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Tutorial on RC Low-Pass Filter in Electronics II

Learn about RC low-pass filters: layout, function, gain, cutoff frequency, passband, stopband, and calculation examples.

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Tutorial on RC Low-Pass Filter in Electronics II

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  1. Anglicky v odborných předmětech"Support ofteachingtechnicalsubjects in English“ Tutorial: Mechanic – electrician Topic: Elektronics II. class RC Filters: RC LowPassFilter Prepared by: Ing. Jaroslav Bernkopf Projekt Anglicky v odborných předmětech, CZ.1.07/1.3.09/04.0002 je spolufinancován Evropským sociálním fondem a státním rozpočtem České republiky.

  2. Definition A low-pass filter is a circuit that passes low-frequency signals but attenuates signals with frequencies higher than the cutoff frequency. -3 dB Slope: -20 dB/decade (-6 dB/octave) Cutofffrequency Passband Stopband f RC Filters

  3. Description The simplest low-pass filter consists of one resistor and one capacitor. We call it the RC low-pass filter. -3 dB A Slope: -20 dB/decade (-6 dB/octave) Cutofffrequency Passband Stopband f RC Filters

  4. Description Let‘sconstructthegain-frequencycharacteristicofthe RC low-pass filter. Let‘s apply a voltage Vinof a very lowfrequency and ofanamplitudeof 10V to the input of the circuit in the figure. If we let the frequency become lower and lower, the input voltagewillbecome a DC voltage. This input voltage Vinof 10V willchargethecapacitor and in a moment the output voltageVoutwillreach 10V and willbethesame as the input voltage Vin. 1 Av 0 f RC Filters

  5. Description The output voltage Vout = 10 V is the same as the input voltage Vin = 10 V. Therefore = The voltage gain Av is We have the first point of the gain-frequency characteristic: At zero frequency the voltage gain Av is equal to unity. 1 Av A = 1 0 f f = 0 RC Filters

  6. Description Let‘s apply a voltage Vin of a very high frequency to the input of the circuit. At a very high frequency the capacitor represents a short circuit – similar to a wire link. If the output pin is shorted with ground, there can‘t be any signal on it. Therefore = The voltage gain Av is 1 Av A = 0 0 f f = ∞ RC Filters

  7. Description We have the second point of the gain-frequency characteristic: At infinite frequency the voltage gain Av is equal to zero. 1 Av Av = 0 0 f f = ∞ RC Filters

  8. Description Between these two points there is a point where the unity gain ends and the gain is starting to fall. We call this point the cutoff frequency. 1 Unitygain ends Av = 0,707 Av Gainis starting to fall 0 f fc RC Filters

  9. Description In thepassbandallsignalpassesfromthe input to the output. ThevoltagegainAvisequal to unity. -3 dB A Slope: -20 dB/decade (-6 dB/octave) Cutofffrequency Passband Stopband f RC Filters

  10. Description In thestopbandthehigherthefrequency, thelowerthevoltagegainAv. ThegainAvfalls off at 20dB per decade (or 6dB per octave, whichtellsthesame). When the frequency increases by a factor of 10, the gain decreasesby a factor of 10 (i.e. 20 dB). When the frequency increases by a factor of 2, the gain decreases by a factor of 2 (i.e. 6 dB). -3 dB A Slope: -20 dB/decade (-6 dB/octave) Cutofffrequency Passband Stopband f RC Filters

  11. Description At thecutofffrequencyfcthevoltagegainAvfalls to . In otherwordsthegainisreduced by 3 dB. Hereis the formula for the cut-off frequency: -3 dB A Slope: -20 dB/decade (-6 dB/octave) Cutofffrequency Passband Stopband f RC Filters

  12. Task Calculate the cut-off frequency for the circuit below and state if it is high pass or low pass. 10k 10n RC Filters

  13. Solution Thecut-offfrequencyofthecircuitis 1 592 Hz. A signalofthelowestfrequency – a DC signal – passesthroughtheresistorwithoutbeingreduced by thecapacitor. Thecircuitis a low-passfilter. 10k 10n RC Filters

  14. References • http://www.wikipedia.com • http://www.thefreedictionary.com • http://www.animations.physics.unsw.edu.au/jw/calculus.htm • http://openlearn.open.ac.uk/ RC Filters

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