223
PL
<ŽŶĮŐƵƌĂĐũĂĐnjħƐƚŽƚůŝǁŽƑĐŝŵŝŐĂŶŝĂůĂŵƉLJďųLJƐŬŽǁĞũ
njħƐƚŽƚůŝǁŽƑđũĞƐƚƌĞŐƵůŽǁĂŶĂĞůĞŬƚƌŽŶŝĐnjŶĞƉƌnjĞnjůĂŵƉħďųLJƐŬŽǁČ
EŝƐŬĂĐnjħƐƚŽƚůŝǁŽƑđ
EŝƐŬĂĐnjħƐƚŽƚůŝǁŽƑđƉŽĚĐnjĂƐŽƚǁŝĞƌĂŶŝĂǁLJƐŽŬĂƉŽĚĐnjĂƐnjĂŵLJŬĂŶŝĂ
tLJďſƌƚƌLJďƵĚnjŝĂųĂŶŝĂŽƑǁŝĞƚůĞŶŝĂĚŽĚĂƚŬŽǁĞŐŽ
ĞnjĂŬƚLJǁŽǁĂŶĞ
/DWh>^KtKƑǁŝĞƚůĞŶŝĞǁųČĐnjĂƐŝħŶĂŬƌſƚŬŽŶĂƉŽĐnjČƚŬƵŬĂǏĚĞŐŽŵĂŶĞǁƌƵ
tBKEKƑǁŝĞƚůĞŶŝĞũĞƐƚǁųČĐnjŽŶĞƉƌnjĞnjĐĂųLJĐnjĂƐƚƌǁĂŶŝĂŵĂŶĞǁƌƵ
ŽĚϯĚŽϵϬƐKƑǁŝĞƚůĞŶŝĞƉŽnjŽƐƚĂũĞǁųČĐnjŽŶĞƉŽnjĂŬŽŷĐnjĞŶŝƵŵĂŶĞǁƌƵƉƌnjĞnjnjĂƉƌŽŐƌĂŵŽǁĂŶLJĐnjĂƐ
ŽĚϮĚŽϵŵŝŶƵƚKƑǁŝĞƚůĞŶŝĞƉŽnjŽƐƚĂũĞǁųČĐnjŽŶĞƉŽnjĂŬŽŷĐnjĞŶŝƵŵĂŶĞǁƌƵƉƌnjĞnjnjĂƉƌŽŐƌĂŵŽǁĂŶLJĐnjĂƐ
<ŽŶĮŐƵƌĂĐũĂƐƚLJŬƵnjĞŐĂƌĂ;KZKͿ
WŽĂŬƚLJǁĂĐũŝĨƵŶŬĐũŝnjĞŐĂƌĂďƌĂŵĂŽƚǁŝĞƌĂƐŝħŝƉŽnjŽƐƚĂũĞŽƚǁĂƌƚĂƉƌnjĞnjĐnjĂƐnjĂƉƌŽŐƌĂŵŽǁĂŶLJǁnjĞŐĂƌnjĞWŽƵƉųLJ-
ǁŝĞĐnjĂƐƵnjĂƉƌŽŐƌĂŵŽǁĂŶĞŐŽǁƵƌnjČĚnjĞŶŝƵnjĞǁŶħƚƌnjŶLJŵ;njĞŐĂƌͿďƌĂŵĂƐŝħnjĂŵLJŬĂ
WŽĂŬƚLJǁĂĐũŝĨƵŶŬĐũŝnjĞŐĂƌĂďƌĂŵĂŽƚǁŝĞƌĂƐŝħŝƉŽnjŽƐƚĂũĞŽƚǁĂƌƚĂtƐnjLJƐƚŬŝĞƐLJŐŶĂųLJƐƚĞƌŽǁŶŝĐnjĞƐČŝŐŶŽƌŽǁĂŶĞ
WŽĂŬƚLJǁĂĐũŝĨƵŶŬĐũŝnjĞŐĂƌĂďƌĂŵĂŽƚǁŝĞƌĂƐŝħŝƉŽnjŽƐƚĂũĞŽƚǁĂƌƚĂtƐnjLJƐƚŬŝĞƐLJŐŶĂųLJƐƚĞƌŽǁŶŝĐnjĞƐČƉƌnjLJũŵŽǁĂŶĞ
WŽƉŽŶŽǁŶLJŵĐĂųŬŽǁŝƚLJŵŽƚǁĂƌĐŝƵďƌĂŵLJĨƵŶŬĐũĂnjĞŐĂƌĂƉŽŶŽǁŶŝĞnjŽƐƚĂũĞĂŬƚLJǁŽǁĂŶĂ
ŬƚLJǁĂĐũĂŐǁĂƌĂŶĐũŝnjĂŵŬŶŝħĐŝĂŽƚǁĂƌĐŝĂ
ŬƚLJǁĂĐũĂƚĞŐŽƉĂƌĂŵĞƚƌƵĚĂũĞŐǁĂƌĂŶĐũħǏĞďƌĂŵĂŶŝĞƉŽnjŽƐƚĂŶŝĞŽƚǁĂƌƚĂnjƉŽǁŽĚƵŶĂĐŝƑŶŝħĐŝĂŶŝĞƉƌĂǁŝ-
ĚųŽǁĞŐŽŝůƵďƉƌnjLJƉĂĚŬŽǁĞŐŽƉƌnjLJĐŝƐŬƵ
&ƵŶŬĐũĂƐŝħE/ĂŬƚLJǁƵũĞũĞǏĞůŝ
ͻ ďƌĂŵĂnjŽƐƚĂŶŝĞnjĂƚƌnjLJŵĂŶĂƉƌnjLJĐŝƐŬŝĞŵ^dKW
ͻ ĂŬƚLJǁƵũĞ Ɛŝħ ůŝƐƚǁĂ ŬƌĂǁħĚnjŝŽǁĂ ŝ ǁLJŬƌLJǁĂ ƉƌnjĞƐnjŬŽĚħ ǁ ŬŝĞƌƵŶŬƵ ǁ ŬƚſƌLJŵ ũĞƐƚ ǁLJŬŽŶLJǁĂŶĂ
ĂŬƚLJǁŽǁĂŶĂĨƵŶŬĐũĂ:ĞǏĞůŝŶĂƚŽŵŝĂƐƚůŝƐƚǁĂŬƌĂǁħĚnjŝŽǁĂǁLJŬƌLJũĞƉƌnjĞƐnjŬŽĚħƉŽĚĐnjĂƐƌƵĐŚƵǁŬŝĞƌƵŶŬƵ
ƉƌnjĞĐŝǁŶLJŵŶŝǏŐǁĂƌĂŶƚŽǁĂŶLJĨƵŶŬĐũĂƉŽnjŽƐƚĂũĞĂŬƚLJǁŶĂ
ͻ njŽƐƚĂŶČǁLJŬŽŶĂŶĞƉƌſďLJnjĂŵŬŶŝħĐŝĂnjĂƉƌŽŐƌĂŵŽǁĂŶĞǁƉĂƌĂŵĞƚƌnjĞ$.
ͻ ũĞǏĞůŝŶŝĞŵĂŬŽŶƚƌŽůŝƉŽnjLJĐũŝ;ǁLJƐnjƵŬĂđƉŽnjLJĐũħƉĂƚƌnjƌŽnjĚnjŝĂųϭϵͿ
ĞnjĂŬƚLJǁŽǁĂŶĞWĂƌĂŵĞƚƌŶŝĞũĞƐƚǁLJƑǁŝĞƚůĂŶLJ
ŬƚLJǁĂĐũĂŐǁĂƌĂŶĐũŝnjĂŵŬŶŝħĐŝĂWŽƵƉųLJǁŝĞĐnjĂƐƵnjĂƉƌŽŐƌĂŵŽǁĂŶĞŐŽǁƉĂƌĂŵĞƚƌnjĞĐĞŶƚƌĂůĂǁųČĐnjĂ
ŵŝŐĂŶŝĞŽƐƚƌnjĞŐĂǁĐnjĞƚƌǁĂũČĐĞϱƐŶŝĞnjĂůĞǏŶŝĞŽĚƉĂƌĂŵĞƚƌƵ$ĂŶĂƐƚħƉŶŝĞnjĂŵLJŬĂďƌĂŵħ
ŬƚLJǁĂĐũĂŐǁĂƌĂŶĐũŝnjĂŵŬŶŝħĐŝĂŝŽƚǁĂƌĐŝĂ
:ĞǏĞůŝďƌĂŵĂnjĂƚƌnjLJŵĂƐŝħƉŽŶĂĐŝƑŶŝħĐŝƵƉƌnjLJĐŝƐŬƵƚƌLJďƵŬƌŽŬŽǁĞŐŽƉŽƵƉųLJǁŝĞĐnjĂƐƵnjĂƉƌŽŐƌĂŵŽǁĂŶĞŐŽǁƉĂ-
ƌĂŵĞƚƌnjĞĐĞŶƚƌĂůĂǁųČĐnjĂŵŝŐĂŶŝĞŽƐƚƌnjĞŐĂǁĐnjĞƚƌǁĂũČĐĞϱƐŶŝĞnjĂůĞǏŶŝĞŽĚƉĂƌĂŵĞƚƌƵ$ĂďƌĂŵĂƐŝħnjĂŵLJŬĂ
:ĞǏĞůŝƉŽĚĐnjĂƐŵĂŶĞǁƌƵnjĂŵLJŬĂŶŝĂďƌĂŵĂnjĂƚƌnjLJŵĂƐŝħnjƉŽǁŽĚƵnjĂĚnjŝĂųĂŶŝĂƐLJƐƚĞŵƵǁLJŬƌLJǁĂũČĐĞŐŽƉƌnjĞƐnjŬŽ-
ĚLJƉŽƵƉųLJǁŝĞĐnjĂƐƵnjĂƉƌŽŐƌĂŵŽǁĂŶĞŐŽǁƉĂƌĂŵĞƚƌnjĞďƌĂŵĂƐŝħnjĂŵLJŬĂ
:ĞǏĞůŝƉŽĚĐnjĂƐŵĂŶĞǁƌƵŽƚǁŝĞƌĂŶŝĂďƌĂŵĂnjĂƚƌnjLJŵĂƐŝħnjƉŽǁŽĚƵnjĂĚnjŝĂųĂŶŝĂƐLJƐƚĞŵƵǁLJŬƌLJǁĂũČĐĞŐŽƉƌnjĞƐnjŬŽ-
ĚLJƉŽƵƉųLJǁŝĞĐnjĂƐƵnjĂƉƌŽŐƌĂŵŽǁĂŶĞŐŽǁƉĂƌĂŵĞƚƌnjĞďƌĂŵĂƐŝħŽƚǁŝĞƌĂ
ZĞŐƵůĂĐũĂĐnjĂƐƵĂŬƚLJǁĂĐũŝŐǁĂƌĂŶĐũŝnjĂŵŬŶŝħĐŝĂŽƚǁĂƌĐŝĂ
ht'WĂƌĂŵĞƚƌŶŝĞũĞƐƚǁŝĚŽĐnjŶLJũĞǏĞůŝƉĂƌĂŵĞƚƌ = .
KĚϮĚŽϵϬƐŽĐnjĞŬŝǁĂŶŝĂ
KĚϮĚŽϵŵŝŶŽĐnjĞŬŝǁĂŶŝĂ
WƌnjLJǁƌĂĐĂŶŝĞƐƚĂŶĚĂƌĚŽǁLJĐŚƵƐƚĂǁŝĞŷĨĂďƌLJĐnjŶLJĐŚ
UWAGA. dĂƉƌŽĐĞĚƵƌĂũĞƐƚŵŽǏůŝǁĂƚLJůŬŽũĞǏĞůŝE/ƵƐƚĂǁŝŽŶŽŚĂƐųĂĐŚƌŽŶŝČĐĞŐŽĚĂŶĞ
P1
P2
x4 s
+
-
KƐƚƌŽǏŶŝĞWƌnjLJǁƌſĐĞŶŝĞƵƐƚĂǁŝĞŷĨĂďƌLJĐnjŶLJĐŚŬĂƐƵũĞǁƐnjLJƐƚŬŝĞǁĐnjĞƑŶŝĞũƐnjĞƵƐƚĂǁŝĞŶŝĂŽƉƌſĐnjƉĂƌĂŵĞƚƌƵ
$ƐƉƌĂǁĚnjŝđĐnjLJǁƐnjLJƐƚŬŝĞƉĂƌĂŵĞƚƌLJƐČĚŽƐƚŽƐŽǁĂŶĞĚŽŝŶƐƚĂůĂĐũŝ
^ƚĂŶĚĂƌĚŽǁĞ ƵƐƚĂǁŝĞŶŝĂ ĨĂďƌLJĐnjŶĞ ŵŽǏŶĂ ƉƌnjLJǁƌſĐŝđ ƌſǁŶŝĞǏ ƉƌnjLJĐŝƐŬĂŵŝ + ;ƉůƵƐͿ ŝ - ;ŵŝŶƵƐͿ ƚĂŬ ũĂŬ
ŽƉŝƐĂŶŽƉŽŶŝǏĞũ
ͻ tLJųČĐnjLJđnjĂƐŝůĂŶŝĞ
ͻ EĂĐŝƐŶČđƉƌnjLJĐŝƐŬŝ+;ƉůƵƐͿŝ-;ŵŝŶƵƐͿŝƉƌnjLJƚƌnjLJŵƵũČĐũĞǁųČĐnjLJđnjĂƐŝůĂŶŝĞ
ͻ WŽϰƐǁLJƑǁŝĞƚůĂĐnjŵŝŐĂU(V.
ͻ ^ƚĂŶĚĂƌĚŽǁĞƵƐƚĂǁŝĞŶŝĂĨĂďƌLJĐnjŶĞnjŽƐƚĂųLJƉƌnjLJǁƌſĐŽŶĞ