Topic 7 Flashcards
Chapter 9 (23 cards)
What type of voltage/current are AC circuits driven by?
Sinusoidal voltage/current.
It has alternating positive and negative values.
What is the equation for a sine wave?
Where Vm is Amplitude.
(wt+Φ) = Argument of sinusoid.
w is the angular frequency in rad/s.
Φ is the phase in degrees or radians.
What is phase?
The angle in which we are moving the waveform , left or right from the origin.
Equation for a period for a sinusoid?
Where T is the period
And w is the angular frequency
What is the formula for cyclic frequency (f)?
Reciprocal of the period (T). Measured in Hertz.
What is the formula for angular frequency?
Where f = 1/T
What is lagging and leading?
A sinusoid is said to lag another sinusoid if it starts later, and it leads if its earlier. If a signal lags another by x number of degrees, its phase is -x.
Important units tip to remember when evaluating sinusoidal functions?
w is in radians/sec
but phase may be given in radians or degrees
Must be converted
Important trigonometric identities?
What is a phasor?
A method for representing sinusoids. It is a complex number that represents the amplitude and phase of a sinusoid. It supresses the time factor, and assumes a fixed frequency.
What is the time-domian representation?
To obtain a time-domain representations of a given phasor (bold V), we use a cosine function with the same magnitude (Vm) and the argument (wt) plus the phase.
What is phasor-domain representation?
Simply the amplitude of the signal followed by the phase angle.
What happens when differentiating a sinusoid?
It is equivalent to multiplying the phasor by jw.
What happens when you integrate a sinusoid?
It is equivalent to dividing the phasor by jw.
How does frequency affect your ability to perform phasor analysis on multiple sinusoids?
The frequency must be constant, and the same across all sinusoids. To perform phasor analysis on multiple frequencies, superposition is required.
2 main differences between sinusoids and their corresponding phasors?
v(t) is time dependent, while bold V (phasor) is a constant.
v(t) is always a real function, while bold V is a complex number.
Why is a phasor the real part?
When representing a sinusoid as a phasor, we disregard all parameters and variables that are time dependent, being the Imaginary part.
What is the formula for the voltage across a capacitor if the voltage is a sinusoidal signal?
Since dv/dt = multiplying by jw. Voltage and current are out of phase, with current leading by 90 degrees (j).
What is the formula for the voltage across an inductor if the voltage is a sinusoidal signal?
Notice how it is the evidently the opposite of the capacitor voltage. The voltage is leading by 90 degrees.
How do extreme cases of w affect the impedance of capacitors and inductors?
At low frequencies, w=0,
ZC –> infinity
ZL –> 0
At high frequencies, w=infinity
ZC –> 0
ZL –> Infinity
What is impedance (Z)?
How any element affects current flow, broader than resistance. Measured in Ohms. Using impedance, capacitors and inductors can be shown to represent Ohm’s law.
What does the sign of the reactance tell us?
Positive: Inductive or voltage leads current
Negative: Capacitive or voltage lags current
What is admittance?
The reciprocal of Impedance. It is measured in Siemens (S), just like conductance.
