CHAPTER 6 Frequency Response, Bode Plots, and Resonance 1. State the fundamental concepts of Fourier analysis. 2. Determine the output of a filter for a given input consisting of sinusoidal components using the filters transfer function. ELECTRICA L

ENGINEERING Principles and Chapter 6 Frequency Response, Bode Plots, and Resonance 3. Use circuit analysis to determine the transfer functions of simple circuits. 4. Draw first-order lowpass or highpass filter circuits and sketch their transfer functions. 5. Understand decibels, logarithmic

frequency scales, and Bode plots. ELECTRICA L ENGINEERING Principles and Chapter 6 Frequency Response, Bode Plots, and Resonance 6. Draw the Bode plots for transfer functions of first-order filters.

ELECTRICA L ENGINEERING Principles and Chapter 6 Frequency Response, Bode Plots, and Resonance ELECTRICA L ENGINEERING Principles and

Chapter 6 Frequency Response, Bode Plots, and Resonance Fourier Analysis All real-world signals are sums of sinusoidal components having various frequencies, amplitudes, and phases. ELECTRICA L ENGINEERING Principles and

Chapter 6 Frequency Response, Bode Plots, and Resonance ELECTRICA L ENGINEERING Principles and Chapter 6 Frequency Response, Bode Plots, and Resonance Filters

Filters process the sinusoid components of an input signal differently depending of the frequency of each component. Often, the goal of the filter is to retain the components in certain frequency ranges and to reject components in other ELECTRICA ranges. L ENGINEERING Principles and

Chapter 6 Frequency Response, Bode Plots, and Resonance ELECTRICA L ENGINEERING Principles and Chapter 6 Frequency Response, Bode Plots, and Resonance Transfer Functions

The transfer function H(f ) of the two-port filter is defined to be the ratio of the phasor output voltage to the phasor input voltage as a function of frequency: Vout H f Vin ELECTRICA L ENGINEERING

Principles and Chapter 6 Frequency Response, Bode Plots, and Resonance Vout H f Vin The magnitude of the transfer function shows how the amplitude of each frequency component is affected by the filter. Similarly, the phase of the transfer function shows how the phase

of each ELECTRICA L frequency component is affected by Chapter 6 ENGINEERING the filter.Frequency Response, Bode Plots, and Resonance Principles and ELECTRICA L ENGINEERING Principles and

Chapter 6 Frequency Response, Bode Plots, and Resonance Determining the output of a filter for an input with multiple components: 1. Determine the frequency and phasor representation for each input component. 2. Determine the (complex) value of the transfer function for each

component. ELECTRICA L ENGINEERING Principles and Chapter 6 Frequency Response, Bode Plots, and Resonance 3. Obtain the phasor for each output component by multiplying the phasor for each input component by the

corresponding transfer-function value. 4. Convert the phasors for the output components into time functions of various frequencies. Add these time functions to produce the output. ELECTRICA L ENGINEERING Principles and Chapter 6 Frequency Response, Bode Plots, and Resonance

Linear circuits behave as if they: 1. Separate the input signal into components having various frequencies. 2. Alter the amplitude and phase of each component depending on its frequency. 3. Add the altered components to produce the output signal.

ELECTRICA L ENGINEERING Principles and Chapter 6 Frequency Response, Bode Plots, and Resonance ELECTRICA L ENGINEERING Principles and

Chapter 6 Frequency Response, Bode Plots, and Resonance ELECTRICA L ENGINEERING Principles and Chapter 6 Frequency Response, Bode Plots, and Resonance ELECTRICA L

ENGINEERING Principles and Chapter 6 Frequency Response, Bode Plots, and Resonance ELECTRICA L ENGINEERING Principles and Chapter 6 Frequency Response, Bode Plots, and Resonance

FIRST-ORDER LOWPASS FILTERS 1 fB 2RC H f 1 1 f fB 2

f 1 H f arctan H f 1 j f f B fB ELECTRICA L ENGINEERING Principles and Chapter 6

Frequency Response, Bode Plots, and Resonance H f 1 1 f fB 2 ELECTRICA L ENGINEERING Principles and

Chapter 6 Frequency Response, Bode Plots, and Resonance ELECTRICA L ENGINEERING Principles and Chapter 6 Frequency Response, Bode Plots, and Resonance ELECTRICA

L ENGINEERING Principles and Chapter 6 Frequency Response, Bode Plots, and Resonance ELECTRICA L ENGINEERING Principles and Chapter 6

Frequency Response, Bode Plots, and Resonance ELECTRICA L ENGINEERING Principles and Chapter 6 Frequency Response, Bode Plots, and Resonance DECIBELS, THE CASCADE CONNECTION, AND LOGARITHMIC FREQUENCY

SCALES H f dB 20 log H f ELECTRICA L ENGINEERING Principles and Chapter 6 Frequency Response, Bode Plots, and Resonance ELECTRICA L

ENGINEERING Principles and Chapter 6 Frequency Response, Bode Plots, and Resonance ELECTRICA L ENGINEERING Principles and Chapter 6 Frequency Response, Bode Plots, and Resonance

ELECTRICA L ENGINEERING Principles and Chapter 6 Frequency Response, Bode Plots, and Resonance Cascaded Two-Port Networks H f H 1 f H 2 f

H f dB H 1 f dB H 2 f dB ELECTRICA L ENGINEERING Principles and Chapter 6 Frequency Response, Bode Plots, and Resonance

ELECTRICA L ENGINEERING Principles and Chapter 6 Frequency Response, Bode Plots, and Resonance Logarithmic Frequency Scales On a logarithmic scale, the variable is multiplied by a

given factor for equal increments of length along the axis. ELECTRICA L ENGINEERING Principles and Chapter 6 Frequency Response, Bode Plots, and Resonance A decade is a range of frequencies

for which the ratio of the highest frequency to the lowest is 10. f2 number of decades log f1 An octave is a two-to-one change in frequenc f 2 log f 2 f1 number of octaves log 2 f1 log 2

ELECTRICA L ENGINEERING Principles and Chapter 6 Frequency Response, Bode Plots, and Resonance ELECTRICA L ENGINEERING Principles and

Chapter 6 Frequency Response, Bode Plots, and Resonance FIRST-ORDER HIGHPASS FILTERS Vout j f f B H f Vin 1 j f f B 1 fB

2RC ELECTRICA L ENGINEERING Principles and Chapter 6 Frequency Response, Bode Plots, and Resonance ELECTRICA L ENGINEERING Principles and

Chapter 6 Frequency Response, Bode Plots, and Resonance ELECTRICA L ENGINEERING Principles and Chapter 6 Frequency Response, Bode Plots, and Resonance ELECTRICA

L ENGINEERING Principles and Chapter 6 Frequency Response, Bode Plots, and Resonance ELECTRICA L ENGINEERING Principles and Chapter 6

Frequency Response, Bode Plots, and Resonance DIGITAL SIGNAL PROCESSING ELECTRICA L ENGINEERING Principles and Chapter 6 Frequency Response, Bode Plots, and Resonance

ELECTRICA L ENGINEERING Principles and Chapter 6 Frequency Response, Bode Plots, and Resonance Conversion of Signals from Analog to Digital Form If a signal contains no components with frequencies higher than fH, the

signal can be exactly reconstructed from its samples, provided that the sampling rate fs is selected to be more than twice fH. ELECTRICA L ENGINEERING Principles and Chapter 6 Frequency Response, Bode Plots, and Resonance ELECTRICA

L ENGINEERING Principles and Chapter 6 Frequency Response, Bode Plots, and Resonance