Experiment 6: RC, LC-R Low-pass Filters PDF

ELP101 Laboratory Semester-I: 2024-25 (24/07/2024 ~ 14/11/2024) Experiment No: 6 RC, LC-R Low-pass Fi...

ELP101 Laboratory Semester-I: 2024-25 (24/07/2024 ~ 14/11/2024) Experiment No: 6 RC, LC-R Low-pass Filters Aim: (1) To observe and analyse the given “Low-pass filter” performance. (2) To compute the RC low-pass filter cut-off frequency and measure the output voltage (across capacitor) magnitude at various frequencies (on either sides of cut-off frequency). (3) To compute the LC-R low-pass filter cut-off frequency and measure the output voltage (across capacitor) magnitude at various frequencies (on either sides of cut-off frequency). Apparatus: S. No Components/Instruments/ Meters 1 (a) Breadboard, Connecting wires, Passive R, L, C components, (b) Voltmeters, Ammeters, Digital Multi-meter, (c) Digital Storage Oscilloscope, (d) DC power supply Brief Description: A low-pass filter (LPF) is a passive circuit that passes signals on to the output side having frequency lower than a cut-off frequency (fc) and attenuates the signals with frequencies higher than “fc”. The magnitude of various frequency components on the output side depends on the filter components (L, C and R) selection. Typical application of LPF is to reduce high-frequency noise on the output side so that the output signal contains only low frequency components (less than “fc”). A simple low pass circuit shown in Fig. 1 consists of a resistor (R) in series with the capacitance (C). The capacitor exhibits high reactance at low frequencies, and also blocks low- frequency signals. At higher frequencies the reactance drops, and the output signal across the capacitor reduces. At very high frequencies its impedance is close to zero or short circuit. Test-1: RC Low-pass Filter Circuit (Refer Fig. 2) Table-1. Parameters (Referring to Fig. 2) R L C 1.0 kΩ ~ 5.0 kΩ 2.0 H 100 nF ~ 220 nF Signal generator settings Vp-p = 10 Volts (Square wave, Duty ratio: 50%); Frequency (fs) = 10 Hz, 100 Hz, 500 Hz, 1000 Hz, 5000 Hz, 50 kHz 1 M.Veerachary ELP101 Laboratory Semester-I: 2024-25 (24/07/2024 ~ 14/11/2024) VP Vavg 0 TS t fS= 1/TS (a) Square wave Vavg DC 0 t 0 t VP fS 0 TS t 0 t fS= 1/TS 3fS 0 t 5fS (b) Fourier Series representation Fig. 1. Square wave signal. The “Fourier series” of square wave signal is: 2 M.Veerachary  ELP101 Laboratory Semester-I: 2024-25 (24/07/2024 ~ 14/11/2024)  Vin (t )  Vavg   an cos( n0t ) (1) n 1 where the average value of the waveform (frequency = 0 Hz) is Vavg  (Duty ratio)  V p (2) and for (n=1, 3, 5, 7, 11, 13,...); the peak value of various harmonic components is: 2V pp  n  an  sin   (3) n  2  The RMS value of “nth” harmonic components is: a  An   n  (4)  2 3 M.Veerachary  ELP101 Laboratory Semester-I: 2024-25 (24/07/2024 ~ 14/11/2024) Low Pass vin(s) Filter v0(s) VP (LPF) V0 0 0 T t t (a) Low-pass filter circuit block diagram. R To vin(s) C v0(s) VP DSO 0 T Function Generator (b) R-C low-pass filter circuit Fig. 2. R-C circuit. The transfer function of R-C circuit (Fig. 2) is  1  v0 ( s )   1   sC   (5) vin ( s )  1  1  sCR   R  sC  The cut-off frequency of R-C circuit is 1 fc   2πRC  (6) 4 M.Veerachary  ELP101 Laboratory Semester-I: 2024-25 (24/07/2024 ~ 14/11/2024) Test-2: LC-R Low-pass Filter Circuit (Refer Fig. 3) L To vin(s) C v0(s) VP R DSO 0 T Function Generator Fig. 3. LC-R circuit. The transfer function of LC-R circuit (Fig. 3) is v0 ( s )  R    (7) vin ( s)  ( LCR) s 2  (rRC  L ) s  ( R  r )  If inductance series resistance is very small (i.e. r “MATH” -> Ch-1: Displays “Violet colour” trace) 6. Observe the harmonic components (various frequency components; Use DSO -> Cursor -> settings -> “MATH” (Tracking)) and tabulate in Table-2 (or) Table-3. 7. Using mathematical formulations (Eqns. 1 to 4) compute the “Square wave” input signal Harmonic components and verify with observations given in Table-2. 8. Use different combinations for R and C values and make a tabular column of observations. Discuss the reasons for the deviation in the computed and measured values of Harmonic components. Important Note: Here, the capacitor (voltage across-C) gives low-pass filter action while the resistance voltage (voltage across-R) will be of high-pass filtering action. It is not possible to measure the voltage drop across the resistor and capacitor simultaneously as the Oscilloscope (DSO) has common ground amongst all channels. So for observing output waveforms across the two elements, one should use an indirect method of measuring two signals w.r.t ground and then use MATH function of DSO. Precautions: 1. The square waveform from the function generator may be measured using DSO and adjusted to proper values before applying to the circuit. The “Time/div” scale of DSO should be adjusted such that 2 ~ 4 cycles of the input signal are displayed on the “DSO- screen”. 2. Once proper square wave is synchronized on the DSO screen and the time scale is adjusted, the trigger setting should not be changed. 6 M.Veerachary ELP101 Laboratory Semester-I: 2024-25 (24/07/2024 ~ 14/11/2024) 3. Do not connect two probes of “DSO” to measure voltage drop across the “R” and “C” simultaneously, instead use MATH function (with Channel-1-Channel-2) as per the equations given for the circuit. Table-2: Observations for Low-pass filter performance with Square wave signal Frequency Input supply Voltage across Attenuation factor Input f (Hz) voltage Capacitor (Vc/Vin) supply ( Vin ) ( Vc ) voltage (Square wave signal) (Volts) (fs) 10 0 10 3fs 10 5fs 10 7fs 10 11fs 10 13fs 5 0 5 3fs 5 5fs 5 7fs 5 11fs 5 13fs 7 M.Veerachary ELP101 Laboratory Semester-I: 2024-25 (24/07/2024 ~ 14/11/2024) Table-3: Observations for Low-pass filter performance with Sine wave signal Frequency Input supply Voltage across Attenuation factor Input f (Hz) voltage Capacitor (Vc/Vin) supply ( Vin ) ( Vc ) voltage (Sine wave signal peak value) (Volts) 10 0 10 3fs 10 5fs 10 7fs 10 11fs 10 13fs 5 0 5 3fs 5 5fs 5 7fs 5 11fs 5 13fs (Important Note: Vin( RMS )  Vin( p)   2 ;Vc( RMS )  Vc( p ) 2  8 M.Veerachary  ELP101 Laboratory Semester-I: 2024-25 (24/07/2024 ~ 14/11/2024) Sample calculations and plots: Using Eqns. 1 to 10 compute theoretical values and compare with experimental observations. References: Edward Hughes, “Electrical and Electronic Technology”, 10 th Edition, Pearson/ Prentice Hall. Smith and Dorf, “Circuits, Devices and Systems”, 5 th Edition, Wiley Publishers. Format for report submission: 1) Aim of the Experiment 2) Apparatus used in the Experimental setup 3) Circuit diagram along with proper labelling 4) Theoretical formulations 5) Measurements/Tabular columns 6) Sample calculations and verifications 7) Conclusions (Important Note for Report submission: Use A4-size plain white sheets for “Report” preparation) 9 M.Veerachary