SlideShare uma empresa Scribd logo
e, Phasor, and
Sinusoidal Steady-State Analysis
Chien-Jung Li
Department of Electronic Engineering
National Taipei University of Technology
Department of Electronic Engineering, NTUT
Compound Interest
• 複利公式: 本金P, 年利率r, 一年複利n次,
t年後本金加利息之總和為
 
  
 
1
nt
r
S P
n
• Let P=1, r=1, and t=1
 
  
 
1
1
n
S
n
When n goes to infinite, S converges to 2.718… (= e)
 Let P=10萬, r/n=10%/12, t=1 S=11,0471
 Let P=10萬, r/n=10%, and n=36, t=1 S=3,091,268
2/33
Department of Electronic Engineering, NTUT
Development of Logarithm
• Michael Stifel (1487-1567)
• John Napier (1550-1617)
• 利用對數而將乘法變成加法的特性,刻卜勒成功
計算了火星繞日的軌道。
 
  
2 52 5 7
m m m m
 
 
7 7 4 3
4
m m m
m
  
  
2 2 3 1
3
1m m m
mm
  
3 2 1 0 1 2 3
, , , , 1, , , ,m m m m m m m
3/33
Department of Electronic Engineering, NTUT
Definition of dB (分貝)
• , where
• Power gain
• Voltage gain
• Power (dBW)
• Power (dBm)
• Voltage (dBV)
• Voltage (dBuV)
  10 logdB G   aG
b
    
 
2
1
10 log
P
P
    
 
2
1
20 log
V
V
  10 log
1-W
P
  10 log
1-mW
P
  20 log
1-Volt
V
 
 20 log
1- V
V
相對量 (比例, 比值, 無單位, dB)
絕對量 (因相對於一絕對單位,
因此可表示一絕對量. 有單位,
單位即為dBW, dBm, dBV…)
4/33
Department of Electronic Engineering, NTUT
In some textbooks, phasor may be
represented as
Euler’s Formula
• Euler’s Formula cos sinjx
e x j x 
     
      
  
      cos Re Re
j t j j t
p p pv t V t V e V e e

   
def
j
p pV V e V
• Phasor (相量)
 Don’t be confused with Vector (向量) which is commonly
denoted as A
(How it comes?)
取實部 (即cosine部分) phasor
Consider a real signal v(t) that can be represented as:
V
V
5/33
Department of Electronic Engineering, NTUT
Definition of e
lim 1
n
x
n
x
e
n
 
  
 
2 3
lim 1 1
1! 2! 3!
n
x
n
x x x x
e
n
 
       
 
x jx
   
2 3
1
1! 2! 3!
jx jx jxjx
e     
• Euler played a trick let , where 1j  
1
lim 1
n
n
e
n
 
  
 
6/33
Department of Electronic Engineering, NTUT
• Since , , ,
How It Comes…
1j   2
1j   3
1j    4
1j 
   
            
   
2 4 3 5
1
2! 4! 3! 5!
x x x x
j x
2 4
cos 1
2! 4!
x x
x     
3 5
sin
3! 5!
x x
x x    
cos sinjx
e x j x 
cos sinjx
e x j x
 
cos
2
jx jx
e e
x





sin
2
jx jx
e e
x
j
       
2 3
1
1! 2! 3!
jx jx jxjx
e
• Use and
we have
(姊妹式)
7/33
Department of Electronic Engineering, NTUT
Coordinate Systems
x-axis
y-axis
x-axis
y-axis
P(r,θ)
θ
r
P(x,y)
2 2
r x y 
1
tan
y
x
 

cosx r 
siny r 
 Cartesian Coordinate System
(笛卡兒座標系, 直角座標系)
 Polar Coordinate System
(極坐標系)
(x,0)
(0,y)
 cos ,0r 
 0, sinr 
Projection
on x-axis
Projection
on y-axis
8/33
Department of Electronic Engineering, NTUT
Sine Waveform
x-axis
y-axis
P(x,y)
x
y
r
θ θθ
y
θ
0 π/2 π 3π/2 2π
 Go along the circle, the projection on y-axis results in a sine wave.
9/33
Department of Electronic Engineering, NTUT
x
θ
0
π/2
π
3π/2
Cosine Waveform
x-axis
y-axis
θ
 Go along the circle, the projection
on x-axis results in a cosine wave.
 Sinusoidal waves relate to a Circle
very closely.
 Complete going along the circle to
finish a cycle, and the angle θ
rotates with 2π rads and you are
back to the original starting-point
and. Complete another cycle
again, sinusoidal waveform in one
period repeats again. Keep going
along the circle, the waveform will
periodically appear.
10/33
Department of Electronic Engineering, NTUT
Complex Plan (I)
It seems to be the same thing with x-y plan, right?
• Carl Friedrich Gauss (1777-1855) defined the complex plan.
He defined the unit length on Im-axis is equal to “j”.
A complex Z=x+jy can be denoted as (x, yj) on the complex plan.
(sometimes, ‘j’ may be written as ‘i’ which represent imaginary)
Re-axis
Im-axis
Re-axis
Im-axis
P(r,θ)
θ
r
P(x,yj)
2 2
r x y 
1
tan
y
x
 

cosx r 
siny r 
(x,0j)
(0,yj)
 cos ,0r 
 0, sinr 
 1j  
11/33
Department of Electronic Engineering, NTUT
Complex Plan (II)
Re-axis
Im-axis
1
Every time you multiply something by j, that thing will rotate
90 degrees.
1j   2
1j   3
1j    4
1j 
1*j=j
j
j*j=-1
-1
-j
-1*j=-j -j*j=1
(0.5,0.2j)
(-0.2, 0.5j)
(-0.5, -0.2j)
(0.2, -0.5j)
• Multiplying j by j and so on:
12/33
Department of Electronic Engineering, NTUT
Sine Waveform
Re-axis
Im-axis
P(x,y)
x
y
r
θ θθ
y=rsinθ
θ
0 π/2 π 3π/2 2π
To see the cosine waveform, the same operation can be applied
to trace out the projection on Re-axis.
13/33
Department of Electronic Engineering, NTUT
Phasor Representation (I) – Sine Basis
          
    sin Im Imj j t j j
sv t A t Ae e Ae e
Re-axis
Im-axis
P(A,ф)
y=Asin ф
θ
0 π/2 π 3π/2 2π
ф
t 
Given the phasor denoted as a point on the complex-plan, you
should know it represents a sinusoidal signal. Keep this in
mind, it is very very important!
time-domain waveform
14/33
Department of Electronic Engineering, NTUT
Phasor Representation (II) – Cosine Basis
          
    cos Re Rej j t j j
sv t A t Ae e Ae e
Re-axis
Im-axis
P(A,ф)
y=Acos ф
θ
0 π/2 π 3π/2 2π
ф
t 
time-domain waveform
15/33
Department of Electronic Engineering, NTUT
Phasor Representation (III)
      
    1
1 1 1 1sin Im j j t
v t A t A e e
Re-axis
Im-axis
P(A1,ф1)
ф1
P(A2,ф2)
P(A3,ф3)
θ
0 π/2 π 3π/2 2π
t 
A1sin ф1
      
    2
2 2 2 2sin Im j j t
v t A t A e e
      
    3
3 3 3 3sin Im j j t
v t A t A e e
A2sin ф2
A3sin ф3
16/33
Department of Electronic Engineering, NTUT
Mathematical Operation
j t
j tde
j e
dt


 
1j t j t
e dt e
j
 

 
   0
1 t
v t i t dt
C
 
  

  0
1 1t
j t j t j t
Ve Ie dt I e
C j C

  
1
CV I Z I
j C
 
 di t
v t L
dt

 
 
  
j t
j t j t
d Ie
Ve L j LI e
dt
   LV j L I Z I

 
1 1
CZ
j C sC
 LZ j L sL
• L and C: from time-domain to phasor-domain analysis
(s is the Laplace operator)
     , here let 0s j
17/33
Department of Electronic Engineering, NTUT
Phasor is what you always face with
• 電路學、電子學: Phasor 常見為一個固定值 (亦可為變量)
• 電磁學、微波工程: Phasor 常見為變動量, 隨傳播方向變化
• 通訊系統: Phasor 常見為變動量, 隨時間變化
 此變動的phasor也經常被稱作複數波包(complex envelope)、波包
(envelope),或帶通訊號的等效低通訊號(equivalent lowpass signal of
the bandpass signal)。Phasor如果被拆成正交兩成分,常稱作I/Q訊
號,而在數位通訊裡表示I/Q訊號的複數平面(座標系)也被稱為星座
圖(constellation)。
• Don’t be afraid of phasor, you will see it many times in your
E.E. life. It just appears with different names, and it is just a
representation or an analysis technique.
• Keep in mind that a phasor represents a signal, it’s like a
head on your body.
18/33
Department of Electronic Engineering, NTUT
Simple Relation Between Sine and Cosine
• Sine Cosine
π/2 π 3π/2 2π
sinθ
θ
0
cosθ
• Negative sine or cosine
   cos sin 90
   sin cos 90
    cos cos 180
    sin sin 180
Try to transform into sine-form:cos
               cos sin 90 sin 270 sin 90
19/33
Department of Electronic Engineering, NTUT
Cosine as a Basis
   
 cos Re j t
pv t V t Ve
 0pV V
   
 
 
    
 
sin cos Re
2
j t
p pv t V t V t Ve
   90pV V
     
      cos cos Re j t
p pv t V t V t Ve
 180pV V
   
 
 
     
 
sin cos Re
2
j t
p pv t V t V t Ve
 90pV V
 cosine
 sine
 negative cosine
 negative sine
Phasor
Phasor
Phasor
Phasor
20/33
Department of Electronic Engineering, NTUT
Sine as a Basis
   
 sin Im j t
pv t V t Ve
 0pV V
   
 
 
    
 
cos sin Im
2
j t
p pv t V t V t Ve
 90pV V
     
      sin sin Im j t
p pv t V t V t Ve
 180pV V
   
 
 
     
 
cos sin Im
2
j t
p pv t V t V t Ve
   90pV V
Phasor
Phasor
Phasor
Phasor
 cosine
 sine
 negative cosine
 negative sine
21/33
Department of Electronic Engineering, NTUT
Addition of Sinusoidal
 A basic property of sinusoidal functions is that the sum of an arbitrary
number of sinusoids of the same frequency is equivalent to a single
sinusoid of the given frequency. It must be emphasized that all sinusoids
must be of the same frequency.
     sinpv t V t
 1 1 1pV V
 2 2 2pV V
 n pn nV V
   1 2 nV V V V
                  1 1 2 2sin sin sinp p pn nv t V t V t V t
 1v t  2v t  nv t
22/33
Department of Electronic Engineering, NTUT
Example
      0 1 2v t v t v t
    1 20cos 100 120v t t      2 15sin 100 60v t t
    1 20 30 17.3205 10V j
     2 15 120 7.5 12.9904V j
       0 17.3205 10 7.5 12.9904V j j
    0 25sin 100 66.87v t t
    9.8205 22.9904 25 66.87j
     1 20 120 10 17.321V j
    2 15 150 12.9904 7.5V j
        0 10 17.321 12.9904 7.5V j j
    22.9904 9.8205 25 23.13j
    0 25cos 100 23.13v t t
  25sin 100 66.87t
Choose the basis you like, and the results are identical.
and For
calculate
 use sine function as a basis  use cosine function as a basis
23/33
Department of Electronic Engineering, NTUT
Steady-state Impedance
  
V
Z R jX
I
• Steady-state impedance
resistance
reactance
  
I
Y G jB
Z
• Steady-state admittance
conductance
susceptance
 30 40Z j
 30R
 40X
  

1
0.012 0.016
30 40
Y j
j
 0.012G S
 0.016X S
24/33
Department of Electronic Engineering, NTUT
Conversion to Phasor-domain
 i t
 v t V
I
RR
 i t
 v t
 i t
 v t
C
L

1
j C
V
I
j LV
I
 V R I

 
1
V I
j C
 V j L I
V
I
V
I
V
I
V and I are in-phase
V lags I by 90o
V leads I by 90o
R
C
L
25/33
Department of Electronic Engineering, NTUT
Frequency Response
Frequency-independent
All pass
Frequency-dependent
High-pass
Frequency-dependent
Low-pass
V
I
R

1
j C
V
I
j LV
I
  Z R jX R

  
1
Z R jX
C
  2 f
  2 f
  2 f
  Z R jX L
26/33
Department of Electronic Engineering, NTUT
Calculate the Impedance (I)

1
j C
V
• Calculate the impedance of a 0.01-uF capacitor at (a) f=50Hz
(b) 1kHz (c) 1MHz
  
      
  6
1
0 318.309 k
2 50 0.01 10
Z R jX j
j
  318.309 kX  318.309 kZ
I
(a) f = 50 Hz
  
      
  3 6
1
0 15.92 k
2 1 10 0.01 10
Z R jX j
j
  15.92 kX  15.92 kZ
(b) f = 1 kHz
  
      
  6 6
1
0 15.92
2 1 10 0.01 10
Z R jX j
j
  15.92X  15.92Z
(c) f = 1 MHz
 0.01 μFC
27/33
Department of Electronic Engineering, NTUT
Calculate the Impedance (II)
• Calculate the impedance of a 100-mH inductor at (a) f=50Hz
(b) 1kHz (c) 1MHz
  
       3
0 2 50 100 10 31.42Z R jX j j
 31.42X  31.42Z
(a) f = 50 Hz
  
        3 3
0 2 1 10 100 10 628.32Z R jX j j
 628.32X  628.32Z
(b) f = 1 kHz
  
        6 3
0 2 1 10 100 10 628.32 kZ R jX j j
 628.32 kX  628.32 kZ
(c) f = 1 MHz
j LV
I
 100 mHL
28/33
Department of Electronic Engineering, NTUT
Calculate the Impedance (III)
• Calculate the impedance of following circuit at (a) f=50Hz
(b) 1kHz (c) 1MHz
 
 
 
      
  6
1
200 0.2 318.309 k
2 50 0.01 10
Z R jX j
j
 318.309 kZ
(a) f = 50 Hz
 
 
 
      
  3 6
1
200 0.2 15.92 k
2 1 10 0.01 10
Z R jX j
j
 15.92 kZ
(b) f = 1 kHz
 
 
 
      
  6 6
1
200 200 15.92
2 1 10 0.01 10
Z R jX j
j
 200.63Z
(c) f = 1 MHz

1
j C
 0.01 μFC
R
 200R
   318.309k 89.96Z
   15.92k 89.26Z
  200.63 -4.55Z
29/33
Department of Electronic Engineering, NTUT
Calculate the Impedance (IV)
• Calculate the impedance of following circuit at (a) f=50Hz
(b) 1kHz (c) 1MHz
    
        3
200 2 50 100 10 200 31.42Z R jX j j
 202.45Z
(a) f = 50 Hz
    
         3 3
200 2 1 10 100 10 200 628.32Z R jX j j
 659.38Z
(b) f = 1 kHz
    
         6 3
200 2 1 10 100 10 0.2 628.32 kZ R jX j j
 628.32 kZ
(c) f = 1 MHz
j L
 100 mHL
R
 200R
  202.45 8.93Z
  659.38 72.34Z
  628.32 k 89.98Z
30/33

Mais conteúdo relacionado

Mais procurados

射頻電子 - [第二章] 傳輸線理論
射頻電子 - [第二章] 傳輸線理論射頻電子 - [第二章] 傳輸線理論
射頻電子 - [第二章] 傳輸線理論
Simen Li
 
電路學 - [第六章] 二階RLC電路
電路學 - [第六章] 二階RLC電路電路學 - [第六章] 二階RLC電路
電路學 - [第六章] 二階RLC電路
Simen Li
 
電路學 - [第二章] 電路分析方法
電路學 - [第二章] 電路分析方法電路學 - [第二章] 電路分析方法
電路學 - [第二章] 電路分析方法
Simen Li
 
電路學 - [第三章] 網路定理
電路學 - [第三章] 網路定理電路學 - [第三章] 網路定理
電路學 - [第三章] 網路定理
Simen Li
 
RF Module Design - [Chapter 1] From Basics to RF Transceivers
RF Module Design - [Chapter 1] From Basics to RF TransceiversRF Module Design - [Chapter 1] From Basics to RF Transceivers
RF Module Design - [Chapter 1] From Basics to RF Transceivers
Simen Li
 
Circuit Network Analysis - [Chapter2] Sinusoidal Steady-state Analysis
Circuit Network Analysis - [Chapter2] Sinusoidal Steady-state AnalysisCircuit Network Analysis - [Chapter2] Sinusoidal Steady-state Analysis
Circuit Network Analysis - [Chapter2] Sinusoidal Steady-state Analysis
Simen Li
 
射頻電子 - [實驗第一章] 基頻放大器設計
射頻電子 - [實驗第一章] 基頻放大器設計射頻電子 - [實驗第一章] 基頻放大器設計
射頻電子 - [實驗第一章] 基頻放大器設計
Simen Li
 
電路學 - [第四章] 儲能元件
電路學 - [第四章] 儲能元件電路學 - [第四章] 儲能元件
電路學 - [第四章] 儲能元件
Simen Li
 
專題製作發想與報告撰寫技巧
專題製作發想與報告撰寫技巧專題製作發想與報告撰寫技巧
專題製作發想與報告撰寫技巧
Simen Li
 
RF Circuit Design - [Ch1-2] Transmission Line Theory
RF Circuit Design - [Ch1-2] Transmission Line TheoryRF Circuit Design - [Ch1-2] Transmission Line Theory
RF Circuit Design - [Ch1-2] Transmission Line Theory
Simen Li
 
射頻電子 - [實驗第四章] 微波濾波器與射頻多工器設計
射頻電子 - [實驗第四章] 微波濾波器與射頻多工器設計射頻電子 - [實驗第四章] 微波濾波器與射頻多工器設計
射頻電子 - [實驗第四章] 微波濾波器與射頻多工器設計
Simen Li
 
RF Circuit Design - [Ch3-1] Microwave Network
RF Circuit Design - [Ch3-1] Microwave NetworkRF Circuit Design - [Ch3-1] Microwave Network
RF Circuit Design - [Ch3-1] Microwave Network
Simen Li
 
射頻電子 - [第六章] 低雜訊放大器設計
射頻電子 - [第六章] 低雜訊放大器設計射頻電子 - [第六章] 低雜訊放大器設計
射頻電子 - [第六章] 低雜訊放大器設計
Simen Li
 
電路學 - [第八章] 磁耦合電路
電路學 - [第八章] 磁耦合電路電路學 - [第八章] 磁耦合電路
電路學 - [第八章] 磁耦合電路
Simen Li
 
射頻電子 - [第五章] 射頻放大器設計
射頻電子 - [第五章] 射頻放大器設計射頻電子 - [第五章] 射頻放大器設計
射頻電子 - [第五章] 射頻放大器設計
Simen Li
 
RF Module Design - [Chapter 8] Phase-Locked Loops
RF Module Design - [Chapter 8] Phase-Locked LoopsRF Module Design - [Chapter 8] Phase-Locked Loops
RF Module Design - [Chapter 8] Phase-Locked Loops
Simen Li
 
Circuit Network Analysis - [Chapter3] Fourier Analysis
Circuit Network Analysis - [Chapter3] Fourier AnalysisCircuit Network Analysis - [Chapter3] Fourier Analysis
Circuit Network Analysis - [Chapter3] Fourier Analysis
Simen Li
 
射頻電子 - [第一章] 知識回顧與通訊系統簡介
射頻電子 - [第一章] 知識回顧與通訊系統簡介射頻電子 - [第一章] 知識回顧與通訊系統簡介
射頻電子 - [第一章] 知識回顧與通訊系統簡介
Simen Li
 
RF Circuit Design - [Ch2-1] Resonator and Impedance Matching
RF Circuit Design - [Ch2-1] Resonator and Impedance MatchingRF Circuit Design - [Ch2-1] Resonator and Impedance Matching
RF Circuit Design - [Ch2-1] Resonator and Impedance Matching
Simen Li
 
Voltage Controlled Oscillator Design - Short Course at NKFUST, 2013
Voltage Controlled Oscillator Design - Short Course at NKFUST, 2013Voltage Controlled Oscillator Design - Short Course at NKFUST, 2013
Voltage Controlled Oscillator Design - Short Course at NKFUST, 2013
Simen Li
 

Mais procurados (20)

射頻電子 - [第二章] 傳輸線理論
射頻電子 - [第二章] 傳輸線理論射頻電子 - [第二章] 傳輸線理論
射頻電子 - [第二章] 傳輸線理論
 
電路學 - [第六章] 二階RLC電路
電路學 - [第六章] 二階RLC電路電路學 - [第六章] 二階RLC電路
電路學 - [第六章] 二階RLC電路
 
電路學 - [第二章] 電路分析方法
電路學 - [第二章] 電路分析方法電路學 - [第二章] 電路分析方法
電路學 - [第二章] 電路分析方法
 
電路學 - [第三章] 網路定理
電路學 - [第三章] 網路定理電路學 - [第三章] 網路定理
電路學 - [第三章] 網路定理
 
RF Module Design - [Chapter 1] From Basics to RF Transceivers
RF Module Design - [Chapter 1] From Basics to RF TransceiversRF Module Design - [Chapter 1] From Basics to RF Transceivers
RF Module Design - [Chapter 1] From Basics to RF Transceivers
 
Circuit Network Analysis - [Chapter2] Sinusoidal Steady-state Analysis
Circuit Network Analysis - [Chapter2] Sinusoidal Steady-state AnalysisCircuit Network Analysis - [Chapter2] Sinusoidal Steady-state Analysis
Circuit Network Analysis - [Chapter2] Sinusoidal Steady-state Analysis
 
射頻電子 - [實驗第一章] 基頻放大器設計
射頻電子 - [實驗第一章] 基頻放大器設計射頻電子 - [實驗第一章] 基頻放大器設計
射頻電子 - [實驗第一章] 基頻放大器設計
 
電路學 - [第四章] 儲能元件
電路學 - [第四章] 儲能元件電路學 - [第四章] 儲能元件
電路學 - [第四章] 儲能元件
 
專題製作發想與報告撰寫技巧
專題製作發想與報告撰寫技巧專題製作發想與報告撰寫技巧
專題製作發想與報告撰寫技巧
 
RF Circuit Design - [Ch1-2] Transmission Line Theory
RF Circuit Design - [Ch1-2] Transmission Line TheoryRF Circuit Design - [Ch1-2] Transmission Line Theory
RF Circuit Design - [Ch1-2] Transmission Line Theory
 
射頻電子 - [實驗第四章] 微波濾波器與射頻多工器設計
射頻電子 - [實驗第四章] 微波濾波器與射頻多工器設計射頻電子 - [實驗第四章] 微波濾波器與射頻多工器設計
射頻電子 - [實驗第四章] 微波濾波器與射頻多工器設計
 
RF Circuit Design - [Ch3-1] Microwave Network
RF Circuit Design - [Ch3-1] Microwave NetworkRF Circuit Design - [Ch3-1] Microwave Network
RF Circuit Design - [Ch3-1] Microwave Network
 
射頻電子 - [第六章] 低雜訊放大器設計
射頻電子 - [第六章] 低雜訊放大器設計射頻電子 - [第六章] 低雜訊放大器設計
射頻電子 - [第六章] 低雜訊放大器設計
 
電路學 - [第八章] 磁耦合電路
電路學 - [第八章] 磁耦合電路電路學 - [第八章] 磁耦合電路
電路學 - [第八章] 磁耦合電路
 
射頻電子 - [第五章] 射頻放大器設計
射頻電子 - [第五章] 射頻放大器設計射頻電子 - [第五章] 射頻放大器設計
射頻電子 - [第五章] 射頻放大器設計
 
RF Module Design - [Chapter 8] Phase-Locked Loops
RF Module Design - [Chapter 8] Phase-Locked LoopsRF Module Design - [Chapter 8] Phase-Locked Loops
RF Module Design - [Chapter 8] Phase-Locked Loops
 
Circuit Network Analysis - [Chapter3] Fourier Analysis
Circuit Network Analysis - [Chapter3] Fourier AnalysisCircuit Network Analysis - [Chapter3] Fourier Analysis
Circuit Network Analysis - [Chapter3] Fourier Analysis
 
射頻電子 - [第一章] 知識回顧與通訊系統簡介
射頻電子 - [第一章] 知識回顧與通訊系統簡介射頻電子 - [第一章] 知識回顧與通訊系統簡介
射頻電子 - [第一章] 知識回顧與通訊系統簡介
 
RF Circuit Design - [Ch2-1] Resonator and Impedance Matching
RF Circuit Design - [Ch2-1] Resonator and Impedance MatchingRF Circuit Design - [Ch2-1] Resonator and Impedance Matching
RF Circuit Design - [Ch2-1] Resonator and Impedance Matching
 
Voltage Controlled Oscillator Design - Short Course at NKFUST, 2013
Voltage Controlled Oscillator Design - Short Course at NKFUST, 2013Voltage Controlled Oscillator Design - Short Course at NKFUST, 2013
Voltage Controlled Oscillator Design - Short Course at NKFUST, 2013
 

Destaque

RF Circuit Design - [Ch4-2] LNA, PA, and Broadband Amplifier
RF Circuit Design - [Ch4-2] LNA, PA, and Broadband AmplifierRF Circuit Design - [Ch4-2] LNA, PA, and Broadband Amplifier
RF Circuit Design - [Ch4-2] LNA, PA, and Broadband Amplifier
Simen Li
 
Circuit Network Analysis - [Chapter1] Basic Circuit Laws
Circuit Network Analysis - [Chapter1] Basic Circuit LawsCircuit Network Analysis - [Chapter1] Basic Circuit Laws
Circuit Network Analysis - [Chapter1] Basic Circuit Laws
Simen Li
 
RF Circuit Design - [Ch4-1] Microwave Transistor Amplifier
RF Circuit Design - [Ch4-1] Microwave Transistor AmplifierRF Circuit Design - [Ch4-1] Microwave Transistor Amplifier
RF Circuit Design - [Ch4-1] Microwave Transistor Amplifier
Simen Li
 
Circuit Network Analysis - [Chapter4] Laplace Transform
Circuit Network Analysis - [Chapter4] Laplace TransformCircuit Network Analysis - [Chapter4] Laplace Transform
Circuit Network Analysis - [Chapter4] Laplace Transform
Simen Li
 
Circuit Network Analysis - [Chapter5] Transfer function, frequency response, ...
Circuit Network Analysis - [Chapter5] Transfer function, frequency response, ...Circuit Network Analysis - [Chapter5] Transfer function, frequency response, ...
Circuit Network Analysis - [Chapter5] Transfer function, frequency response, ...
Simen Li
 
射頻電子實驗手冊 [實驗1 ~ 5] ADS入門, 傳輸線模擬, 直流模擬, 暫態模擬, 交流模擬
射頻電子實驗手冊 [實驗1 ~ 5] ADS入門, 傳輸線模擬, 直流模擬, 暫態模擬, 交流模擬射頻電子實驗手冊 [實驗1 ~ 5] ADS入門, 傳輸線模擬, 直流模擬, 暫態模擬, 交流模擬
射頻電子實驗手冊 [實驗1 ~ 5] ADS入門, 傳輸線模擬, 直流模擬, 暫態模擬, 交流模擬
Simen Li
 
全端物聯網探索之旅 - 重點整理版
全端物聯網探索之旅 - 重點整理版全端物聯網探索之旅 - 重點整理版
全端物聯網探索之旅 - 重點整理版
Simen Li
 

Destaque (7)

RF Circuit Design - [Ch4-2] LNA, PA, and Broadband Amplifier
RF Circuit Design - [Ch4-2] LNA, PA, and Broadband AmplifierRF Circuit Design - [Ch4-2] LNA, PA, and Broadband Amplifier
RF Circuit Design - [Ch4-2] LNA, PA, and Broadband Amplifier
 
Circuit Network Analysis - [Chapter1] Basic Circuit Laws
Circuit Network Analysis - [Chapter1] Basic Circuit LawsCircuit Network Analysis - [Chapter1] Basic Circuit Laws
Circuit Network Analysis - [Chapter1] Basic Circuit Laws
 
RF Circuit Design - [Ch4-1] Microwave Transistor Amplifier
RF Circuit Design - [Ch4-1] Microwave Transistor AmplifierRF Circuit Design - [Ch4-1] Microwave Transistor Amplifier
RF Circuit Design - [Ch4-1] Microwave Transistor Amplifier
 
Circuit Network Analysis - [Chapter4] Laplace Transform
Circuit Network Analysis - [Chapter4] Laplace TransformCircuit Network Analysis - [Chapter4] Laplace Transform
Circuit Network Analysis - [Chapter4] Laplace Transform
 
Circuit Network Analysis - [Chapter5] Transfer function, frequency response, ...
Circuit Network Analysis - [Chapter5] Transfer function, frequency response, ...Circuit Network Analysis - [Chapter5] Transfer function, frequency response, ...
Circuit Network Analysis - [Chapter5] Transfer function, frequency response, ...
 
射頻電子實驗手冊 [實驗1 ~ 5] ADS入門, 傳輸線模擬, 直流模擬, 暫態模擬, 交流模擬
射頻電子實驗手冊 [實驗1 ~ 5] ADS入門, 傳輸線模擬, 直流模擬, 暫態模擬, 交流模擬射頻電子實驗手冊 [實驗1 ~ 5] ADS入門, 傳輸線模擬, 直流模擬, 暫態模擬, 交流模擬
射頻電子實驗手冊 [實驗1 ~ 5] ADS入門, 傳輸線模擬, 直流模擬, 暫態模擬, 交流模擬
 
全端物聯網探索之旅 - 重點整理版
全端物聯網探索之旅 - 重點整理版全端物聯網探索之旅 - 重點整理版
全端物聯網探索之旅 - 重點整理版
 

Semelhante a RF Circuit Design - [Ch1-1] Sinusoidal Steady-state Analysis

Multiband Transceivers - [Chapter 1]
Multiband Transceivers - [Chapter 1] Multiband Transceivers - [Chapter 1]
Multiband Transceivers - [Chapter 1]
Simen Li
 
Neutral Electronic Excitations: a Many-body approach to the optical absorptio...
Neutral Electronic Excitations: a Many-body approach to the optical absorptio...Neutral Electronic Excitations: a Many-body approach to the optical absorptio...
Neutral Electronic Excitations: a Many-body approach to the optical absorptio...
Claudio Attaccalite
 
A-tutorial.pdf
A-tutorial.pdfA-tutorial.pdf
A-tutorial.pdf
FernandoAlbornoz16
 
sp12Part2 CIRCUITS AND SYSTEMS FOR COMPUTER ENGINEERING .pptx
sp12Part2 CIRCUITS AND SYSTEMS FOR COMPUTER ENGINEERING .pptxsp12Part2 CIRCUITS AND SYSTEMS FOR COMPUTER ENGINEERING .pptx
sp12Part2 CIRCUITS AND SYSTEMS FOR COMPUTER ENGINEERING .pptx
Elisée Ndjabu
 
Lecture 5: Junctions
Lecture 5: JunctionsLecture 5: Junctions
Lecture 5: Junctions
University of Liverpool
 
Field exams mxq proplems engineering with solution
Field exams mxq proplems engineering with solutionField exams mxq proplems engineering with solution
Field exams mxq proplems engineering with solution
BaaselMedhat
 
Brief 5AC RL and RC CircuitsElectrical Circuits Lab
Brief 5AC RL and RC CircuitsElectrical Circuits Lab Brief 5AC RL and RC CircuitsElectrical Circuits Lab
Brief 5AC RL and RC CircuitsElectrical Circuits Lab
VannaSchrader3
 
RF Module Design - [Chapter 7] Voltage-Controlled Oscillator
RF Module Design - [Chapter 7] Voltage-Controlled OscillatorRF Module Design - [Chapter 7] Voltage-Controlled Oscillator
RF Module Design - [Chapter 7] Voltage-Controlled Oscillator
Simen Li
 
EC8553 Discrete time signal processing
EC8553 Discrete time signal processing EC8553 Discrete time signal processing
EC8553 Discrete time signal processing
ssuser2797e4
 
RF Module Design - [Chapter 5] Low Noise Amplifier
RF Module Design - [Chapter 5]  Low Noise AmplifierRF Module Design - [Chapter 5]  Low Noise Amplifier
RF Module Design - [Chapter 5] Low Noise Amplifier
Simen Li
 
A Simple Communication System Design Lab #3 with MATLAB Simulink
A Simple Communication System Design Lab #3 with MATLAB SimulinkA Simple Communication System Design Lab #3 with MATLAB Simulink
A Simple Communication System Design Lab #3 with MATLAB Simulink
Jaewook. Kang
 
Light induced real-time dynamics for electrons
Light induced real-time dynamics for electronsLight induced real-time dynamics for electrons
Light induced real-time dynamics for electrons
Claudio Attaccalite
 
PART VII.3 - Quantum Electrodynamics
PART VII.3 - Quantum ElectrodynamicsPART VII.3 - Quantum Electrodynamics
PART VII.3 - Quantum Electrodynamics
Maurice R. TREMBLAY
 
s3-Ellipsometry.ppt
s3-Ellipsometry.ppts3-Ellipsometry.ppt
s3-Ellipsometry.ppt
DevendraBhale
 
Anomalous Synchronization Stability of Power-grid Network
Anomalous Synchronization Stability of Power-grid NetworkAnomalous Synchronization Stability of Power-grid Network
Anomalous Synchronization Stability of Power-grid Network
Heetae Kim
 
2017 a
2017 a2017 a
Transmission Lines Part 1 (TL Theory).pptx
Transmission Lines Part 1 (TL Theory).pptxTransmission Lines Part 1 (TL Theory).pptx
Transmission Lines Part 1 (TL Theory).pptx
Rituparna Mitra
 
Notes 2 5317-6351 Transmission Lines Part 1 (TL Theory).pptx
Notes 2 5317-6351 Transmission Lines Part 1 (TL Theory).pptxNotes 2 5317-6351 Transmission Lines Part 1 (TL Theory).pptx
Notes 2 5317-6351 Transmission Lines Part 1 (TL Theory).pptx
DibyadipRoy1
 
Filter- IIR - Digital signal processing(DSP)
Filter- IIR - Digital signal processing(DSP)Filter- IIR - Digital signal processing(DSP)
Filter- IIR - Digital signal processing(DSP)
tamil arasan
 
Transmission Lines Part 4 (Smith Charts).pptx
Transmission Lines Part 4 (Smith Charts).pptxTransmission Lines Part 4 (Smith Charts).pptx
Transmission Lines Part 4 (Smith Charts).pptx
PawanKumar391848
 

Semelhante a RF Circuit Design - [Ch1-1] Sinusoidal Steady-state Analysis (20)

Multiband Transceivers - [Chapter 1]
Multiband Transceivers - [Chapter 1] Multiband Transceivers - [Chapter 1]
Multiband Transceivers - [Chapter 1]
 
Neutral Electronic Excitations: a Many-body approach to the optical absorptio...
Neutral Electronic Excitations: a Many-body approach to the optical absorptio...Neutral Electronic Excitations: a Many-body approach to the optical absorptio...
Neutral Electronic Excitations: a Many-body approach to the optical absorptio...
 
A-tutorial.pdf
A-tutorial.pdfA-tutorial.pdf
A-tutorial.pdf
 
sp12Part2 CIRCUITS AND SYSTEMS FOR COMPUTER ENGINEERING .pptx
sp12Part2 CIRCUITS AND SYSTEMS FOR COMPUTER ENGINEERING .pptxsp12Part2 CIRCUITS AND SYSTEMS FOR COMPUTER ENGINEERING .pptx
sp12Part2 CIRCUITS AND SYSTEMS FOR COMPUTER ENGINEERING .pptx
 
Lecture 5: Junctions
Lecture 5: JunctionsLecture 5: Junctions
Lecture 5: Junctions
 
Field exams mxq proplems engineering with solution
Field exams mxq proplems engineering with solutionField exams mxq proplems engineering with solution
Field exams mxq proplems engineering with solution
 
Brief 5AC RL and RC CircuitsElectrical Circuits Lab
Brief 5AC RL and RC CircuitsElectrical Circuits Lab Brief 5AC RL and RC CircuitsElectrical Circuits Lab
Brief 5AC RL and RC CircuitsElectrical Circuits Lab
 
RF Module Design - [Chapter 7] Voltage-Controlled Oscillator
RF Module Design - [Chapter 7] Voltage-Controlled OscillatorRF Module Design - [Chapter 7] Voltage-Controlled Oscillator
RF Module Design - [Chapter 7] Voltage-Controlled Oscillator
 
EC8553 Discrete time signal processing
EC8553 Discrete time signal processing EC8553 Discrete time signal processing
EC8553 Discrete time signal processing
 
RF Module Design - [Chapter 5] Low Noise Amplifier
RF Module Design - [Chapter 5]  Low Noise AmplifierRF Module Design - [Chapter 5]  Low Noise Amplifier
RF Module Design - [Chapter 5] Low Noise Amplifier
 
A Simple Communication System Design Lab #3 with MATLAB Simulink
A Simple Communication System Design Lab #3 with MATLAB SimulinkA Simple Communication System Design Lab #3 with MATLAB Simulink
A Simple Communication System Design Lab #3 with MATLAB Simulink
 
Light induced real-time dynamics for electrons
Light induced real-time dynamics for electronsLight induced real-time dynamics for electrons
Light induced real-time dynamics for electrons
 
PART VII.3 - Quantum Electrodynamics
PART VII.3 - Quantum ElectrodynamicsPART VII.3 - Quantum Electrodynamics
PART VII.3 - Quantum Electrodynamics
 
s3-Ellipsometry.ppt
s3-Ellipsometry.ppts3-Ellipsometry.ppt
s3-Ellipsometry.ppt
 
Anomalous Synchronization Stability of Power-grid Network
Anomalous Synchronization Stability of Power-grid NetworkAnomalous Synchronization Stability of Power-grid Network
Anomalous Synchronization Stability of Power-grid Network
 
2017 a
2017 a2017 a
2017 a
 
Transmission Lines Part 1 (TL Theory).pptx
Transmission Lines Part 1 (TL Theory).pptxTransmission Lines Part 1 (TL Theory).pptx
Transmission Lines Part 1 (TL Theory).pptx
 
Notes 2 5317-6351 Transmission Lines Part 1 (TL Theory).pptx
Notes 2 5317-6351 Transmission Lines Part 1 (TL Theory).pptxNotes 2 5317-6351 Transmission Lines Part 1 (TL Theory).pptx
Notes 2 5317-6351 Transmission Lines Part 1 (TL Theory).pptx
 
Filter- IIR - Digital signal processing(DSP)
Filter- IIR - Digital signal processing(DSP)Filter- IIR - Digital signal processing(DSP)
Filter- IIR - Digital signal processing(DSP)
 
Transmission Lines Part 4 (Smith Charts).pptx
Transmission Lines Part 4 (Smith Charts).pptxTransmission Lines Part 4 (Smith Charts).pptx
Transmission Lines Part 4 (Smith Charts).pptx
 

Mais de Simen Li

2018 VLSI/CAD Symposium Tutorial (Aug. 7, 20:00-21:00 Room 3F-VII)
2018 VLSI/CAD Symposium Tutorial (Aug. 7, 20:00-21:00 Room 3F-VII)2018 VLSI/CAD Symposium Tutorial (Aug. 7, 20:00-21:00 Room 3F-VII)
2018 VLSI/CAD Symposium Tutorial (Aug. 7, 20:00-21:00 Room 3F-VII)
Simen Li
 
Node.js Event Loop & EventEmitter
Node.js Event Loop & EventEmitterNode.js Event Loop & EventEmitter
Node.js Event Loop & EventEmitter
Simen Li
 
Phase-locked Loops - Theory and Design
Phase-locked Loops - Theory and DesignPhase-locked Loops - Theory and Design
Phase-locked Loops - Theory and Design
Simen Li
 
ADF4113 Frequency Synthesizer 驅動程式實作
ADF4113 Frequency Synthesizer 驅動程式實作ADF4113 Frequency Synthesizer 驅動程式實作
ADF4113 Frequency Synthesizer 驅動程式實作
Simen Li
 
Agilent ADS 模擬手冊 [實習3] 壓控振盪器模擬
Agilent ADS 模擬手冊 [實習3] 壓控振盪器模擬Agilent ADS 模擬手冊 [實習3] 壓控振盪器模擬
Agilent ADS 模擬手冊 [實習3] 壓控振盪器模擬
Simen Li
 
Agilent ADS 模擬手冊 [實習2] 放大器設計
Agilent ADS 模擬手冊 [實習2]  放大器設計Agilent ADS 模擬手冊 [實習2]  放大器設計
Agilent ADS 模擬手冊 [實習2] 放大器設計
Simen Li
 
Agilent ADS 模擬手冊 [實習1] 基本操作與射頻放大器設計
Agilent ADS 模擬手冊 [實習1] 基本操作與射頻放大器設計Agilent ADS 模擬手冊 [實習1] 基本操作與射頻放大器設計
Agilent ADS 模擬手冊 [實習1] 基本操作與射頻放大器設計
Simen Li
 
射頻電子實驗手冊 - [實驗8] 低雜訊放大器模擬
射頻電子實驗手冊 - [實驗8] 低雜訊放大器模擬射頻電子實驗手冊 - [實驗8] 低雜訊放大器模擬
射頻電子實驗手冊 - [實驗8] 低雜訊放大器模擬
Simen Li
 
射頻電子實驗手冊 - [實驗7] 射頻放大器模擬
射頻電子實驗手冊 - [實驗7] 射頻放大器模擬射頻電子實驗手冊 - [實驗7] 射頻放大器模擬
射頻電子實驗手冊 - [實驗7] 射頻放大器模擬
Simen Li
 
射頻電子實驗手冊 [實驗6] 阻抗匹配模擬
射頻電子實驗手冊 [實驗6] 阻抗匹配模擬射頻電子實驗手冊 [實驗6] 阻抗匹配模擬
射頻電子實驗手冊 [實驗6] 阻抗匹配模擬
Simen Li
 
[ZigBee 嵌入式系統] ZigBee Architecture 與 TI Z-Stack Firmware
[ZigBee 嵌入式系統] ZigBee Architecture 與 TI Z-Stack Firmware[ZigBee 嵌入式系統] ZigBee Architecture 與 TI Z-Stack Firmware
[ZigBee 嵌入式系統] ZigBee Architecture 與 TI Z-Stack Firmware
Simen Li
 
[ZigBee 嵌入式系統] ZigBee 應用實作 - 使用 TI Z-Stack Firmware
[ZigBee 嵌入式系統] ZigBee 應用實作 - 使用 TI Z-Stack Firmware[ZigBee 嵌入式系統] ZigBee 應用實作 - 使用 TI Z-Stack Firmware
[ZigBee 嵌入式系統] ZigBee 應用實作 - 使用 TI Z-Stack Firmware
Simen Li
 
[嵌入式系統] MCS-51 實驗 - 使用 IAR (3)
[嵌入式系統] MCS-51 實驗 - 使用 IAR (3)[嵌入式系統] MCS-51 實驗 - 使用 IAR (3)
[嵌入式系統] MCS-51 實驗 - 使用 IAR (3)
Simen Li
 
[嵌入式系統] MCS-51 實驗 - 使用 IAR (2)
[嵌入式系統] MCS-51 實驗 - 使用 IAR (2)[嵌入式系統] MCS-51 實驗 - 使用 IAR (2)
[嵌入式系統] MCS-51 實驗 - 使用 IAR (2)
Simen Li
 
[嵌入式系統] MCS-51 實驗 - 使用 IAR (1)
[嵌入式系統] MCS-51 實驗 - 使用 IAR (1)[嵌入式系統] MCS-51 實驗 - 使用 IAR (1)
[嵌入式系統] MCS-51 實驗 - 使用 IAR (1)
Simen Li
 
深入淺出C語言
深入淺出C語言深入淺出C語言
深入淺出C語言
Simen Li
 
[嵌入式系統] 嵌入式系統進階
[嵌入式系統] 嵌入式系統進階[嵌入式系統] 嵌入式系統進階
[嵌入式系統] 嵌入式系統進階
Simen Li
 
Multiband Transceivers - [Chapter 7] Spec. Table
Multiband Transceivers - [Chapter 7]  Spec. TableMultiband Transceivers - [Chapter 7]  Spec. Table
Multiband Transceivers - [Chapter 7] Spec. Table
Simen Li
 
Multiband Transceivers - [Chapter 7] Multi-mode/Multi-band GSM/GPRS/TDMA/AMP...
Multiband Transceivers - [Chapter 7]  Multi-mode/Multi-band GSM/GPRS/TDMA/AMP...Multiband Transceivers - [Chapter 7]  Multi-mode/Multi-band GSM/GPRS/TDMA/AMP...
Multiband Transceivers - [Chapter 7] Multi-mode/Multi-band GSM/GPRS/TDMA/AMP...
Simen Li
 
Multiband Transceivers - [Chapter 6] Multi-mode and Multi-band Transceivers
Multiband Transceivers - [Chapter 6] Multi-mode and Multi-band TransceiversMultiband Transceivers - [Chapter 6] Multi-mode and Multi-band Transceivers
Multiband Transceivers - [Chapter 6] Multi-mode and Multi-band Transceivers
Simen Li
 

Mais de Simen Li (20)

2018 VLSI/CAD Symposium Tutorial (Aug. 7, 20:00-21:00 Room 3F-VII)
2018 VLSI/CAD Symposium Tutorial (Aug. 7, 20:00-21:00 Room 3F-VII)2018 VLSI/CAD Symposium Tutorial (Aug. 7, 20:00-21:00 Room 3F-VII)
2018 VLSI/CAD Symposium Tutorial (Aug. 7, 20:00-21:00 Room 3F-VII)
 
Node.js Event Loop & EventEmitter
Node.js Event Loop & EventEmitterNode.js Event Loop & EventEmitter
Node.js Event Loop & EventEmitter
 
Phase-locked Loops - Theory and Design
Phase-locked Loops - Theory and DesignPhase-locked Loops - Theory and Design
Phase-locked Loops - Theory and Design
 
ADF4113 Frequency Synthesizer 驅動程式實作
ADF4113 Frequency Synthesizer 驅動程式實作ADF4113 Frequency Synthesizer 驅動程式實作
ADF4113 Frequency Synthesizer 驅動程式實作
 
Agilent ADS 模擬手冊 [實習3] 壓控振盪器模擬
Agilent ADS 模擬手冊 [實習3] 壓控振盪器模擬Agilent ADS 模擬手冊 [實習3] 壓控振盪器模擬
Agilent ADS 模擬手冊 [實習3] 壓控振盪器模擬
 
Agilent ADS 模擬手冊 [實習2] 放大器設計
Agilent ADS 模擬手冊 [實習2]  放大器設計Agilent ADS 模擬手冊 [實習2]  放大器設計
Agilent ADS 模擬手冊 [實習2] 放大器設計
 
Agilent ADS 模擬手冊 [實習1] 基本操作與射頻放大器設計
Agilent ADS 模擬手冊 [實習1] 基本操作與射頻放大器設計Agilent ADS 模擬手冊 [實習1] 基本操作與射頻放大器設計
Agilent ADS 模擬手冊 [實習1] 基本操作與射頻放大器設計
 
射頻電子實驗手冊 - [實驗8] 低雜訊放大器模擬
射頻電子實驗手冊 - [實驗8] 低雜訊放大器模擬射頻電子實驗手冊 - [實驗8] 低雜訊放大器模擬
射頻電子實驗手冊 - [實驗8] 低雜訊放大器模擬
 
射頻電子實驗手冊 - [實驗7] 射頻放大器模擬
射頻電子實驗手冊 - [實驗7] 射頻放大器模擬射頻電子實驗手冊 - [實驗7] 射頻放大器模擬
射頻電子實驗手冊 - [實驗7] 射頻放大器模擬
 
射頻電子實驗手冊 [實驗6] 阻抗匹配模擬
射頻電子實驗手冊 [實驗6] 阻抗匹配模擬射頻電子實驗手冊 [實驗6] 阻抗匹配模擬
射頻電子實驗手冊 [實驗6] 阻抗匹配模擬
 
[ZigBee 嵌入式系統] ZigBee Architecture 與 TI Z-Stack Firmware
[ZigBee 嵌入式系統] ZigBee Architecture 與 TI Z-Stack Firmware[ZigBee 嵌入式系統] ZigBee Architecture 與 TI Z-Stack Firmware
[ZigBee 嵌入式系統] ZigBee Architecture 與 TI Z-Stack Firmware
 
[ZigBee 嵌入式系統] ZigBee 應用實作 - 使用 TI Z-Stack Firmware
[ZigBee 嵌入式系統] ZigBee 應用實作 - 使用 TI Z-Stack Firmware[ZigBee 嵌入式系統] ZigBee 應用實作 - 使用 TI Z-Stack Firmware
[ZigBee 嵌入式系統] ZigBee 應用實作 - 使用 TI Z-Stack Firmware
 
[嵌入式系統] MCS-51 實驗 - 使用 IAR (3)
[嵌入式系統] MCS-51 實驗 - 使用 IAR (3)[嵌入式系統] MCS-51 實驗 - 使用 IAR (3)
[嵌入式系統] MCS-51 實驗 - 使用 IAR (3)
 
[嵌入式系統] MCS-51 實驗 - 使用 IAR (2)
[嵌入式系統] MCS-51 實驗 - 使用 IAR (2)[嵌入式系統] MCS-51 實驗 - 使用 IAR (2)
[嵌入式系統] MCS-51 實驗 - 使用 IAR (2)
 
[嵌入式系統] MCS-51 實驗 - 使用 IAR (1)
[嵌入式系統] MCS-51 實驗 - 使用 IAR (1)[嵌入式系統] MCS-51 實驗 - 使用 IAR (1)
[嵌入式系統] MCS-51 實驗 - 使用 IAR (1)
 
深入淺出C語言
深入淺出C語言深入淺出C語言
深入淺出C語言
 
[嵌入式系統] 嵌入式系統進階
[嵌入式系統] 嵌入式系統進階[嵌入式系統] 嵌入式系統進階
[嵌入式系統] 嵌入式系統進階
 
Multiband Transceivers - [Chapter 7] Spec. Table
Multiband Transceivers - [Chapter 7]  Spec. TableMultiband Transceivers - [Chapter 7]  Spec. Table
Multiband Transceivers - [Chapter 7] Spec. Table
 
Multiband Transceivers - [Chapter 7] Multi-mode/Multi-band GSM/GPRS/TDMA/AMP...
Multiband Transceivers - [Chapter 7]  Multi-mode/Multi-band GSM/GPRS/TDMA/AMP...Multiband Transceivers - [Chapter 7]  Multi-mode/Multi-band GSM/GPRS/TDMA/AMP...
Multiband Transceivers - [Chapter 7] Multi-mode/Multi-band GSM/GPRS/TDMA/AMP...
 
Multiband Transceivers - [Chapter 6] Multi-mode and Multi-band Transceivers
Multiband Transceivers - [Chapter 6] Multi-mode and Multi-band TransceiversMultiband Transceivers - [Chapter 6] Multi-mode and Multi-band Transceivers
Multiband Transceivers - [Chapter 6] Multi-mode and Multi-band Transceivers
 

Último

Comparative analysis between traditional aquaponics and reconstructed aquapon...
Comparative analysis between traditional aquaponics and reconstructed aquapon...Comparative analysis between traditional aquaponics and reconstructed aquapon...
Comparative analysis between traditional aquaponics and reconstructed aquapon...
bijceesjournal
 
Hematology Analyzer Machine - Complete Blood Count
Hematology Analyzer Machine - Complete Blood CountHematology Analyzer Machine - Complete Blood Count
Hematology Analyzer Machine - Complete Blood Count
shahdabdulbaset
 
官方认证美国密歇根州立大学毕业证学位证书原版一模一样
官方认证美国密歇根州立大学毕业证学位证书原版一模一样官方认证美国密歇根州立大学毕业证学位证书原版一模一样
官方认证美国密歇根州立大学毕业证学位证书原版一模一样
171ticu
 
Casting-Defect-inSlab continuous casting.pdf
Casting-Defect-inSlab continuous casting.pdfCasting-Defect-inSlab continuous casting.pdf
Casting-Defect-inSlab continuous casting.pdf
zubairahmad848137
 
Properties Railway Sleepers and Test.pptx
Properties Railway Sleepers and Test.pptxProperties Railway Sleepers and Test.pptx
Properties Railway Sleepers and Test.pptx
MDSABBIROJJAMANPAYEL
 
哪里办理(csu毕业证书)查尔斯特大学毕业证硕士学历原版一模一样
哪里办理(csu毕业证书)查尔斯特大学毕业证硕士学历原版一模一样哪里办理(csu毕业证书)查尔斯特大学毕业证硕士学历原版一模一样
哪里办理(csu毕业证书)查尔斯特大学毕业证硕士学历原版一模一样
insn4465
 
BPV-GUI-01-Guide-for-ASME-Review-Teams-(General)-10-10-2023.pdf
BPV-GUI-01-Guide-for-ASME-Review-Teams-(General)-10-10-2023.pdfBPV-GUI-01-Guide-for-ASME-Review-Teams-(General)-10-10-2023.pdf
BPV-GUI-01-Guide-for-ASME-Review-Teams-(General)-10-10-2023.pdf
MIGUELANGEL966976
 
LLM Fine Tuning with QLoRA Cassandra Lunch 4, presented by Anant
LLM Fine Tuning with QLoRA Cassandra Lunch 4, presented by AnantLLM Fine Tuning with QLoRA Cassandra Lunch 4, presented by Anant
LLM Fine Tuning with QLoRA Cassandra Lunch 4, presented by Anant
Anant Corporation
 
132/33KV substation case study Presentation
132/33KV substation case study Presentation132/33KV substation case study Presentation
132/33KV substation case study Presentation
kandramariana6
 
spirit beverages ppt without graphics.pptx
spirit beverages ppt without graphics.pptxspirit beverages ppt without graphics.pptx
spirit beverages ppt without graphics.pptx
Madan Karki
 
Redefining brain tumor segmentation: a cutting-edge convolutional neural netw...
Redefining brain tumor segmentation: a cutting-edge convolutional neural netw...Redefining brain tumor segmentation: a cutting-edge convolutional neural netw...
Redefining brain tumor segmentation: a cutting-edge convolutional neural netw...
IJECEIAES
 
CHINA’S GEO-ECONOMIC OUTREACH IN CENTRAL ASIAN COUNTRIES AND FUTURE PROSPECT
CHINA’S GEO-ECONOMIC OUTREACH IN CENTRAL ASIAN COUNTRIES AND FUTURE PROSPECTCHINA’S GEO-ECONOMIC OUTREACH IN CENTRAL ASIAN COUNTRIES AND FUTURE PROSPECT
CHINA’S GEO-ECONOMIC OUTREACH IN CENTRAL ASIAN COUNTRIES AND FUTURE PROSPECT
jpsjournal1
 
The Python for beginners. This is an advance computer language.
The Python for beginners. This is an advance computer language.The Python for beginners. This is an advance computer language.
The Python for beginners. This is an advance computer language.
sachin chaurasia
 
NATURAL DEEP EUTECTIC SOLVENTS AS ANTI-FREEZING AGENT
NATURAL DEEP EUTECTIC SOLVENTS AS ANTI-FREEZING AGENTNATURAL DEEP EUTECTIC SOLVENTS AS ANTI-FREEZING AGENT
NATURAL DEEP EUTECTIC SOLVENTS AS ANTI-FREEZING AGENT
Addu25809
 
Generative AI leverages algorithms to create various forms of content
Generative AI leverages algorithms to create various forms of contentGenerative AI leverages algorithms to create various forms of content
Generative AI leverages algorithms to create various forms of content
Hitesh Mohapatra
 
Unit-III-ELECTROCHEMICAL STORAGE DEVICES.ppt
Unit-III-ELECTROCHEMICAL STORAGE DEVICES.pptUnit-III-ELECTROCHEMICAL STORAGE DEVICES.ppt
Unit-III-ELECTROCHEMICAL STORAGE DEVICES.ppt
KrishnaveniKrishnara1
 
Understanding Inductive Bias in Machine Learning
Understanding Inductive Bias in Machine LearningUnderstanding Inductive Bias in Machine Learning
Understanding Inductive Bias in Machine Learning
SUTEJAS
 
Advanced control scheme of doubly fed induction generator for wind turbine us...
Advanced control scheme of doubly fed induction generator for wind turbine us...Advanced control scheme of doubly fed induction generator for wind turbine us...
Advanced control scheme of doubly fed induction generator for wind turbine us...
IJECEIAES
 
Literature Review Basics and Understanding Reference Management.pptx
Literature Review Basics and Understanding Reference Management.pptxLiterature Review Basics and Understanding Reference Management.pptx
Literature Review Basics and Understanding Reference Management.pptx
Dr Ramhari Poudyal
 
Harnessing WebAssembly for Real-time Stateless Streaming Pipelines
Harnessing WebAssembly for Real-time Stateless Streaming PipelinesHarnessing WebAssembly for Real-time Stateless Streaming Pipelines
Harnessing WebAssembly for Real-time Stateless Streaming Pipelines
Christina Lin
 

Último (20)

Comparative analysis between traditional aquaponics and reconstructed aquapon...
Comparative analysis between traditional aquaponics and reconstructed aquapon...Comparative analysis between traditional aquaponics and reconstructed aquapon...
Comparative analysis between traditional aquaponics and reconstructed aquapon...
 
Hematology Analyzer Machine - Complete Blood Count
Hematology Analyzer Machine - Complete Blood CountHematology Analyzer Machine - Complete Blood Count
Hematology Analyzer Machine - Complete Blood Count
 
官方认证美国密歇根州立大学毕业证学位证书原版一模一样
官方认证美国密歇根州立大学毕业证学位证书原版一模一样官方认证美国密歇根州立大学毕业证学位证书原版一模一样
官方认证美国密歇根州立大学毕业证学位证书原版一模一样
 
Casting-Defect-inSlab continuous casting.pdf
Casting-Defect-inSlab continuous casting.pdfCasting-Defect-inSlab continuous casting.pdf
Casting-Defect-inSlab continuous casting.pdf
 
Properties Railway Sleepers and Test.pptx
Properties Railway Sleepers and Test.pptxProperties Railway Sleepers and Test.pptx
Properties Railway Sleepers and Test.pptx
 
哪里办理(csu毕业证书)查尔斯特大学毕业证硕士学历原版一模一样
哪里办理(csu毕业证书)查尔斯特大学毕业证硕士学历原版一模一样哪里办理(csu毕业证书)查尔斯特大学毕业证硕士学历原版一模一样
哪里办理(csu毕业证书)查尔斯特大学毕业证硕士学历原版一模一样
 
BPV-GUI-01-Guide-for-ASME-Review-Teams-(General)-10-10-2023.pdf
BPV-GUI-01-Guide-for-ASME-Review-Teams-(General)-10-10-2023.pdfBPV-GUI-01-Guide-for-ASME-Review-Teams-(General)-10-10-2023.pdf
BPV-GUI-01-Guide-for-ASME-Review-Teams-(General)-10-10-2023.pdf
 
LLM Fine Tuning with QLoRA Cassandra Lunch 4, presented by Anant
LLM Fine Tuning with QLoRA Cassandra Lunch 4, presented by AnantLLM Fine Tuning with QLoRA Cassandra Lunch 4, presented by Anant
LLM Fine Tuning with QLoRA Cassandra Lunch 4, presented by Anant
 
132/33KV substation case study Presentation
132/33KV substation case study Presentation132/33KV substation case study Presentation
132/33KV substation case study Presentation
 
spirit beverages ppt without graphics.pptx
spirit beverages ppt without graphics.pptxspirit beverages ppt without graphics.pptx
spirit beverages ppt without graphics.pptx
 
Redefining brain tumor segmentation: a cutting-edge convolutional neural netw...
Redefining brain tumor segmentation: a cutting-edge convolutional neural netw...Redefining brain tumor segmentation: a cutting-edge convolutional neural netw...
Redefining brain tumor segmentation: a cutting-edge convolutional neural netw...
 
CHINA’S GEO-ECONOMIC OUTREACH IN CENTRAL ASIAN COUNTRIES AND FUTURE PROSPECT
CHINA’S GEO-ECONOMIC OUTREACH IN CENTRAL ASIAN COUNTRIES AND FUTURE PROSPECTCHINA’S GEO-ECONOMIC OUTREACH IN CENTRAL ASIAN COUNTRIES AND FUTURE PROSPECT
CHINA’S GEO-ECONOMIC OUTREACH IN CENTRAL ASIAN COUNTRIES AND FUTURE PROSPECT
 
The Python for beginners. This is an advance computer language.
The Python for beginners. This is an advance computer language.The Python for beginners. This is an advance computer language.
The Python for beginners. This is an advance computer language.
 
NATURAL DEEP EUTECTIC SOLVENTS AS ANTI-FREEZING AGENT
NATURAL DEEP EUTECTIC SOLVENTS AS ANTI-FREEZING AGENTNATURAL DEEP EUTECTIC SOLVENTS AS ANTI-FREEZING AGENT
NATURAL DEEP EUTECTIC SOLVENTS AS ANTI-FREEZING AGENT
 
Generative AI leverages algorithms to create various forms of content
Generative AI leverages algorithms to create various forms of contentGenerative AI leverages algorithms to create various forms of content
Generative AI leverages algorithms to create various forms of content
 
Unit-III-ELECTROCHEMICAL STORAGE DEVICES.ppt
Unit-III-ELECTROCHEMICAL STORAGE DEVICES.pptUnit-III-ELECTROCHEMICAL STORAGE DEVICES.ppt
Unit-III-ELECTROCHEMICAL STORAGE DEVICES.ppt
 
Understanding Inductive Bias in Machine Learning
Understanding Inductive Bias in Machine LearningUnderstanding Inductive Bias in Machine Learning
Understanding Inductive Bias in Machine Learning
 
Advanced control scheme of doubly fed induction generator for wind turbine us...
Advanced control scheme of doubly fed induction generator for wind turbine us...Advanced control scheme of doubly fed induction generator for wind turbine us...
Advanced control scheme of doubly fed induction generator for wind turbine us...
 
Literature Review Basics and Understanding Reference Management.pptx
Literature Review Basics and Understanding Reference Management.pptxLiterature Review Basics and Understanding Reference Management.pptx
Literature Review Basics and Understanding Reference Management.pptx
 
Harnessing WebAssembly for Real-time Stateless Streaming Pipelines
Harnessing WebAssembly for Real-time Stateless Streaming PipelinesHarnessing WebAssembly for Real-time Stateless Streaming Pipelines
Harnessing WebAssembly for Real-time Stateless Streaming Pipelines
 

RF Circuit Design - [Ch1-1] Sinusoidal Steady-state Analysis

  • 1. e, Phasor, and Sinusoidal Steady-State Analysis Chien-Jung Li Department of Electronic Engineering National Taipei University of Technology
  • 2. Department of Electronic Engineering, NTUT Compound Interest • 複利公式: 本金P, 年利率r, 一年複利n次, t年後本金加利息之總和為        1 nt r S P n • Let P=1, r=1, and t=1        1 1 n S n When n goes to infinite, S converges to 2.718… (= e)  Let P=10萬, r/n=10%/12, t=1 S=11,0471  Let P=10萬, r/n=10%, and n=36, t=1 S=3,091,268 2/33
  • 3. Department of Electronic Engineering, NTUT Development of Logarithm • Michael Stifel (1487-1567) • John Napier (1550-1617) • 利用對數而將乘法變成加法的特性,刻卜勒成功 計算了火星繞日的軌道。      2 52 5 7 m m m m     7 7 4 3 4 m m m m       2 2 3 1 3 1m m m mm    3 2 1 0 1 2 3 , , , , 1, , , ,m m m m m m m 3/33
  • 4. Department of Electronic Engineering, NTUT Definition of dB (分貝) • , where • Power gain • Voltage gain • Power (dBW) • Power (dBm) • Voltage (dBV) • Voltage (dBuV)   10 logdB G   aG b        2 1 10 log P P        2 1 20 log V V   10 log 1-W P   10 log 1-mW P   20 log 1-Volt V    20 log 1- V V 相對量 (比例, 比值, 無單位, dB) 絕對量 (因相對於一絕對單位, 因此可表示一絕對量. 有單位, 單位即為dBW, dBm, dBV…) 4/33
  • 5. Department of Electronic Engineering, NTUT In some textbooks, phasor may be represented as Euler’s Formula • Euler’s Formula cos sinjx e x j x                        cos Re Re j t j j t p p pv t V t V e V e e      def j p pV V e V • Phasor (相量)  Don’t be confused with Vector (向量) which is commonly denoted as A (How it comes?) 取實部 (即cosine部分) phasor Consider a real signal v(t) that can be represented as: V V 5/33
  • 6. Department of Electronic Engineering, NTUT Definition of e lim 1 n x n x e n        2 3 lim 1 1 1! 2! 3! n x n x x x x e n             x jx     2 3 1 1! 2! 3! jx jx jxjx e      • Euler played a trick let , where 1j   1 lim 1 n n e n        6/33
  • 7. Department of Electronic Engineering, NTUT • Since , , , How It Comes… 1j   2 1j   3 1j    4 1j                       2 4 3 5 1 2! 4! 3! 5! x x x x j x 2 4 cos 1 2! 4! x x x      3 5 sin 3! 5! x x x x     cos sinjx e x j x  cos sinjx e x j x   cos 2 jx jx e e x      sin 2 jx jx e e x j         2 3 1 1! 2! 3! jx jx jxjx e • Use and we have (姊妹式) 7/33
  • 8. Department of Electronic Engineering, NTUT Coordinate Systems x-axis y-axis x-axis y-axis P(r,θ) θ r P(x,y) 2 2 r x y  1 tan y x    cosx r  siny r   Cartesian Coordinate System (笛卡兒座標系, 直角座標系)  Polar Coordinate System (極坐標系) (x,0) (0,y)  cos ,0r   0, sinr  Projection on x-axis Projection on y-axis 8/33
  • 9. Department of Electronic Engineering, NTUT Sine Waveform x-axis y-axis P(x,y) x y r θ θθ y θ 0 π/2 π 3π/2 2π  Go along the circle, the projection on y-axis results in a sine wave. 9/33
  • 10. Department of Electronic Engineering, NTUT x θ 0 π/2 π 3π/2 Cosine Waveform x-axis y-axis θ  Go along the circle, the projection on x-axis results in a cosine wave.  Sinusoidal waves relate to a Circle very closely.  Complete going along the circle to finish a cycle, and the angle θ rotates with 2π rads and you are back to the original starting-point and. Complete another cycle again, sinusoidal waveform in one period repeats again. Keep going along the circle, the waveform will periodically appear. 10/33
  • 11. Department of Electronic Engineering, NTUT Complex Plan (I) It seems to be the same thing with x-y plan, right? • Carl Friedrich Gauss (1777-1855) defined the complex plan. He defined the unit length on Im-axis is equal to “j”. A complex Z=x+jy can be denoted as (x, yj) on the complex plan. (sometimes, ‘j’ may be written as ‘i’ which represent imaginary) Re-axis Im-axis Re-axis Im-axis P(r,θ) θ r P(x,yj) 2 2 r x y  1 tan y x    cosx r  siny r  (x,0j) (0,yj)  cos ,0r   0, sinr   1j   11/33
  • 12. Department of Electronic Engineering, NTUT Complex Plan (II) Re-axis Im-axis 1 Every time you multiply something by j, that thing will rotate 90 degrees. 1j   2 1j   3 1j    4 1j  1*j=j j j*j=-1 -1 -j -1*j=-j -j*j=1 (0.5,0.2j) (-0.2, 0.5j) (-0.5, -0.2j) (0.2, -0.5j) • Multiplying j by j and so on: 12/33
  • 13. Department of Electronic Engineering, NTUT Sine Waveform Re-axis Im-axis P(x,y) x y r θ θθ y=rsinθ θ 0 π/2 π 3π/2 2π To see the cosine waveform, the same operation can be applied to trace out the projection on Re-axis. 13/33
  • 14. Department of Electronic Engineering, NTUT Phasor Representation (I) – Sine Basis                sin Im Imj j t j j sv t A t Ae e Ae e Re-axis Im-axis P(A,ф) y=Asin ф θ 0 π/2 π 3π/2 2π ф t  Given the phasor denoted as a point on the complex-plan, you should know it represents a sinusoidal signal. Keep this in mind, it is very very important! time-domain waveform 14/33
  • 15. Department of Electronic Engineering, NTUT Phasor Representation (II) – Cosine Basis                cos Re Rej j t j j sv t A t Ae e Ae e Re-axis Im-axis P(A,ф) y=Acos ф θ 0 π/2 π 3π/2 2π ф t  time-domain waveform 15/33
  • 16. Department of Electronic Engineering, NTUT Phasor Representation (III)            1 1 1 1 1sin Im j j t v t A t A e e Re-axis Im-axis P(A1,ф1) ф1 P(A2,ф2) P(A3,ф3) θ 0 π/2 π 3π/2 2π t  A1sin ф1            2 2 2 2 2sin Im j j t v t A t A e e            3 3 3 3 3sin Im j j t v t A t A e e A2sin ф2 A3sin ф3 16/33
  • 17. Department of Electronic Engineering, NTUT Mathematical Operation j t j tde j e dt     1j t j t e dt e j         0 1 t v t i t dt C         0 1 1t j t j t j t Ve Ie dt I e C j C     1 CV I Z I j C    di t v t L dt         j t j t j t d Ie Ve L j LI e dt    LV j L I Z I    1 1 CZ j C sC  LZ j L sL • L and C: from time-domain to phasor-domain analysis (s is the Laplace operator)      , here let 0s j 17/33
  • 18. Department of Electronic Engineering, NTUT Phasor is what you always face with • 電路學、電子學: Phasor 常見為一個固定值 (亦可為變量) • 電磁學、微波工程: Phasor 常見為變動量, 隨傳播方向變化 • 通訊系統: Phasor 常見為變動量, 隨時間變化  此變動的phasor也經常被稱作複數波包(complex envelope)、波包 (envelope),或帶通訊號的等效低通訊號(equivalent lowpass signal of the bandpass signal)。Phasor如果被拆成正交兩成分,常稱作I/Q訊 號,而在數位通訊裡表示I/Q訊號的複數平面(座標系)也被稱為星座 圖(constellation)。 • Don’t be afraid of phasor, you will see it many times in your E.E. life. It just appears with different names, and it is just a representation or an analysis technique. • Keep in mind that a phasor represents a signal, it’s like a head on your body. 18/33
  • 19. Department of Electronic Engineering, NTUT Simple Relation Between Sine and Cosine • Sine Cosine π/2 π 3π/2 2π sinθ θ 0 cosθ • Negative sine or cosine    cos sin 90    sin cos 90     cos cos 180     sin sin 180 Try to transform into sine-form:cos                cos sin 90 sin 270 sin 90 19/33
  • 20. Department of Electronic Engineering, NTUT Cosine as a Basis      cos Re j t pv t V t Ve  0pV V                sin cos Re 2 j t p pv t V t V t Ve    90pV V             cos cos Re j t p pv t V t V t Ve  180pV V                 sin cos Re 2 j t p pv t V t V t Ve  90pV V  cosine  sine  negative cosine  negative sine Phasor Phasor Phasor Phasor 20/33
  • 21. Department of Electronic Engineering, NTUT Sine as a Basis      sin Im j t pv t V t Ve  0pV V                cos sin Im 2 j t p pv t V t V t Ve  90pV V             sin sin Im j t p pv t V t V t Ve  180pV V                 cos sin Im 2 j t p pv t V t V t Ve    90pV V Phasor Phasor Phasor Phasor  cosine  sine  negative cosine  negative sine 21/33
  • 22. Department of Electronic Engineering, NTUT Addition of Sinusoidal  A basic property of sinusoidal functions is that the sum of an arbitrary number of sinusoids of the same frequency is equivalent to a single sinusoid of the given frequency. It must be emphasized that all sinusoids must be of the same frequency.      sinpv t V t  1 1 1pV V  2 2 2pV V  n pn nV V    1 2 nV V V V                   1 1 2 2sin sin sinp p pn nv t V t V t V t  1v t  2v t  nv t 22/33
  • 23. Department of Electronic Engineering, NTUT Example       0 1 2v t v t v t     1 20cos 100 120v t t      2 15sin 100 60v t t     1 20 30 17.3205 10V j      2 15 120 7.5 12.9904V j        0 17.3205 10 7.5 12.9904V j j     0 25sin 100 66.87v t t     9.8205 22.9904 25 66.87j      1 20 120 10 17.321V j     2 15 150 12.9904 7.5V j         0 10 17.321 12.9904 7.5V j j     22.9904 9.8205 25 23.13j     0 25cos 100 23.13v t t   25sin 100 66.87t Choose the basis you like, and the results are identical. and For calculate  use sine function as a basis  use cosine function as a basis 23/33
  • 24. Department of Electronic Engineering, NTUT Steady-state Impedance    V Z R jX I • Steady-state impedance resistance reactance    I Y G jB Z • Steady-state admittance conductance susceptance  30 40Z j  30R  40X     1 0.012 0.016 30 40 Y j j  0.012G S  0.016X S 24/33
  • 25. Department of Electronic Engineering, NTUT Conversion to Phasor-domain  i t  v t V I RR  i t  v t  i t  v t C L  1 j C V I j LV I  V R I    1 V I j C  V j L I V I V I V I V and I are in-phase V lags I by 90o V leads I by 90o R C L 25/33
  • 26. Department of Electronic Engineering, NTUT Frequency Response Frequency-independent All pass Frequency-dependent High-pass Frequency-dependent Low-pass V I R  1 j C V I j LV I   Z R jX R     1 Z R jX C   2 f   2 f   2 f   Z R jX L 26/33
  • 27. Department of Electronic Engineering, NTUT Calculate the Impedance (I)  1 j C V • Calculate the impedance of a 0.01-uF capacitor at (a) f=50Hz (b) 1kHz (c) 1MHz             6 1 0 318.309 k 2 50 0.01 10 Z R jX j j   318.309 kX  318.309 kZ I (a) f = 50 Hz             3 6 1 0 15.92 k 2 1 10 0.01 10 Z R jX j j   15.92 kX  15.92 kZ (b) f = 1 kHz             6 6 1 0 15.92 2 1 10 0.01 10 Z R jX j j   15.92X  15.92Z (c) f = 1 MHz  0.01 μFC 27/33
  • 28. Department of Electronic Engineering, NTUT Calculate the Impedance (II) • Calculate the impedance of a 100-mH inductor at (a) f=50Hz (b) 1kHz (c) 1MHz           3 0 2 50 100 10 31.42Z R jX j j  31.42X  31.42Z (a) f = 50 Hz            3 3 0 2 1 10 100 10 628.32Z R jX j j  628.32X  628.32Z (b) f = 1 kHz            6 3 0 2 1 10 100 10 628.32 kZ R jX j j  628.32 kX  628.32 kZ (c) f = 1 MHz j LV I  100 mHL 28/33
  • 29. Department of Electronic Engineering, NTUT Calculate the Impedance (III) • Calculate the impedance of following circuit at (a) f=50Hz (b) 1kHz (c) 1MHz                6 1 200 0.2 318.309 k 2 50 0.01 10 Z R jX j j  318.309 kZ (a) f = 50 Hz                3 6 1 200 0.2 15.92 k 2 1 10 0.01 10 Z R jX j j  15.92 kZ (b) f = 1 kHz                6 6 1 200 200 15.92 2 1 10 0.01 10 Z R jX j j  200.63Z (c) f = 1 MHz  1 j C  0.01 μFC R  200R    318.309k 89.96Z    15.92k 89.26Z   200.63 -4.55Z 29/33
  • 30. Department of Electronic Engineering, NTUT Calculate the Impedance (IV) • Calculate the impedance of following circuit at (a) f=50Hz (b) 1kHz (c) 1MHz              3 200 2 50 100 10 200 31.42Z R jX j j  202.45Z (a) f = 50 Hz               3 3 200 2 1 10 100 10 200 628.32Z R jX j j  659.38Z (b) f = 1 kHz               6 3 200 2 1 10 100 10 0.2 628.32 kZ R jX j j  628.32 kZ (c) f = 1 MHz j L  100 mHL R  200R   202.45 8.93Z   659.38 72.34Z   628.32 k 89.98Z 30/33