This document summarizes an experiment to study the sinusoidal steady-state response of a parallel RLC circuit using LTspice software. The parallel RLC circuit can be used as a tuning circuit or bandpass filter. The experiment involves simulating a circuit with R=1.5kΩ, L=0.2mH and C=150μF to determine the resonant frequency, bandwidth, and quality factor. The theoretical resonant frequency of 918.88Hz matched closely with the observed value of 918.82Hz from the LTspice simulation. The results and applications of parallel RLC circuits are discussed.

1. Aim:
To study the sinusoidal steady-state response of the given parallel RLC circuit
which can be used in tuning circuits.
Software Required:
LTspice software
Theory & Circuit Diagram:
The parallel RLC circuit is shown in the above figure. The RLC parallel circuit
can be used as a shunt bandpass filter by placing a series L and C in series
parallel with the load resistor.The parallel RLC circuits can be used for tuning
in radio receiver circuits. It is the dual of the series RLC circuit.
The admittance of a parallel RLC circuit is given by
𝑌 =
𝐼
𝑉
=
1
𝑅
+ 𝑗 (𝜔𝑐 −
1
𝜔𝐿
) (1)
Resonance occurs when (𝜔𝑐 −
1
𝜔𝐿
) = 0 (2) Resonant frequency of the parallel
RLC circuit is given by
𝜔𝑂 =
1
√𝐿𝐶
(3)
Quality factor of the parallel RLC circuit Q=ω0RC
Sinusoidal Steady State Response of Parallel RLC
circuit
(Series Band pass filter using passive components)

2. 𝐵𝑎𝑛𝑑𝑤𝑖𝑑𝑡ℎ =
𝜔0
𝑄
(4)
Lower Half power Frequency
𝜔1 = 𝜔0 −
𝐵
2
(5)
Upper Half power Frequency
𝜔2 = 𝜔0 −
𝐵
2
(6)
A parallel RLC circuit has R=1.5kΩ, L=0.2mH and C=150µF.Determine:
(a) the resonant frequency
(b) the bandwidth
(c) the quality factor
Procedure:
1. Open LTspice. Go to File New Schematic.
2. On the File Menu, click on Edit Component.

3. 3. Place the voltage sources, resistor, inductor , capacitor and ground on to
schematic and make necessary connections as shown in the Figure.
Circuit for simulating Parallel RLC circuit:
V1
SINE(0 50 100)
R1
50
L1
20m
C1
5µ
;ac lin 1 100 100
.tran 50m startup

4. Results:Plot of Voltage across the circuit and current through the circuit

5. Circuit for simulating Parallel RLC resonance:
4. As shown in the figures above, Right click on the AC voltage source V1 and
set its magnude as 10V.
5. Go to Edit → SPICE analysis. Set the type of sweep to Decade, Number of
points to 101 and start and stop frequency to 10 and 100k respectivelyy
each in the AC Analysis command as shown in the figure below and run the
simulation. (run symbol on the menu bar).
AC 10
V1
R1
1.5k
L1
0.2m
C1
150µ
R2
1
VS
.ac dec 101 10 100k

6. 6. Observe the supply voltage Vs and and the total current through the
circuit.Verify the resonance frequency with the theoretical calculation.

8. Observation table:
S. No. Parameter Theoretical Value Observed Value
1.
Resonant
Frequency(ω0)
918.88 918.82
2.
Current I through the
circuit
10 10
3.
Voltage V across the
circuit at resonance.
10 10
Result & Inferences:
Thus, a parallel RLC circuit has been designed and implemented in LTspice
software, and the current amplitude and phase angle is observed as ---- A
and --------respectively which is matching with Theoretical Values. From
the waveforms, it is also observed that the current leads the voltage.
Practical Applications:
The three circuit elements, R, L, and C can be combined in several different
topologies by connecting them in series or parallel. RLC circuits have many
applications as follows:
 Variable tuned circuit
 Filters - Band-pass filter, Band-stop filter, Low-pass filter or High-pass
filter
Course Outcome:
CO2. Analyze AC power circuits and networks, its measurement and safety
concerns
CO6. Design and conduct experiments to analyze and interpret data

9. Student Learning Outcomes (SLO):
SLO1. Having an ability to apply mathematics and science in engineering
applications
SLO9. Having problem-solving ability- solving social issues and engineering
problems