Post on 14-Mar-2020
Introduction to Electric Circuits
Chapter 10 Sinusoidal Steady-State AnalysisPart 1
Sinusoidal function
Sinusoidal function
Sine and Cosine Functions
Sine and Cosine Functions
Advancing in time
Delaying in time
Oscilloscope
Phasors and Sinusoids
Sinusoidal source(a known fixed single frequency) Steady state, forced response
Euler’s formula
Time domain, Frequency domain
cos sinje j
Motivating Example: RC circuit
:
cos ,
cos , (0) 1
KVLdvRi v e t i Cdt
dvRC v t vdt
Motivating Example: RC circuit
Euler’s formula
Assume the solution:
cos sin
cos Re
cos
j t
j t
j t
e t j t
t e
dv dvRC v t RC v edt dt
( )j t j j tv Ve Ve e
Motivating Example: RC circuit Assume the solution:
( )
( )( )
( ) ( )
tan
2
1 1 11 1
1 1
j t j j t
j tj t j t
j t j t j t j j t j j t j t
j j j
j
v Ve Ve edVeRC Ve e
dtj RCVe Ve e j RCVe e Ve e ej RCVe Ve j RC Ve
Ve ej RC RC
1
( ) 1
2
1Re cos( tan )1
RC
j tVe t RCRC
Arithmetic using Phasors
KVL in Phasor
Impedances
Ohm’s Law for AC circuits
Impedance and admittance
( ) ( ) ( )1 ( )( )( ) ( )
V Z IIY
Z V
Capacitor( ) cos( ) V
( ) ( ) sin( ) cos( 90 ) A
C
C C
v t A tdi t C v t C A t C A tdt
Inductor( ) cos( ) A
( ) ( ) sin( ) cos( 90 ) V
L
L L
i t A tdv t L i t L A t L A tdt
Resistor( ) cos( )
( )( ) cos( )
R
RR
v t A tv t Ai t t
R R
Series Impedance
Parallel Impedance
1 21 2
1 2
1 2
1|| 1 1eqZ ZZ Z Z
Z ZZ Z
Voltage and Current Division
In the frequency domain
( 80)80|| 40 4080 80
|| 40 40 12 20|| 50 (40 40) 17
(1.372 59.04 )(48 75 ) 65.9 15.96
C
CS S S
L C
jZ R jj
Z R j jV V V VZ Z R j j