TS616
Component Calculation
Let us consider the equivalent circuit for a sin-
gle-ended configuration as shown in Figure 69.
Figure 69: Single ended equivalent circuit
+
Vi
_
½ R1
R2
R3
Rs1
Vo°
Vo
-1
½ RL
Vo
=
V
i
1
+
2--R--R---1--2--
+
RR-----23--
----------------1-----–----RR----------23--------------------
–
R---1--s---–-1---I-RR----o-----23--u-----t ,(
eq3)
By identification of both equations (eq2) and
(eq3), the synthesized impedance is, with
Rs1=Rs2=Rs:
Ro = 1-----–R-----RR-s---------23---- ,(eq4)
Figure 70: Equivalent schematic. Ro is the
synthesized impedance.
Ro
Iout
Let us consider the unloaded system. Assuming
the currents through R1, R2 and R3
are respectively:
2-R---V--1---i, (---V----i---R–-----V2----o----°---) and(---V----i--R-+----3-V-----o---)-
as Vo° equals Vo without load, the gain in this
case becomes :
G = V-----o----(--n----o----l-o----a----d----) = 1-----+-----2----R----R------1----2-------+-----RR----------23----
Vi
1 – RR-----23--
The gain, for the loaded system will be (eq1):
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---- ,(eq1)
As shown in Figure70, this system is an ideal gen-
erator with a synthesized impedance as the inter-
nal impedance of the system. From this, the out-
put voltage becomes:
Vo = (ViG) – (RoIout),(eq2)
with Ro the synthesized impedance and Iout the
output current. On the other hand Vo can be ex-
pressed as:
Vi.Gi
1/2RL
Unlike the level Vo° required for a passive imped-
ance, Vo° will be smaller than 2Vo in our case. Let
us write Vo°=kVo with k the matching factor vary-
ing between 1 and 2. Assuming that the current
through R3 is negligible, (eq4) becomes the fol-
lowing :
Ro = R-----L-k---V-+----o-2--R--R---L--s---1--
After choosing the k factor, Rs will equal to
1/2RL(k-1).
A good impedance matching assumes:
R o = 12-- RL,(eq5)
(eq4) and (eq5) give :
RR-----23-- = 1 – 2--R--R---L--s- ,(eq6)
By fixing an arbitrary value of R2, (eq6) becomes :
R3 = 1-----–--R---2----2R----R-----L----s----
Finally, the values of R2 and R3 allow us to extract
R1 from (eq1), and it becomes:
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