Electronics Technology Fundamentals Chapter 15 Frequency Response and Passive Filters

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Frequency Response: Curves and Measurements – P1 Attenuation – the signal loss that may be caused by the frequency response of a circuit

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Frequency Response: Curves and Measurements – P2 Attenuation (Continued)

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Frequency Response: Curves and Measurements – P3 Frequency Response Curves Sometimes described in terms how circuit gain (the ratio of V out to V in ) is affected by a change in frequency When V out /V in = 1, the ratio is at its maximum

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Frequency Response: Curves and Measurements – P4 Cutoff Frequency (f C ) – the frequency at which the power gain of a circuit drops to 50%

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Frequency Response: Curves and Measurements – P5 Filters

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Frequency Response: Curves and Measurements – P6 Bandwidth and Center Frequency – the range, or band, of frequencies between the cutoff frequencies of a component or circuit where BW = the bandwidth of the component or circuit, in Hz f C2 = the upper cutoff frequency f C1 = the lower cutoff frequency

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Frequency Response: Curves and Measurements – P7 Center Frequency (f 0 ) – is the frequency that equals the geometric average of the cutoff frequencies Frequency Calculations

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Frequency Response: Curves and Measurements – P8 Filter Quality (Q) – indicates how closely the characteristics of a bandpass or notch filter come to those of an ideal circuit

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Frequency Response: Curves and Measurements – P9 Average Frequency (f ave ) – is the frequency that lies halfway between the cutoff frequencies If f 0 and Q are known:

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Frequency Response: Curves and Measurements – P10 Frequency Approximations – When a bandpass or notch filter has a value of Q  2, the center and average frequencies can be assumed to be approximately equal in value

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Frequency Response: Curves and Measurements – P11 Frequency Scales Logarithmic Scale – the value of each increment is a whole-number multiple of the previous increment Decade – frequency multiplier of ten Octave – frequency multiplier of two Used because: Algebraic scale can be extremely long Center frequency falls in the physical center of the curve

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Frequency Response: Curves and Measurements – P12 Frequency Scales (Continued)

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Frequency Response: Curves and Measurements – P13 Critical Frequencies: Putting It All Together Filter TypeCharacteristics High-passPasses all frequencies above its cutoff frequency (f C ) Low-passPasses all frequencies below its cutoff frequency (f C ) Band-passPasses all frequencies that lie between its lower cutoff frequency (f C1 ) and its upper cutoff frequency (f C2 ). Normally described in terms of its geometric center frequency (f o ) and its bandwidth (BW).* Band-stopAlso called a notch filter. Rejects (attenuates) all frequencies that lie between its lower cutoff frequency (f C1 ) and its upper cutoff frequency (f C2 ). Normally described in terms of its geometric center frequency (f o ) and its bandwidth (BW).* *For a band-pass or notch filter, and BW = f C2 – f C1

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Amplitude Measurements: dB Power Gain – P1 Decibels (dB) A logarithmic representation of a number Allows very large and very small values to be easily represented where A p = the power gain, P out /P in

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Amplitude Measurements: dB Power Gain – P2 Converting dB Power Gain to Standard Numeric Form where log -1 = the inverse log function

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Amplitude Measurements: dB Power Gain – P3 Multistage Filter Gain Cascaded Filters – filters connected in series Stage – each filter in the cascade Overall dB gain:

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Amplitude Measurements: dB Power Gain – P4 The dBm Reference – represents a power level (rather than power gain) that is referenced to 1 mW

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Amplitude Measurements: dB Voltage and Current Gain – P1 Voltage Gain (A v ) Ratio of circuit output voltage to input voltage Voltage gain is 70.7% of its maximum value at the cutoff frequencies

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Amplitude Measurements: dB Voltage and Current Gain – P2 dB Voltage Gain where A v = the ratio of output voltage to input voltage

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Amplitude Measurements: dB Voltage and Current Gain – P3 Converting dB Voltage Gain to Standard Numeric Form

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Amplitude Measurements: dB Voltage and Current Gain – P4 Changes in dB Gain – even though dB values of voltage and power are calculated differently, they change at the same rate where  A p(dB) = the change in dB power gain  A v(dB) = the change in dB voltage gain

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Amplitude Measurements: dB Voltage and Current Gain – P5 Current Gain (A i ) – the ratio of circuit output current to input current

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved RC and RL Low-Pass Filters – P1 RC Low-Pass Filters Capacitor acts as an open circuit when f in = 0 Hz Capacitor acts as a short circuit when f in approaches infinity Shunt Component – signal path to ground connection

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved RC and RL Low-Pass Filters – P2 RC Low-Pass Filters (Continued)

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved RC and RL Low-Pass Filters – P3 Cutoff Frequency (f C ) where R = the total circuit resistance as seen by the capacitor C = the value of the filter capacitor

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved RC and RL Low-Pass Filters – P4 Upper Cutoff Frequency (f C ) (Continued)

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved RC and RL Low-Pass Filters – P5 Bode Plots – a normalized graph that represents frequency response as a change in gain (  A v ) versus operating frequency

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved RC and RL Low-Pass Filters – P6 Filter Roll-Off Rate – the constant drop in gain of a low-pass filter at frequencies above the circuit’s cutoff frequency

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved RC and RL Low-Pass Filters – P7 RL Low-Pass Filters – the inductor is the series component and the resistor is the shunt component

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved RC and RL Low-Pass Filters – P8 Maximum Voltage Gain (A v(max) )

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved RC and RL Low-Pass Filters – P9 Cutoff Frequency (f C )

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved RC and RL High-Pass Filters – P1 RC High-Pass Filters

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved RC and RL High-Pass Filters – P2 Maximum Voltage Gain (A v(max) ) Lower Cutoff Frequency (f C )

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved RC and RL High-Pass Filters – P3 High-Pass Filter Bode Plots and Roll-Off Rates – as is the case with RC low-pass filters, RC high-pass filters all have roll-off rates of 6 dB per octave (20 dB per decade)

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved RC and RL High-Pass Filters – P4 RL High-Pass Filters

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved RC and RL High-Pass Filters – P5 Circuit Operation

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved RC and RL High-Pass Filters – P6 Maximum Voltage Gain (A v(max) ) Lower Cutoff Frequency (f C )

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Bandpass and Notch Filters – P1 Series LC Bandpass Filters

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Bandpass and Notch Filters – P2

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Bandpass and Notch Filters – P3 Series LC Bandpass Filters (Continued) Insert Figure 15.32

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Bandpass and Notch Filters – P4 Shunt LC Bandpass Filters

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Bandpass and Notch Filters – P5 Filter Quality (Q) – since the quality of a circuit can be no higher than its lowest-quality component, the unloaded Q of an LC filter is normally assumed to equal the Q of the inductor

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Bandpass and Notch Filters – P6 Series Filter Frequency Analysis where f r = the resonant frequency of the resonant filter Q L = the loaded Q of the filter

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Bandpass and Notch Filters – P7 Series Filter Frequency Analysis Loaded Q – the quality of the circuit when a load in connected to its output terminals

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Bandpass and Notch Filters – P8 Series Filter Frequency Analysis (Continued) When Q L  2, f ave  f r where f ave = the frequency that lies half-way between the cutoff frequencies

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Bandpass and Notch Filters – P9 Series Filter Frequency Analysis (Continued) When Q L < 2

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Bandpass and Notch Filters – P10 Shunt Filter Frequency Analysis where Q = the unloaded Q of the filter

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Bandpass and Notch Filters – P11 Maximum Voltage Gain Divide both sides by V in : where

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Bandpass and Notch Filters – P12 The Effects of Q on Filter Gain and Roll-Off Insert Figure 15.38

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Bandpass and Notch Filters – P13 Series LC Notch Filters

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Bandpass and Notch Filters – P14 Shunt LC Notch Filters – identical frequency response as the Series LC Notch Filter