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vb.net barcode reader code Part I in Software
Part I Recognizing QR In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. QR Code 2d Barcode Drawer In None Using Barcode creator for Software Control to generate, create QR image in Software applications. Circuits
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The magnitude and phase plots for the frequency response of the bandpass lter of Figure 619 are shown in Figure 620 These plots have been normalized to have the lter passband centered at the frequency = 1 rad/s The frequency response plots of Figure 620 suggest that, in some sense, the bandpass lter acts as a combination of a highpass and a lowpass lter As illustrated in the previous cases, it should be evident that one can adjust the lter response as desired simply by selecting appropriate values for L, C, and R The expression for the frequency response of a secondorder bandpass lter (equation 629) can also be rearranged to illustrate two important features of this circuit: the quality factor, Q, and the resonant frequency, 0 Let 1 0 = LC Then we can write CR = 0 CR =Q 0 0 0 and Q = 0 CR = R 0 L (633) and rearrange equation 629 as follows: Vo (j ) = Vi jQ j 0
+ jQ +1 0
(634) In equation 634, the resonant frequency, 0 , corresponds to the center frequency of the lter, while Q, the quality factor, indicates the sharpness of the resonance, 6
Frequency Response and System Concepts
Bandpass filter amplitude response 1 08 Amplitude 06 04 02 0 _ 10 3 10 1 100 101 Radian frequency (logarithmic scale) Bandpass filter phase response
50 Phase, degrees
0 _50 _3 _2 10 1 100 101 Radian frequency (logarithmic scale) Figure 620 Frequency response of RLC bandpass lter
that is, how narrow or wide the shape of the passband of the lter is The width of the passband is also referred to as the bandwidth, and it can easily be shown that the bandwidth of the lter is given by the expression B= 0 Q (635) Thus, a highQ lter has a narrow bandwidth, while a lowQ lter has a large bandwidth and is therefore less selective The quality factor of a lter provides an immediate indication of the nature of the lter The following examples illustrate the signi cance of these parameters in the response of various RLC lters EXAMPLE 66 Frequency Response of BandPass Filter
Problem
Compute the frequency response of the bandpass lter of Figure 619 for two sets of component values
Multisim
Solution
Known Quantities: (a) R = 1 k ; C = 10 F; L = 5 mH (b) R = 10 ; C = 10 F; L = 5 mH
Find: The frequency response, HV (j ) Part I
Circuits
Assumptions: None Analysis: We write the frequency response of the bandpass lter as in equation 629: HV (j ) = = Vo j CR (j ) = Vi 1 + j CR + (j )2 LC CR 1 2 LC
+ ( CR)2 CR arctan 2 1 2 LC
We can now evaluate the response for two different values of the series resistance The frequency response plots for case a (large series resistance) are shown in Figure 621 Those for case b (small series resistance) are shown in Figure 622 Let us calculate some quantities for each case Since L and C are the same in both cases, the resonant frequency of the two circuits will be the same: 1 0 = = 447 103 rad/s LC On the other hand, the quality factor, Q, will be substantially different: Qa = 0 CR 045 Qb = 0 CR 45 case a case b From these values of Q we can calculate the approximate bandwidth of the two lters: 0 10,000 rad/s case a Ba = Qa 0 100 rad/s case b Bb = Qb The frequency response plots in Figures 621 and 622 con rm these observations Broadband filter amplitude response 1 08 Amplitude 06 04 02 0 101 102 103 104 105 Radian frequency (logarithmic scale) Broadband filter phase response 106 107 50 Phase, degrees
0 _50 103 104 105 Radian frequency (logarithmic scale) Figure 621 Frequency response of broadband bandpass lter of Example 66
6
Frequency Response and System Concepts
Narrowband filter amplitude response 1 08 Amplitude 06 04 02 0 101 102 103 104 105 Radian frequency (logarithmic scale) Narrowband filter phase response 106 107

