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Basic Electronics Ninth Edition Basic Electronics Ninth Edition ©2002 The McGraw-Hill Companies Grob Schultz

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Basic Electronics Ninth Edition Basic Electronics Ninth Edition ©2003 The McGraw-Hill Companies 27 CHAPTER Filters

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Topics Covered in Chapter 27 Examples of Filtering Direct Current Combined with Alternating Current Transformer Coupling Capacitive Coupling Bypass Capacitors Filter Circuits

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Topics Covered in Chapter 27 (continued) Low-Pass Filters High-Pass Filters Analyzing Filter Circuits Decibels and Frequency Response Curves Resonant Filters Interference Filters

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Low-Pass Filters Low-pass filters pass dc and the lower frequencies, but block higher frequencies. For a practical low-pass filter: The resistor or inductor is in series with the load. The associated capacitor is shunted across the line.

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High-Pass Filters High-pass filters block dc and lower frequencies and pass higher frequencies. For a practical high-pass filter: The capacitor is in series with the load. The associated resistor or inductor is shunted across the line.

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Pulsating DC Pulsating direct current or voltage consists of: An average dc value An ac component that goes above and below the average dc value. Filters can be used to separate the dc and ac components.

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RC Bypass and RC Coupling Circuits An RC bypass circuit is effectively a low-pass filter (often used to reject noise). RC bypass circuits pass dc (0 Hz). An RC coupling circuit is effectively a high-pass filter. RC coupling blocks dc (0 Hz).

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Volts 0 -2 +7 +5 +2 Time in ms 0312 +3 1 k 10 F 4 V P-P 1 kHz 5 V B B A A RC coupling blocks the DC component. AC+DC AC 0 V 5 V

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Cutoff Frequency At the cutoff frequency (f c ): The output voltage is reduced to 70.7% of maximum output voltage. X L or X C is equal to R. f c = 1/(2 RC) for RC filters. f c = R/(2 L) for RL filters. The phase angle is 45°.

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10 7 4 1 0.20.40.60.810 1 k 1 F 10 V v OUT v OUT in Volts Frequency Response of an RC Low-Pass Filter Frequency in kHz 0 -90 -30 -60 Phase angle in degrees f

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1 0.20.40.60.810 Frequency in kHz 10 7 4 1 v OUT in Volts 0 90 60 30 Phase angle in degrees Frequency Response of an RC High-Pass Filter 1 k 1 F 10 V v OUT f

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Log-Log Graph (4 cycle by 2 cycle) 1101001 k10 k 0.1 1 10 1 decade 1 octave 30 500 2

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The dB Unit of Measurement The decibel (dB) unit of measure is often used to compare output to input. The formula for the dB power ratio is: N dB = 10 log(P out /P in ) The formula for the dB voltage ratio is: N dB = 20 log(V out /V in )

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The Half-Power Point The cutoff frequency of a filter is where the output power drops to half of maximum output (-3 dB). f c = 10 log(P out /P in ) = 10 log(0.5) = -3 dB Power varies as the square of the voltage. P = V 2 /R Doubling the logarithm of a quantity is the same as squaring the quantity. f c = 20 log(V out /V in ) = 20 log (0.707) = -3 dB

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Bandpass/Bandstop Filters Low-pass and high-pass filters can be combined to pass or block a certain band of frequencies. A bandpass filter passes only a selected band of frequencies. A bandstop filter passes all frequencies except those in a selected band.

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1 k 0.47 F f 10 k 4.7 nF v OUT 100 k 0.47 nF v OUT in dB Frequency in Hz 101001 k10 k 0 -20 -10 RC Bandpass Filter (1.3 dB passband loss) BW = 2.2 kHz 3 dB cutoff

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12345678910 Frequency in MHz 5 0 3 4 2 1 Current in A 4 20 V 1 nF 1 H MHz xxx LC f r 03.5 101 12 1 2 1 96 Resonant filters work well at radio frequencies. f

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500 k f 30 k 10 nF v OUT 30 k RC Bandstop (notch) Filter 15 k 5 nF 11 4 1 CR f N R1R1 C1C1 C1C1 2C 1 2R 1 kHz nk xk xx f N 06.1 5156.12 1

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v OUT in dB 0 -20 -40 -80 -60 Frequency in kHz 0.1 110 RC Bandstop (notch) Filter HP LP

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