1.CHAPTER 5FILTERS

2. PASSIVE FITERS ACTIVE FITERS 3. PASSIVE FILTER Introduction Made up of Passive components such as resistors,capacitors and inductors. No amplifying elements and no signal gain. Not restricted by the bandwidth limitation and canbe used at very high frequencies. Can handle larger current or voltage levels thanactive devices. Buffer amplifier might be required. 4. PASSIVE SINGLE POLE LOWPASSFILTER Its passes low frequencies but rejects high frequencies. 5. This "Cut-off", "Corner" or "Breakpoint" frequencyis defined as being the frequency point where thecapacitive reactance and resistance are equal.R = XC (for the RC filter), or R = XL (for the RLfilter). When this occurs the output signal is attenuatedto 70.7% of the input signal value or -3dB (20 log(Vout/Vin)) of the input. Although R = Xc, This isbecause the output voltage is attenuated by afactor of 0.707 of the input. Vout/Vin = 1/2 =0.707. When the frequency of the input signal increases,the capacitors reactance decreases and thecapacitor draws more current, which in turn 6. As the filter contains a capacitor and produces adelay. This is due to the time taken to charge theplates of the capacitor as the input voltagechanges, resulting in the output voltage (thevoltage across the capacitor) "lagging" behindthat of the input signal. The Phase Angle () of the output signal LAGSbehind that of the input. At the cutoff frequency, the output voltage lags by-45 . The higher the input frequency applied to the filterthe more the capacitor lags and the circuitbecomes more and more "out of phase". 7. As the frequency increases, XL also increases,thus increasing the total impedance of the filter.Since R doesnt change, more and more of thesignal are dropped across L at higherfrequencies, leaving less and less across R andavailable at VOUT. The inductor produces a delay. At very lowfrequency, the output voltage follows the input. When frequency rises, the output start lagging theinput with 45 . 8. The magnitude of H: At cut-off frequency, the magnitude is 9. Phase of H The angular cutoff Frequency C = 2 fC and cut- off frequency is 10. The magnitude of H: 11. Phase of H Cut-off frequency 12. PASSIVE SINGLE POLE HIGH-PASS FILTER Its passes high frequencies but rejects low frequency. 13. When input voltage is very low in frequency, thecapacitors reactance is very high, and hardly anysignal is passed to the output. When the frequency rises. The capacitor reactancedecreases, and a little attenuation at the output. The signal is attenuated or damped at lowfrequencies with the output increasing at+20dB/Decade (6dB/Octave) until the frequencyreaches the cut-off point (c) where again R = Xc. Ithas a response curve that extends down from infinityto the cut-off frequency, where the output voltageamplitude is 1/2 = 70.7% of the input signal value or-3dB (20 log (Vout/Vin)) of the input value. 14. At very low frequency the output leads the inputin phase 90 . When the frequencies rises to the cut-offfrequency, the output lead by 45 . When the frequency goes toward infinity, thephase approaches 0, the point where capacitoracts like a short. 15. The magnitude of H: Phase of H Cut-off frequency 16. PASSIVE SINGLE POLE RL HIGH-PASS FILTER The transfer function becomes 17. The magnitude of H: Phase of H The cut-off frequency 18. When the input is very low in frequency, theinductors reactance is very low, so most of thecurrent is diverted to ground. The signal isattenuated at the output. When the frequencies rise, the inductorsreactance increases and less current is passed toground- the gain increases. At low frequency the output leads the input inphase by 90o. And the cut-off the output leads by45o. When the frequency goes to infinity, the phaseapproaches 0, the point where inductor acts likean open circuit. 19. PASSIVE RCL SERIES BANDPASS FILTERRLC circuit as a series band-pass filter in series with the line 20. RLC band-pass filter acts to pass a narrow range of frequencies (band) while attenuating or rejecting all other frequencies. 21. Resonant Frequency (Center frequency),fr is the frequency at XL=XC. 22. The point of maximum output gain is generally the geometric mean of the two -3dB value between the lower and upper cut-off points and is called the "Centre Frequency" or "Resonant Peak" value r. 23. At resonance for a series circuit causes the following: Total Reactive impedance XT is equal to zero. Z = R. Total current (IT) is maximum. Phase angle is 0o. 24. Quality factor (Q) is the ratio of reactance (XL orXC) to resistance R at resonant frequency. 25. Bandwidth (BW) is the ratio that used to determine the range of frequency a resonant circuit will be passed. The cut-off points are at about 70% of the maximum output voltage. These are called the low-frequency cutoff and high-frequency cut-off. BW 26. RLC circuit as a parallel band-pass filter in shunt across the line 27. PROPERTY SERIES RLC PARALLEL RLC Resonant Frequency Voltage Across R maximum at fRconstant = V0 Current Through Rconstant = V0/R minimum at fRQ BandwidthImpedance below Resonance Capacitive InductiveImpedance above ResonanceInductiveCapacitive Effect of changing Rincreasing R increases BWincreasing R decreases BWEffect of changing L/Cincreasing L/C decreases BW increasing L/C increases BW 28. ACTIVE FILTER No inductor Made up of Op-Amps, resistor and capacitors. Generally much easier to design. High input impedance prevent excessive loadingof the driving source. Low output impedance prevents the filter frombeing affected by the load. At high frequencies is limited by the gain-bandwidth of the Op-Amps. Easy to adjust over a wide frequency rangewithout altering the desire response. 29. ACTIVE SINGLE POLE LOW PASSFILTER Non-inverting unity gain, AV Cut-off frequency: Non-inverting with voltagegain,AV Inverting with voltage gain 30. ACTIVE SECOND ORDER POLELOW PASS FILTER In second order filter, the circuit voltage gain and cut-offfrequency are the same with first order filter except that thefilter response drops faster with 40dB/decade compareswith first order in 20dB/decade. 31. ACTIVE SINGLE POLE HIGH PASSFILTER Non-inverting unity gain, A V Non-Inverting with voltagegain Inverting with voltage gain 32. ACTIVE TWO POLE HIGH PASSFILTER 33. ACTIVE BAND PASS FILTER The center frequency, The quality factor,