RC Low Pass Filter
Objective:
Design and Observe the working of Low Pass Filter
Outcomes:
At the end of this lab, student should be able to
a) Design an RC Low Pass Filter for a given cut off frequency
b) Plot the graph of the solution
The Low Pass Filter:
A low-pass filter is a circuit offering easy passage to low-frequency signals and difficult passage to highfrequency signals. The filter achieves this by having a cutoff frequency, which is the frequency point
where the filter starts to attenuate the signal. Frequencies below the cutoff pass through the filter with
little or no reduction, while frequencies above the cutoff are gradually attenuated as their frequencies
increase.
Circuit Diagram:
Working of the Low Pass filter:
The filter I have used in the experiment consists of a resistor and a capacitor. The resistor determines
the load on the filter and sets the output impedance while the capacitor provides the frequencydependent impedance required for filtering.
The passive RC (Resistor-Capacitor) low pass filter works based on the time constant of the RC circuit.
The time constant (τ) is given by the product of the resistance (R) and the capacitance (C):
τ=R*C
The cutoff frequency (fc) of the low pass filter is the frequency at which the output signal's amplitude is
reduced to approximately 70.7% (1/e) of the original signal's amplitude. It can be calculated using the
formula:
fc = 1 / (2 * π * R * C)
When the input signal's frequency is much lower than the cutoff frequency (fc), the capacitor allows the
signal to pass through with minimal attenuation. As the input frequency approaches and exceeds the
cutoff frequency, the capacitor's impedance increases, causing attenuation of higher-frequency
components. This effectively suppresses frequencies above the cutoff, reducing their amplitudes in the
output signal.
Gain: Gain is the ratio of output observed to the applied input. For a given cut-off frequency, gain is
supposed to be 0.707 theoretically.
Experimental Setup:
The experiment was carried out in the project laboratory of Electrical department. Function generator
was employed to generate signals of different frequencies while the oscilloscope determined the output
values of the circuit and the readings were taken.
Calculations:
Roll No. = 26 ==> Resistance = 26k ohms.
Capacitance = 33nF.
Cut off Frequency (fc) = 1 / (2*pi*R*C) = 185.5 Hz.
Vin (peak to peak) = 5 Volts.
Frequency (Hz) Gain (Vout/Vin) Remarks
50
75
100
125
150
175
185.5 (fc)
200
225
250
275
300
325
0.964
0.994
0.896
0.848
0.808
0.752
0.716
0.7
0.664
0.632
0.592
0.568
0.528
Below fc: gain is very high
Below fc: gain is very high
Below fc: gain is high
Below fc gain is high
Below fc: gain is high
Below fc: gain is high
1.27% error w.r.t 0.707
Beyond fc: gain starts to get low
Beyond fc: gain gets lower
Beyond fc: gain is low
Beyond fc: gain is low
Beyond fc: gain is low
Beyond fc: gain is low
Frequency Vs Gain
0.95
0.85
0.75
0.65
0.55
0.45
0
50
100
150
200
250
300
RC High Pass Filter
Objective:
Design and Observe the working of High Pass Filter.
Outcomes:
At the end of this lab, student should be able to
a) Design an RC High Pass Filter for a given cut off frequency
b) Plot the graph of the solution
The High Pass Filter:
High-pass filter’s task is just the opposite of a low-pass filter: to offer easy passage of a high-frequency
signal and difficult passage to a low-frequency signal. The filter achieves this by having a cut-off
frequency, which is the frequency point where the filter starts to attenuate the signal. Frequencies
beyond the cut-off pass through the filter with little or no reduction, while frequencies below the cutoff
are gradually attenuated as their frequencies decrease.
Circuit Diagram:
Working of the High Pass Filter:
In the case of a high pass filter, when the input signal's frequency is much higher than the cutoff
frequency (fc), the capacitor has enough time to charge or discharge through the resistor completely.
This results in the capacitor offering low impedance to the AC signal, allowing high-frequency
components to pass through with minimal attenuation.
However, as the input signal's frequency approaches and falls below the cutoff frequency, the capacitor
doesn't have enough time to charge or discharge fully between successive cycles of the AC signal. This
causes the capacitor's impedance to decrease, resulting in attenuation of lower-frequency components.
Thus, frequencies below the cutoff are effectively suppressed, and the output signal is attenuated with
decreasing frequency.
Gain: The cut-off frequency for the high pass filter is the same as the low pass filter. Gain is supposed
to be 0.707 at cut-off frequency theoretically.
Calculation:
Roll No. = 26 ==> Resistance = 26k ohms, Capacitance = 33nF.
Cut off Frequency (fc) = 1 / (2*pi*R*C) = 185.5 Hz.
Vin (peak to peak) = 5 Volts.
Frequency (Hz) Gain (Vout/Vin) Remarks
50
75
100
125
150
175
185.5 (fc)
200
225
250
275
300
325
0.296
0.414
0.512
0.608
0.662
0.704
0.724
0.776
0.816
0.852
0.884
0.9
0.924
Below fc: gain is very low
Below fc: gain is low
Below fc: gain is low
Below fc gain is low
Below fc: gain increases near fc
Below fc: still low but increasing
2.4% error w.r.t 0.707
Beyond fc: gain starts to get higher
Beyond fc: gain gets even higher
Beyond fc: gain high
Beyond fc: gain is high
Beyond fc: gain is very high
Beyond fc: gain is very high
Frequency Vs Gain
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0
50
100
150
200
250
300
Conclusion:
The experiment examining RC high pass and low pass filters has provided valuable insights into their
respective behaviors and characteristics. The high pass filter demonstrated its effectiveness in allowing
higher frequency signals to pass while attenuating lower frequencies, making it suitable for applications
where higher-frequency signals are desired. On the other hand, the low pass filter proved adept at
passing lower-frequency signals while blocking higher frequencies, making it useful for applications
requiring filtering out unwanted high-frequency noise. Overall, this experiment deepened our
understanding of RC filters and their practical applications in signal processing and electronics.