RLC circuits
•To understand an RLC circuit let us first discuss LC circuits
•For a Series LC circuit there is a special frequency at which Impedance of the LC
circuit, ZLC will be zero and the current will be infinite.
•For a parallel LC circuit there is a special frequency at which impedance of the
circuit turns to be infinite and circuit current turns to zero.
•These special frequency for the respective circuits are called their resonance
frequencies.
RLC circuits
•Resonance frequency for both the circuits can be found from the followings:
(Angular form) or
(Non-angular form)
•Why
?
Let us consider the series LC circuit
Let us put
then
in
=
So, Zeq becomes zero when
=0
and hence
RLC circuits
Similarly for the Parallel LC circuit
Zeq turns to infinity when
(since the denominator becomes zero)
and current
•Why resonance frequency is important?
Utilizing this phenomenon we can design frequency selective circuits (example:
radio tuner to select a certain station)
RLC circuits
•An RLC circuit has an additional resistance than the LC circuit. This
additional resistance makes some difference.
•At resonance frequency, zero impedance (for series LC) or infinity
impedance (for parallel LC) are shifted up or down in size due to this
resistance .
RLC circuits
•
Some Common Terms
1. Bandwidth: It is the width of the peak which is
defined by the distance between the two
half power points ω1 and ω2
2. Center frequency: Center frequency is the frequency ω0 at which the
current in the circuit is the maximum.
3. Q factor: Quality factor or Q factor is a measurement to determine the
sharpness of the curve shown in the above figure which is very
important to know to design a band pass filter.
Series RLC circuit
•What is the resonance frequency?
•What is the Quality factor (unloaded)?
Q
•Show that inductive and capacitive
reactance at resonance are equal but
opposite in phase.
Parallel RLC circuit
•What is the resonance frequency?
•What is the Quality factor (unloaded)?
Q
RLC Series Transient Analysis
Series RLC circuit
Condition:
• The current rises very rapidly to a
value near V0/R (in a time ~L/R and
then decays very slowly back to zero.
Series RLC circuit
Condition:
• The curve is almost the same except
there is no overshoot of the current.
Series RLC circuit
Condition:
•The solution is oscillatory, the amplitude
of the oscillation decays exponentially.