Filters 2


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this is an introduction to the operation of various kinds of filters

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Filters 2

  1. 1. Fundamentals of Electronic Communications The basic principles of filters and radio frequency (r.f.) oscillators
  2. 2. Block diagrams of filters-Band pass
  3. 3. Block diagrams of filters - bandstop <ul><li>The circuit is made up of a high pass filter , a low-pass filter and a summing amplifier . The summing amplifier will have an output that is equal to the sum of the filter output voltages </li></ul>
  4. 4. Bell or Peak/Dip EQ Curve Controls <ul><li>Gain : Boost/Cut (Decibels) </li></ul><ul><li>Center Frequency: (Hertz): selectable: incremental steps </li></ul><ul><li>sweepable: continuous control </li></ul><ul><li>3. Bandwidth: (Octaves) or Q (No Units) </li></ul>
  5. 5. Bandwidth and Q <ul><li>Measurement across points -3 dB from center frequency. </li></ul>Source: Modern Recording Techniques, Huber
  6. 6. Bandwidth and Q <ul><li>Q is another way we can express bandwidth. </li></ul><ul><li>Q=Center Frequency (Hz) / Bandwidth (Hz) </li></ul><ul><li>Inverse relationship. BW increases, Q decreases. </li></ul><ul><li>1 octave bandwidth = 1.41 Q </li></ul><ul><li>2 octave bandwidth = .67 Q </li></ul>
  7. 7. Filter EQ Curves <ul><li>High Pass Filter (HPF): Cuts Lows </li></ul><ul><ul><li>AKA Low Frequency Roll off </li></ul></ul><ul><li>Low Pass Filter (HPF): Cuts Highs </li></ul><ul><li>Band Pass Filter (BPF): Combination of HPF and LPF, Cuts Highs and Lows. </li></ul>
  8. 8. Low Pass Filter <ul><li>Cuts High Frequencies </li></ul><ul><li>Cutoff Freq. </li></ul><ul><li>-3 dB from centerline </li></ul><ul><li>Slope:Rate of Cutoff </li></ul>Source:
  9. 9. HPF has a turnover frequency (at -3 dB) of 700 Hz. Slope = 6 dB / octave LPF has a turnover frequency of 700 Hz. Slope = 12 dB / octave Source: Modern Recording Techniques, Huber & Runstein
  10. 10. Filter Controls <ul><li>HPF & LPF : Frequency Control </li></ul><ul><ul><li>filters only cut, no gain control </li></ul></ul><ul><ul><li>Slope: usually a preset rate. </li></ul></ul><ul><ul><li>Common Slope Rates: 6 dB/octave, </li></ul></ul><ul><ul><li>9 dB / octave, 12 dB / octave, 18 dB / octave </li></ul></ul><ul><li>BPF: Bandwidth control and Center Frequency control, no gain control </li></ul>
  11. 11. EQ Bands <ul><li>Band = A range of frequencies to be affected </li></ul><ul><li>Band = A set of controls </li></ul><ul><li>How many bands? Count the gain controls. </li></ul><ul><ul><li>Note: HPF, LPF, and BPF usually not classified as bands on analog EQ devices. </li></ul></ul><ul><ul><li>A single curve (either peak/ dip or shelving ) is a single band. </li></ul></ul>
  12. 12. What is a Crossover? <ul><li>They are generally described according to the number of frequency bands available (two-way, three-way and four-way). </li></ul>
  13. 13. How it works <ul><li>It uses bandwidth limiting filters to separate the input signal into multiple outputs, each of which has a steep cut-off below and/or above its range (24dB/octave is typical). In some, the cut-off slope (and in some of those, even the type of filter: Bessel/Butterworth/Linkwitz-Riley, etc.) is user-determined. </li></ul>
  14. 14. 3 types of crossover filters <ul><li>High-pass </li></ul><ul><li>Low-pass </li></ul><ul><li>Band-pass </li></ul>
  15. 16. <ul><li>A high-pass filter will block low frequencies </li></ul><ul><li>A low-pass will block high frequencies </li></ul><ul><li>A band-pass will block low and high frequencies below and above crossover points. </li></ul>
  16. 18. Slope <ul><li>Slope is expressed as decibels per octave. </li></ul><ul><li>The rate of attenuation for every octave away from the crossover frequency </li></ul><ul><li>Crossovers do not block undesired frequencies completely (unless you are using digital crossovers) </li></ul><ul><li>Crossovers cut frequencies progressively </li></ul><ul><li>A crossover &quot;slope&quot; describes how effective a crossover is in blocking frequencies </li></ul>
  17. 19. Slope <ul><li>A 6dB per octave crossover reduces signal level by 6dB in every octave starting at the crossover point. </li></ul>
  18. 20. <ul><li>1st order filters have a 6 dB/octave slope </li></ul><ul><li>2nd order filters have a 12 dB/octave slope </li></ul><ul><li>3rd order filters have an 18 dB/octave slope </li></ul><ul><li>4 th order filters have a 24 dB/octave slope </li></ul><ul><li>5 th order filters have a 48 dB/octave slope </li></ul>
  19. 21. - 6db - 12db - 18db - 24db - 48db 500hz 250 K hz 125hz 1Khz 63hz
  20. 22. Crossover Point <ul><li>The nominal dividing line between frequencies sent to two different speaker drivers. </li></ul><ul><li>In a crossover network, the frequency at which the audio signal is directed to the appropriate driver (low frequencies to the woofer, high frequencies to the tweeter). </li></ul><ul><li>The single frequency at which both filters of a crossover network are down 3dB. </li></ul><ul><li>The frequency at which an audio signal is divided. </li></ul>
  21. 24. Cutoff Frequency <ul><li>The &quot;corner point&quot; of a filter, usually the point where the response is down -3dB compared to the midband signal level. </li></ul><ul><li>The signal frequency output of a filter that marks the transition from no attenuation to attenuation. Usually it is defined as the point at which the amplitude of the signal is reduced by 3 dB after passing through the filter. </li></ul>
  22. 25. Decibel (dB) (1) Power Gain in dB : (2) Voltage Gain in dB : (P=V 2 /R) By Definition:
  23. 27. <ul><li>The resonance effect occurs when inductive and capacitive reactances are equal in absolute value. The frequency at which this equality holds for the particular circuit is called the resonant frequency. The resonant frequency of the LC circuit is </li></ul>where L is the inductance in henries , and C is the capacitance in farads
  24. 28. Parallel LC Resonant Circuit <ul><li>Overall response ( V out / V in vs. frequency ) : </li></ul><ul><ul><li>This circuit is sometimes called a tank circuit </li></ul></ul><ul><ul><li>Most often used to select one desired frequency from a signal containing many different frequencies </li></ul></ul><ul><ul><ul><li>Used in radio tuning circuits </li></ul></ul></ul><ul><ul><ul><li>Tuning knob is usually a variable capacitor in a parallel LC circuit </li></ul></ul></ul>Q = quality factor = f 0 /  f 3dB = resonance frequency / width at –3 dB points (Remember that at –3 dB point, V out / V in = 0.7 and output power is reduced by ½ ) Q is a measure of the sharpness of the peak For a parallel RLC circuit:
  25. 29. Oscillation in Parallel LC Resonant Circuit <ul><li>For a pure LC circuit (no resistance), the current and voltage are exactly sinusoidal, constant in amplitude, and have angular frequency </li></ul><ul><ul><li>Can prove with Kirchhoff’s loop rule </li></ul></ul><ul><ul><li>Analogous to mass oscillating on a spring with no friction </li></ul></ul><ul><li>For an RLC circuit (parallel or series), the current and voltage will oscillate (“ring”) with an exponentially decreasing amplitude </li></ul><ul><ul><li>Due to resistance in circuit </li></ul></ul><ul><ul><li>Analogous to damped oscillations of a mass on a spring </li></ul></ul>
  26. 30. The impedance of this circuit is : Z has a maximum when The resonance frequency of the parallel LC circuit I has a maximum when
  27. 31. Oscillators <ul><li>Oscillation: an effect that repeatedly and regularly fluctuates about the mean value </li></ul><ul><li>Oscillator: circuit that produces oscillation </li></ul><ul><li>Characteristics: wave-shape, frequency, amplitude, distortion, stability </li></ul>
  28. 32. Application of Oscillators <ul><li>Oscillators are used to generate signals, e.g. </li></ul><ul><ul><li>Used as a local oscillator to transform the RF signals to IF signals in a receiver; </li></ul></ul><ul><ul><li>Used to generate RF carrier in a transmitter </li></ul></ul><ul><ul><li>Used to generate clocks in digital systems; </li></ul></ul><ul><ul><li>Used as sweep circuits in TV sets and CRO. </li></ul></ul>
  29. 33. Radio-Frequency Amplifiers <ul><li>RF amplifiers differ from audio amplifiers in that wide bandwidth may or may not be required </li></ul><ul><li>Linearity of the output may or may not be required </li></ul><ul><li>Efficiency can be improved through the use of Class C amplifiers </li></ul>
  30. 34. Narrowband Amplifiers <ul><li>Many RF amplifiers are required to operate only within a narrow range of frequencies </li></ul><ul><li>Filters are used to reduce the bandwidth </li></ul><ul><li>The tuned amplifier is set according to the formula: </li></ul>
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