ELEC2134 CH5
Combined Q = w(o)÷BW and Q = Rw(0)C = R/w(0)L we get what? (BW=?)
BW = 1/RC
What happens to the average power P of the resistance at resonance?
The average power dissipated is maximised. Pmax=((Vm/sqrt(2))^2)÷2
What happens to the power at the half-fequencies? wl and wu?
The power will be half of the max power.
Define quality factor (bandwidth).
The quality factor is: w(o):BW or R:L
What can the resonant circuits do (when we relate them to the input V and I) ?
The resonant circuits can generate higher V and I's
What kind of resistor causes a higher quality factor? How does this effect the voltage?
The smaller the resistor, the higher the quality factor and a greater amount of voltage rise during resonance.
What happens to the voltage across the Inductor and Capacitor at resonance, in a series circuit?
They are of equal impedance. VLo = w(0)L/R*Vm VCo = 1/w(o)CR*Vm
What is the resonance frequency also called?
Unity power-factor response
What is the voltage across the: Inductor, (with Q) Capacitor (with Q) in a series circuit at resonance?
VL0 = QVm VC0 = QVm
At resonance the magnitude of: The source voltage The Capacitors Current The Inductors Current is, what, are series resonance?
Vm = Im*r |Ic| = Im*Rw(0)C |Il| = Im*(R/w(0)l)
When does the circuit behave like a resistor?
When the total impedance X = 0, wL = 1/wC V and I are in phase.
When does the circuit behave like an inductor? What is the consequence?
When the total impedance X > 0 wL > 1/wC
When does resonance occur, in electrical circuits?
When the total reactance of the circuit = 0
When does the circuit behave like a capacitor? What is the consequence?
When total impedance X < 0 wL < 1/wC
What is the net reactance when an series RLC circuit is in resonance?
X = wL - 1/wC
What is the impedance of the parallel circuit at resonance frequency?
Y = G + 0B Z = R and ø = 0
What is the total admittance of the RLC circuit?
Y = Yr + Yc +Yl Y = G + jwC + 1÷jwL Y = G + j(wC-1÷wL)
The quality factor selects the _____. If Q is high it has a high _____. If Q is low it has a low _____.
frequency, selectivity, selectivity.
If Q >> 1 then the half frequencies are given by? (fu, fl)
fu ≈ f0 + BW÷2 fl ≈ f0 - BW÷2
If Q > 1 the peak voltage will be _____ than the applied voltage, this is known as _____ voltage rise
greater, resonance
Resonance is always possible in _____ motion
periodic
The w(0) = 1/sqrt(LpC) for a _____ circuit
tuned
What is the Vm(w) = ? or a parallel RLC circuit?
vm(w) = RIm*(1÷sqrt(1+Q^2(w/w(0)-w(0)/w)^2)
A circuit is in resonance when the ____ and ____ at the circuit input terminals are in _____
voltage, current, phase
What is the bandwidth of an RLC series Circuit?
w(H) - w(L)
What is a parallel RLC circuit?
when a current source is in parallel with R, L and C.
What is the resonance frequency?
when w(0) = 1/sqrt(LC) rad/sec
What is the magnitude of Ic and Il are parallel magnitude?
|Il| = |Ic| => Rw(0)C = R/w(o)L
When the coil resistance is small, the Qcoil is _____.
Large.
What is the average power dissipated at the resistance at parallel resonance?
Pmax = (Im/sqrt(2))^2*R = R(Irms)^2
What is the definition of quality factor at parallel resonance?
Q = Rw(o)C = R/w(0)L
What is the quality factor of a series RLC circuit? (Q)
Q = w(0)L/R = 1/w(0)RC
Qcoil is what? in a RLC circuit with a resistance in series with the inducter. A tuned circuit.
Qcoil = w(0)Ls/Rs
Define Resonance
Resonance is the tendency of a system to oscillate at a maximum amplitude at the resonant frequency
Rp = ? Lp = ?
Rp = (Rs^2+w^2Ls^2)÷Rs Lp = (Rs^2+w^2Ls^2)÷Ls Note Xp = wLp
Qcircuit = Rp||R * w(0) * C = ?
Rp||R÷w(0)Lp
What is an RLC circuit?
...-Vm+ -> +R- -> +VL- -> +VC- ->...
What is the upper and lower cut-off frequencies of the RLC series circuit?
1/sqrt(2) * Vm/R
What are the phasor: I, VRo, VLo, VCo or a series circuit in resonance?
I = Vm/R ∠0 VRo = Vm∠0 VLo = QVm∠90 VHo = QVm∠-90
How do we convert a series to parallel?
If we select and R and L, at a given frequency, the admittance can equal the series structure: 1/Rp + 1/jwLp = 1/(Rs+jwLs)
What is the quality factor of a series RLC circuit? (words)
It is the voltage of the inductor and capacitor at resonance.
