电路分析英文Lecture8[文字可编辑]
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ECTE170 – Lecture 8/11
1
Basic Elements and Phasors Chapter 14 – Boylestad
?Sinusoidal response of resistor, inductor and capacitor ?Low and high frequency response of inductors and capacitors ?Average power and Power Factor
6
7
Sinusoidal Response: Resistor
i?
v R
?
Vm sin wt R
?
Im sin wt
where
Im
?
Vm R
or
Vm ? ImR
Vmsin(ωt)
i R
? For a resistor the voltage and current are in phase and are related by Ohm's law
4
5
The Derivative
? The derivative dx/dt is actually the slope of the graph at any instant of time.
? The greatest change in x will occur at the instants wt = 0, p, and 2p.
10
Sinusoidal Response: Waveforms
Inductor
11
Sinusoidal Response: Capacitors
i ? C dv dt
where
v ? Vm sin wt
dv dt
?
Vmwcos wt
?
Vmwsin(wt
?
90 )o Vmsin(ωt)
i ? wCVm sin(wt ? 90o ) ? Im sin(wt ? 90o )
Capacitor
13
Sinusoidal Response
The current through a 5 ohm resistor is i = 40sin (377t + 30°) A. Find the expression for voltage across it.
14
Sinusoidal Response
The current through a 0.1H coil is i = 7sin(377t – 70°) A. Find the voltage across it.
?
90o )
Vmsin(ωt)
v ? wLIm sin(wt ? 90o ) ? Vm sin(wt ? 90o )
XL
?
Vm Im
?
wL
i L
? For an inductor the current lags the voltage by 90 degrees ? XL = wL is called the inductive reactance - unit ??
? The derivative dx/dt is defined as the rate of change of x with respect to time. If x fails to change at a particular instant, dx = 0, and the derivative is zero.
Vm Im
?
1 wC
?
Xc
i C
? For a capacitor the current leads the voltage by 90 degrees ? Xc = 1/?wC is called the capacitive reactance – unit ??
12
Sinusoidal Response: Waveforms
2
Introduction
? The response of the basic R, L, and C elements to a sinusoidal voltage and current will be examined with a special note of how frequency will affect the “opposing” characteristic of each element.
? For the sinusoidal waveform, dx/dt is zero only at the positive and negative peaks (wt = p/2 and 3p/2) since x fails to change at these instants of time.
8
The voltage and current of a resistive element are in phase.
9
SinuLeabharlann Baiduoidal Response: Inductors
v ? L di dt
where
i ? Im sin wt
di dt
?
Imwcos wt
?
I m w sin( wt
? For various values of wt between these maxima and minima, the derivative will exist and will have values from the minimum to the maximum inclusive.
? The derivative of a sine wave is a cosine wave; it has the same period and frequency as the original sinusoidal waveform.
? Phasor notation will then be introduced to establish a method of analysis.
3
The Derivative
? To understand the response of the basic R, L, and C elements to a sinusoidal signal, you need to examine the concept of the derivative.
1
Basic Elements and Phasors Chapter 14 – Boylestad
?Sinusoidal response of resistor, inductor and capacitor ?Low and high frequency response of inductors and capacitors ?Average power and Power Factor
6
7
Sinusoidal Response: Resistor
i?
v R
?
Vm sin wt R
?
Im sin wt
where
Im
?
Vm R
or
Vm ? ImR
Vmsin(ωt)
i R
? For a resistor the voltage and current are in phase and are related by Ohm's law
4
5
The Derivative
? The derivative dx/dt is actually the slope of the graph at any instant of time.
? The greatest change in x will occur at the instants wt = 0, p, and 2p.
10
Sinusoidal Response: Waveforms
Inductor
11
Sinusoidal Response: Capacitors
i ? C dv dt
where
v ? Vm sin wt
dv dt
?
Vmwcos wt
?
Vmwsin(wt
?
90 )o Vmsin(ωt)
i ? wCVm sin(wt ? 90o ) ? Im sin(wt ? 90o )
Capacitor
13
Sinusoidal Response
The current through a 5 ohm resistor is i = 40sin (377t + 30°) A. Find the expression for voltage across it.
14
Sinusoidal Response
The current through a 0.1H coil is i = 7sin(377t – 70°) A. Find the voltage across it.
?
90o )
Vmsin(ωt)
v ? wLIm sin(wt ? 90o ) ? Vm sin(wt ? 90o )
XL
?
Vm Im
?
wL
i L
? For an inductor the current lags the voltage by 90 degrees ? XL = wL is called the inductive reactance - unit ??
? The derivative dx/dt is defined as the rate of change of x with respect to time. If x fails to change at a particular instant, dx = 0, and the derivative is zero.
Vm Im
?
1 wC
?
Xc
i C
? For a capacitor the current leads the voltage by 90 degrees ? Xc = 1/?wC is called the capacitive reactance – unit ??
12
Sinusoidal Response: Waveforms
2
Introduction
? The response of the basic R, L, and C elements to a sinusoidal voltage and current will be examined with a special note of how frequency will affect the “opposing” characteristic of each element.
? For the sinusoidal waveform, dx/dt is zero only at the positive and negative peaks (wt = p/2 and 3p/2) since x fails to change at these instants of time.
8
The voltage and current of a resistive element are in phase.
9
SinuLeabharlann Baiduoidal Response: Inductors
v ? L di dt
where
i ? Im sin wt
di dt
?
Imwcos wt
?
I m w sin( wt
? For various values of wt between these maxima and minima, the derivative will exist and will have values from the minimum to the maximum inclusive.
? The derivative of a sine wave is a cosine wave; it has the same period and frequency as the original sinusoidal waveform.
? Phasor notation will then be introduced to establish a method of analysis.
3
The Derivative
? To understand the response of the basic R, L, and C elements to a sinusoidal signal, you need to examine the concept of the derivative.