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Anglicky v odborných předmětech "Support of teaching technical subjects in English “

Anglicky v odborných předmětech "Support of teaching technical subjects in English “. Tutorial : Mechanic – electrician Topic : Electronics II. class RC Filters : RC High Pass Filter Prepared by: Ing. Jaroslav Bernkopf.

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Anglicky v odborných předmětech "Support of teaching technical subjects in English “

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  1. Anglicky v odborných předmětech"Support ofteachingtechnicalsubjects in English“ Tutorial: Mechanic– electrician Topic: Electronics II. class RC Filters: RC HighPassFilter 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 high-pass filter is a circuit that passes high-frequency signals but attenuates signals with frequencies lowerthan the cutoff frequency. -3 dB Slope: 20 dB/decade (6 dB/octave) Cutofffrequency Stopband Passband f RC Filters

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

  4. Description Let‘sconstructthegain-frequencycharacteristicofthe RC high-pass filter. Let‘s apply a voltage Vinof a very lowfrequency to the input of the circuit. If the frequency becomeslower and lower, the input voltagewillbecome a DC voltage. No DC currentcanpassthroughthecapacitorbecausethereisaninsulatorbetweenitselectrodes. No DC signalcanpassfromthe input ofthiscircuit to its output. 1 Av 0 f RC Filters

  5. Description At zerofrequencytheoutput voltageVoutwillbezero: = The voltage gain Av is 1 Av 0 f = 0 f Av = 0 RC Filters

  6. Description We have the firstpoint of the gain-frequency characteristic: At zerofrequency the voltage gain Av is equal to zero. 1 Av 0 f = 0 f Av = 0 RC Filters

  7. Description Let‘s apply a voltage Vin of a very high frequency and ofanamplitudeof 10V 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 the input pin, there mustbe thesamesignal on it. 1 Av 0 f RC Filters

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

  9. Description Between these two points there is a point where the gain stopsrisingand starts to be unity. We call this point the cutoff frequency. 1 Gainis unity Av = 0,707 Av Gainis rising 0 f fc RC Filters

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

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

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

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

  14. Solution Thecut-offfrequencyofthecircuitis 1 592 Hz. A signalofthelowestfrequency – a DC signal – can‘tpassthroughthecapacitorbecausethereisaninsulatorbetweenitselectrodes. A signalof a highfrequencypasseswithoutattenuationbecausethecapacitorrepresents a shortcircuit. Thecircuitis a high-passfilter. 10k 10n RC Filters

  15. 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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