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Series Resonance: Cut-off Frequencies, Bandwidth &
f
Selectivity
Objective
• To study the phenomenon of series resonance in an RLC circuit.
• To experimentally determine resonant frequency, cut-off (half-power)
frequencies, bandwidth, and Q-factor.
• To verify the theoretical relation between Q-factor and bandwidth.
• To analyze the effect of resistance on selectivity
Theoretical Background
A series RLC circuit consists of a resistor (R), inductor (L), and capacitor (C)
connected in series with an AC
source.
Resonance:
At resonance, inductive reactance equals capacitive reactance.
At resonance:
• Impedance is minimum (Z = R)
• Circuit current is maximum
• Power factor is unity
Half‑Power (Cut‑off) Frequencies
Half‑power points occur when circuit power becomes half of its maximum value. At these
frequencies, current drops to:
Half‑Power (Cut‑off) Frequencies
I = 0.707 I(max) Half‑power points occur when circuit power becomes half of its maximum value. At these frequencies, current drops to:
ff
ff
ff
ff
I = 0.707 I_{max}
The corresponding
frequencies are:
The corresponding
• Lower cut‑o
frequency:frequencies
f(CL) are:
•
Lower cut‑o frequency: f_{CL}
• Upper cut‑o •frequency:
Upper cut‑o f(CH)
frequency: f_{CH}
Bandwidth (BW)
BW = f(CH)- f(CL)
Quality Factor (Q)
Q-factor represents selectivity of the circuit:
Equipment
• Signal Generator
• CRO / Digital Oscilloscope
• Series RLC circuit components
• Resistor (R)
• Inductor (L)
• Capacitor (C)
• Connecting wires
• Multimeter
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462
Picture of the waveforms from Oscilloscope
o
Sample Calculation
Answering Report Questions
1. Derive the relation between Q-factor and Bandwidth in a Series Resonant
circuit.
This shows that bandwidth is inversely proportional to Q factor. High Q
circuits are highly selective with narrow bandwidt
2. A Series RLC circuit has the following parameters:
R = 10Ω, L = 0.014H, C = 100uF. Compute the following:
a. Resonant frequency in rad/sec.
b. Q-factor of the circuit
c. Bandwidth
d. Upper and lower cut-off frequencies
e. The maximum value of voltage appearing across the capacitor if the applied
voltage is v(t) = 2 sin (1000t).
.
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Discussion
• Experimental resonant frequency closely matches theoretical value.
• Increasing resistance reduces Q factor and increases bandwidth.
• Lower resistance produces sharper resonance and higher selectivity.
• Minor deviations occur due to component tolerances and measurement errors.