vb.net barcode reader code Figure 69 A simple RC lter in Software

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Figure 69 A simple RC lter
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An immediate observation upon studying this frequency response is that if the signal frequency, , is zero, the value of the frequency response function is 1 That is, the lter is passing all of the input Why To answer this question, we note that at = 0, the impedance of the capacitor, 1/j C, becomes in nite Thus, the capacitor acts as an open circuit, and the output voltage equals the input: Vo (j = 0) = Vi (j = 0) (617)
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Since a signal at sinusoidal frequency equal to zero is a DC signal, this lter circuit does not in any way affect DC voltages and currents As the signal frequency increases, the magnitude of the frequency response decreases, since the denominator increases with More precisely, equations 618 to 621 describe the magnitude and phase of the frequency response of the RC lter: H (j ) = = = or H (j ) = |H (j )|ej H (j ) with |H (j )| = 1 1+ ( CR)2 = 1 1 + ( / 0 )2 (620) (619) 1 Vo (j ) = Vi 1 + j CR 1 1 1 + ( CR)2 ej 0
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1 + ( CR)2 ej arctan( CR/1) e j arctan( CR)
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(618)
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Frequency Response and System Concepts
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and H (j ) = arctan( CR) = arctan with 0 = 1 RC (622) 0 (621)
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The simplest way to envision the effect of the lter is to think of the phasor voltage Vi = Vi ej i scaled by a factor of |H | and shifted by a phase angle H by the lter at each frequency, so that the resultant output is given by the phasor Vo ej o , with Vo = |H | Vi o = H + i (623)
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and where |H | and H are functions of frequency The frequency 0 is called the cutoff frequency of the lter and, as will presently be shown, gives an indication of the ltering characteristics of the circuit It is customary to represent H (j ) in two separate plots, representing |H | and H as functions of These are shown in Figure 610 in normalized form that is, with |H | and H plotted versus / 0 , corresponding to a cutoff frequency 0 = 1 rad/s Note that, in the plot, the frequency axis has been scaled logarithmically This is a common practice in electrical engineering, because it allows viewing a
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Magnitude response of RC low-pass filter 1 08 Amplitude 06 04 02 0 _ 10 2
100 101 102 Radian frequency (logarithmic scale)
Phase response of RC low-pass filter 0 _20 Phase, degrees _40 _60 _80 10
100 101 102 Radian frequency (logarithmic scale)
Figure 610 Magnitude and phase response plots for RC lter
Part I
Circuits
very broad range of frequencies on the same plot without excessively compressing the low-frequency end of the plot The frequency response plots of Figure 610 are commonly employed to describe the frequency response of a circuit, since they can provide a clear idea at a glance of the effect of a lter on an excitation signal For example, the RC lter of Figure 69 has the property of passing signals at low frequencies ( 1/RC) and of ltering out signals at high frequencies ( 1/RC) This type of lter is called a low-pass lter The cutoff frequency = 1/RC has a special signi cance in that it represents approximately the point where the lter begins to lter out the higher-frequency signals The value of H (j ) at the cutoff frequency is 1/ 2 = 0707 Note how the cutoff frequency depends exclusively on the values of R and C Therefore, one can adjust the lter response as desired simply by selecting appropriate values for C and R, and therefore choose the desired ltering characteristics
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