 + -2--_R-^R---1--2-- + ^RR-----23--_
----------------1-----_–-----_{RR---------23--------------------}
–
-^R----^s----1----^I--^o----^u---^t
1 – ^RR-----23--
Figure 9: Equivalent schematic, where Ro is the synthesized impedance
Ro
Iout
Vi.Gi
1/2RL
By identifying of both Equation 2 and Equation 3, the synthesized impedance is, with Rs1=Rs2=Rs:
Equation 4
Ro = -----^R-----^s------
1 – ^R-----2--
R3
Unlike the level of Vo° required for passive impedance, Vo° will be smaller than 2Vo in this case. Let us
write Vo°=kVo with k the matching factor varying between 1 and 2. Assuming that the current through R3
is negligible, the resistance divider becomes:
Ro = -----^k----^V----^o----^R-----^L------
RL + 2Rs1
After choosing the k factor, Rs will equal to 1/2RL(k-1).
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