Experiment 7: Design a Low Pass Filter and High Pass Filter

Design a low Pass Filter and High Pass Filter

 Objective:-  1)  Design the high pass and low pass filter.    2)Calculate the lower cut off and higher cut-off  Frequency.    3)Calculate  the gain .

Equipments Required:- 1)Function Generator  2)Bread Board  3) DSO

Components required:- Resistors (10K) Capacitors( 0.01uF)

Theory:-A filter is a circuit that passes a specific range of frequencies while rejecting other frequencies. A passive filter consists of passive circuit elements, such as capacitors, inductors, and resistors. The most common way to describe the frequency response of a filter is to plot the filter voltage gain (V_out/V_in) in dB as a function of frequency (f). The frequency at which the output power gain drops to 50% of the maximum value is called the cut-off frequency (f_c). When the filter dB voltage gain is plotted as a function of frequency on a semi log graph using straight lines to approximate the actual frequency response, it is called a Bode plot. A Bode plot is an ideal plot of filter frequency response because it assumes that the voltage gain remains constant until the cut-off frequency is reached. The filter network voltage gain in dB is calculated from the actual voltage gain (A) using the equation   A_dB = 20 log A    where A = V_out/V_in.

Circuit Diagram                 

Low pass filter

Low Pass Filter

A low-pass filter (LPF) is designed to pass all frequencies below the cut-off frequency and reject all frequencies above the cut-off frequency. It is simply an RC series circuit across the input, with the output taken across the capacitor. At the cut-off frequency, the capacitive reactance of capacitor C is equal to the resistance of resistor R, causing the output voltage to be 0.707 times the input voltage (-3 dB). The expected cut-off frequency (f_c) of the low-pass filter based on the circuit component values, can be calculated from   
      

                                                                                                  X_c = R

                

Solving for f_c produces the equation

                                                                                     

A high-pass filter (HPF) is designed to pass all frequencies above the cut-off frequency and reject all frequencies below the cut-off frequency.It is simply an RC series circuit across the input, with the output taken across the resistor. Similar to LPF expected cut-off frequency (f_c) of the HPF is given as

 

                                                                                  

Circuit Diagram

High-Pass Filter

High Pass Filter

PROCEDURE

1.  Set up the circuit as shown taking the output across the capacitor (For HPF set the circuit as shown and take the output across resistor). The input for the filter is taken from output of function generator.  The output is connected to channel 2  of the DSO.

2.  Vary the frequency of the input signal over a wide frequency range (but keep the input amplitude fixed). Note the Values of V_out  for each frequency and calculate the corresponding Gain.

3.  Plot the values of Gain vs Frequency in a semi-log graph paper and find out the cut-off frequency from it (higher cut-off for LPF and lower cut-off for HPF).

Bandwidth cut off frequency measurement (LPF and HPF)

Vin=10Volt(pk-pk)	Frequency(fin)	Vout	Gain in dB
	50Hz
	100Hz
	500Hz
	1Khz
	2khz
	3KHz
	4Khz
	5KHz
	6KHz
	7KHz
	8KHz
	9KHz
	10KHz

Calculated  fc= 1/2πRC		Measured fc
Lowpass	Highpass	Lowpass	Highpass