EEE222 - Electrical Circuit Analysis II
Lab # 9: Series and Parallel Resonant Circuits
Name Muhammad Hassan Shahid
Registration Number FA19-BEE-214
Class BEE(3C)
Instructor’s Name Sir Amir Rasheed
Lab Assessment
Post Lab Total
Pre-Lab In-Lab Data
Data Analysis Writing Style
Presentation
Lab # 9: Series and Parallel Resonant Circuits
Introduction
A resonant circuit, also called a tuned circuit consists of an inductor and a capacitor together
with a voltage or current source. It is one of the most important circuits used in electronics. For
example, a resonant circuit, in one of its many forms, allows us to select a desired radio or
television signal from the vast number of signals that are around us at any time.
A network is in resonance when the voltage and current at the network input terminals are in
phase and the input impedance of the network is purely resistive.
Figure 1. Parallel resonance circuit
Consider the Parallel RLC circuit of figure 1. The steady-state admittance offered by the circuit
is:
Y = 1/R + j( ωC – 1/ωL)
Resonance occurs when the voltage and current at the input terminals are in phase. This
corresponds to a purely real admittance, so that the necessary condition is given by
ωC – 1/ωL = 0
The resonant condition may be achieved by adjusting L, C, or ω. Keeping L and C constant, the
resonant frequency ωo is given by: 𝜔𝑜=1√𝐿𝐶 (rad/s) or ƒ𝒐=𝟏𝟐𝝅√𝑳𝑪 (Hertz)
Frequency Response
It is a plot of the magnitude of output Voltage of a resonance circuit as function of frequency.
The response of course starts at zero, reaches a maximum value in the vicinity of the natural
resonant frequency, and then drops again to zero as ω becomes infinite. The frequency
response is shown in figure 2.
Figure 2. Frequency response of parallel resonant circuit
The two additional frequencies ω1 and ω2 are also indicated which are called half-power
frequencies. These frequencies locate those points on the curve at which the voltage response
is 1/√2 or 0.707 times the maximum value. They are used to measure the band-width of the
response curve. This is called the half-power bandwidth of the resonant circuit and is defined
as:
β = ω2 - ω1
where, 𝝎𝟏=𝝎𝒐√𝟏+(𝟏𝟐𝑸)𝟐- 𝝎𝒐𝟐𝑸 , 𝝎𝟐=𝝎𝒐√𝟏+(𝟏𝟐𝑸)𝟐+ 𝝎𝒐 𝟐𝑸 , Q = 𝝎𝒐 𝜷
Pre Lab Task 1:
Figure 3. Parallel resonant circuit
Bode plot for Figure 3
Pre Lab Task 2:
Figure 4. Series resonant circuit
Bode plot for Figure 4
In-Lab:
Task 1: Parallel resonant circuit
We will set up the circuit shown in Figure 1, with the component values R = 1 KΩ, C = 1
μF and L = 33 mH, Vin = 4 Vpp and then will find the output voltage (Vo) by varying
different frequencies (500Hz-2kHz) and record the measurements in table 1.
Figure 1. Parallel resonant circuit
Simulated Observed
Frequency (Hz)
VIN(pp) Vo(pp) VIN(pp) Vo(pp)
500 4V 600mV 4V 640mV
876 4V 1200mV 4V 840mV
1000 4V 1500mV 4V 792mV
1250 4V 1100mV 4V 776mV
1500 4V 600mV 4V 720mV
1750 4V 450mV 4V 680mV
2000 4V 380mV 4V 640mV
Table 1 Values for Task 1
Sketch Bode Plot of magnitude transfer function of output voltage, using data in table 1.
Bode plot for task 1
Task 2: Series resonant circuit
We will set up the circuit shown in Figure 2, with the component values L = 33mH and C
= 0.01uF and R = 1 KΩ and Vin = 4 Vpp . and then will find the output voltage (V o) by
varying different frequencies from 500Hz-2kHz and record the measurements in table 2.
Figure 2. Series resonant circuit
Simulated Observed
Frequency (Hz)
VIN(pp) Vo(pp) VIN(pp) Vo(pp)
500 4V 120mV 4V 160 mV
1000 4V 300mV 4V 320mV
5000 4V 1.5V 4V 1.68V
8765 4V 3.0V 4V 3.28V
10000 4V 2.8V 4V 3.04V
15000 4V 1.48V 4V 1.68V
20000 4V 1.26V 4V 1.12V
Table 2 Values for Task 2
Sketch Bode Plot of magnitude transfer function of output voltage, using data in table 2
Bode plot for task 2
Post-Lab:
1- A 12 resistor, a 40 F capacitor, and an 8 mH coil are in series across an ac source.
What is the resonant frequency?
A) The resonance frequency will be 281 Hz after using the formula
1
R F=
2 ×3.14 √ LC
Critical Analysis / Conclusion
In this lab, we observed the effect of change of frequency on the output in series and parallel
resonance circuits.Initially, output increses with increasing frequency but after a certain
frequency it starts to decrease, The output is maximum at this frequency called resonance
frequency.
