Impedance and Admittance
Objective of Lecture
 Explain mathematically how a voltage that is applied
to components in series and how a current that enters
the a node shared by components in parallel are
distributed among the components.
 Chapter 9.7 Fundamentals of Electric Circuits
 Chapters 15.4, 15.6, 16.3, 16.5, 17.2, 17.5, 17.7 Principles of
Electric Circuits
 Chapters 10.3, 10.5-6, 12.3, 12.5-6, 13.2, and 13.5 Electric
Circuit Fundamentals
Voltage Dividers
Impedances in series share the same current
Voltage Dividers
From Kirchhoff’s Voltage Law and Ohm’s Law
0   VS  V1  V2
V1  IZ1
and
Therefore, V2 
V1 
Z1
Vs
Z1  Z 2
V2 
Z2
Vs
Z1  Z 2
V2  IZ2
V1
Z2
Z1
Voltage Division
The voltage associated with one impedance Zn in a
chain of multiple impedances in series is:


 Z 
Vn   S n  Vt o t a l or
 Z 
s 
 
s 1

 Zn 
Vn  
 Vt o t a l
 Z e q 
where Vtotal is the total of the voltages applied across
the impedances.
Voltage Division
 Because of changes in phase angle of the voltage that
occur with inductors and capacitors, the calculation of
the percentage of the total voltage associated with a
particular impedance, Zn, is not directly related to the
percentage of the magnitude of that particular
impedance, Zn, relative to the total equivalent
impedance, Zeq.
 Zn = Zn jn
 Zeq = Zeq jeq
Current Division
All components in parallel share the same voltage
Current Division
From Kirchhoff’s Current Law and Ohm’s Law
0  IS  I1  I2  I3
VS  I1Z1
VS  I2 Z 2
Vs  I3 Z 3
Current Division
I1 
I2 
I3 
Z2 Z3
Z1  Z 2 Z 3
Z1 Z 3
Z 2  Z1 Z 3
Z1 Z 2
Z 3  Z1 Z 2
IS
IS
IS
Current Division
Ze q
Z2 Z3
where Z e q  Z 2 Z 3 
and I1 
IS
Z2  Z3
Z1  Z e q
Current Division
The current associated
with one component Z1
in parallel with one other
component is:
 Z2 
I1  
 It o t a l
 Z1  Z 2 
 The current associated
with one component Zm
in parallel with two or
more components is:
 Ze q 
Im  
 It o t a l
 Zm 
where Itotal is the total of the currents entering the
node shared by the components in parallel.
Summary
 The equations used to
 The equations used to
calculate the voltage
calculate the current
across a specific
flowing through a specific
component Zn in a set of
component Zm in a set of
components in series are:
components in parallel are:
 Zn 
Vn  
 Vt o t a l
 Z e q 
 Ye q 
Vn  
 Vt o t a l
 Yn 
Im 
Ze q
Zm
It o t a l
Ym
Im 
It o t a l
Ye q