DEPARTMENT OF AVIONICS ENGINEERING
SUBJECT : ENA lab
SUBJECT CODE : 2084112
LAB NO : 06
TITLE : Band pass filter
SUBMITTED TO : Ms. Rida
SEMESTER : 3rd
SECTION : B
Marks Obtained
Group Member Group Member Group Member
1 2 3
NAME Mahnoor Ifrah gohar
REGISTRATION # 220701002 220701058
LAB REPORT 06 06
PERFORMANCE
TOTAL MARKS
DEADLINE: 20th November,2023
DATE OF SUBMISSION: 20th November,2023
Electrical Network Analysis Lab IST, Islamabad Page 1 of 6
Lab # 6: Passive RLC Bandpass Filter.
Learning Objective:
To find the resonance frequency of passive RLC bandpass filter.
To find the cutoff frequencies of passive RLC bandpass filter.
To determine the transfer function of passive bandpass filter.
To find the bandwidth of passive RLC bandpass filter.
Equipment Required:
Digital multi-meter
Oscilloscope
Breadboard
Probes
Resistors
Capacitors
Inductors
Introduction:
An electrical filter is a circuit that can be designed to modify, reshape or reject all unwanted
frequencies of an electrical signal and accept or pass only those signals wanted by the circuit
designer. In other words, they “filter out” unwanted signals. An ideal filter will separate and
pass sinusoidal input signals based upon their frequency.
Band-pass Filter:
A band-pass filter passes a frequency band in a certain range determined by the user while
rejecting the lower and upper frequencies out of this range. In this filter, inductor and
capacitor are used together. The center frequency at this range is determined by the resonance
frequency at this inductor and capacitor. A little amount of signal is passed below and above
at this resonance frequency and the others are rejected. The wideness of this band depends on
the inductor and capacitor value. A band pass filter circuit and output characteristic curve is
given in fig. 13.1 & fig. 13.2.
Figure 13.1: RLC Band-pass Filter
Electrical Network Analysis Lab IST, Islamabad Page 1 of 6
Figure 13.2: RLC Band-pass Filter Frequency Response
Transfer Function:
We can get the transfer function of band-pass filter by measuring the voltage across the resistor VR
driven by a source Vin. Start with the voltage divider equation:
Centre Frequency:
The H (jω) reaches a maximum when the denominator is a minimum, which occurs when the real part in
the denominator equals 0. In math terms, this means that:
Electrical Network Analysis Lab IST, Islamabad Page 1 of 6
The frequency 𝑓𝑜 is called the center frequency.
Cutoff Frequencies:
The cutoff frequencies are occurs when the real part in the denominator is equal to
Band Width:
The bandwidth BW defines the range of frequencies that pass through the filter relatively
unaffected. Mathematically, it’s defined as:
Quality Factor:
It is defined as the ratio of the centre frequency to the bandwidth.
The RLC series circuit is narrowband when Q>>1 (High Q) and wideband when Q<<1 (low
Q). The separation between the narrowband and wideband response occurs at Q=1.
Electrical Network Analysis Lab IST, Islamabad Page 1 of 6
Calculation:
Calculate the following for the above circuit.
Transfer Function:
Calculated:
H(s) = s (820/560*10-6)
s2 +s (820/560*10-6) + (1/560*10-6 *1*10-6)
H(s) = 1464285.71 s
s2 +1464285.71s + 1785714286
Measured:
H(s) = s (822/506*10-6)
s2 +s (822/506*10-6) + (1/506*10-6 *0.99*10-6)
H(s) = 1624505.92 s
s2 +1624505.92 s + 1996247056
Center Frequency:
CALCULATED:
f0 = 1
2π ((560*10-6) (1*10-6))1/2
f 0 = 6725.5 Hz
Electrical Network Analysis Lab IST, Islamabad Page 1 of 6
MEASURED:
f0 = 1
2π ((506*10-6) (0.99*10-6))1/2
f 0 = 7110.94 Hz
Cutoff frequencies:
CALCULATED:
ω C1 = -820 + √ (820/2*560*10-6)2 + (1/(560*10-6)(1*10-6))
2*560*10-6
ω C1 = 1.218k Hz
ω C2 = 820 + √ (820/2*560*10-6)2 + (1/(560*10-6)(1*10-6))
-6
2*560*10
ω C2 = 1.466MHz
Measured:
ω C1 = -822 + √ (822/2*506*10-6)2 + (1/(506*10-6)(0.99*10-3))
2*506*10-6
ω C1 = 1.227 kHz
ω C2 = 822 + √ (822/2*506*10-6)2 + (1/(506*10-6)(0.99*10-3))
2*506*10-6
ω C2 = 1.625 MHz
Electrical Network Analysis Lab IST, Islamabad Page 1 of 6
Band Width:
Calculated:
BW = 1.458 MHz
Measured:
BW = 1.618MHz
Quality Factor:
CALCULATED:
Q= 1 √ (560*10 -6
)/(1*10-6)
820
Q= 0.0288
MEASURED:
Q= 1 √ (506*10 -6
)/ (0.99*10*-6)
822
Q= 0.0275
Electrical Network Analysis Lab IST, Islamabad Page 1 of 6
Procedure:
1. Build the RLC band-pass filter circuit as shown in Figure. Use appropriate values of
Resistor, Capacitor and Inductor.
2. Measure the actual values of resistor, capacitor and inductor using DMM and LCR
Meter and record them in Table-13.1.Calculate the cutoff frequency.
3. Connect the circuit as shown in Figure-13.3.
4. Connect the function generator at input. Adjust the function generator to produce 10
Vp-p sine wave at a frequency of 10 Hz. Increase the frequency from function
generator until the output voltage Vout is equal to 0.707 times the input voltage. The
frequency where this occurs is the lower cutoff frequency of the filter. Similarly find
the high cutoff frequency. Measure and record this frequency in Table-13.1.
5. Set the frequencies to the values given in Table-13.2, measure and record input,
output voltage and gain. Complete Table-13.2.
6. Plot the semi log graph of the output voltage versus frequency.
Experiment Results:
Table 13.1
Calculated Measured
820 Ω 0.822 KΩ
Resistor
1 µF 0.99 µF
Capacitor
560 µH 506µH
Inductor
1.219KHz 1.227KHz
W1
1.46MHz 1.62MHz
W2
1.458MHz 1.618MHz
BW
0.0288 0.0275
Q
Electrical Network Analysis Lab IST, Islamabad Page 8 of 6
Table 13.2
Measured Calculated
Frequency (Hz)
Vin (Volts) Vout(Volts) Av
600 4.8 4.56 0.95
800 4.8 4.64 0.96
1000 4.8 4.64 0.96
1200 4.8 4.72 0.9833
2000 4.8 4.72 0.9833
4000 4.8 4.72 0.9833
5000 4.8 4.8 1
10k 4.8 4.8 1
20k 4.8 4.72 0.9833
30k 4.8 4.72 0.9833
50k 4.8 4.72 0.9833
70k 4.8 4.64 0.966
100k 4.96 4.64 0.9362
300k 4.96 3.52 0.7096
500k 4.96 2.4 0.4838
1M 4.96 1.28 0.258
1.2M 5 1.04 0.208
1.4M 5.04 0.8 0.158
1.6M 5.04 0.64 0.1269
1.8M 5.12 0.56 0.1093
2M 5.04 0.48 0.095
2.2M 5.04 0.40 0.0793
Gain Vs. Frequency Plot:
ω C1
1200,0.9833
ω C2
1.4M,0.8
Gain
Frequency (Hz)
Conclusion:
From this lab report we have learnt how to find the resonance frequency of passive RLC bandpass filter,
cutoff frequencies of passive RLC bandpass filter, transfer function of passive bandpass filter, bandwidth
of passive RLC bandpass filter.
Also, we have learnt that band-pass filter passes a frequency band in a certain range (band width)
determined by the user while rejecting the lower and upper frequencies out of this range.
We have seen this from our measured values of Vout that it is increasing in start then remains constant or
nearly equal values after cutoff frequency 1 ω c1 then after reaching cutoff frequency ωc2 it starts to
decrease. Which shows that this band pass filter will pass only the certain range of frequencies (which
are between ωc1 and ωc2) while blocking the other.
Electrical Network Analysis Lab IST, Islamabad Page 6 of 6
