Topics Covered in Chapter 27 Examples of Filtering Direct Current Combined with Alternating Current Transformer Coupling Capacitive Coupling Bypass Capacitors Filter Circuits
Topics Covered in Chapter 27 (continued) Low-Pass Filters High-Pass Filters Analyzing Filter Circuits Decibels and Frequency Response Curves Resonant Filters Interference Filters
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.
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.
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.
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).
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
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°.
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
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
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 )
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
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.
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
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
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
v OUT in dB 0 -20 -40 -80 -60 Frequency in kHz 0.1 110 RC Bandstop (notch) Filter HP LP