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vb.net barcode reader code 4 Imaginary part 2 0 2 4 6 10 5 Real part 0 5 in Software
6 4 Imaginary part 2 0 2 4 6 10 5 Real part 0 5 Recognize QR Code In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. Creating Quick Response Code In None Using Barcode creation for Software Control to generate, create QR Code ISO/IEC18004 image in Software applications. Figure 633 Zero pole plot for the circuit of Figure 632
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Draw QRCode In VB.NET Using Barcode creation for VS .NET Control to generate, create QRCode image in .NET framework applications. Printing GS1128 In None Using Barcode creation for Software Control to generate, create UCC.EAN  128 image in Software applications. Circuits
Universal Product Code Version A Creation In None Using Barcode printer for Software Control to generate, create UPC A image in Software applications. Encode USS Code 128 In None Using Barcode maker for Software Control to generate, create Code 128C image in Software applications. EXAMPLE 612 Poles of a SecondOrder Circuit
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Codabar Maker In None Using Barcode creator for Software Control to generate, create Code 2 of 7 image in Software applications. Draw Code128 In ObjectiveC Using Barcode drawer for iPad Control to generate, create Code 128B image in iPad applications. Determine the poles of the circuit of Example 511
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Creating Data Matrix 2d Barcode In ObjectiveC Using Barcode creation for iPhone Control to generate, create Data Matrix image in iPhone applications. GS1 128 Creator In None Using Barcode printer for Microsoft Word Control to generate, create GS1 128 image in Office Word applications. Known Quantities: Values of resistor, inductor, and capacitor Find: Poles of the circuit Assumptions: None Analysis: The differential equation describing the circuit of Example 511 was found to Encode UPCA In Visual C#.NET Using Barcode creator for VS .NET Control to generate, create UPCA Supplement 5 image in Visual Studio .NET applications. Code128 Encoder In Visual Studio .NET Using Barcode printer for Reporting Service Control to generate, create Code 128 Code Set A image in Reporting Service applications. be d 2i R di 1 + + i=0 dt 2 L dt LC with characteristic equation given by 1 R s+ =0 L LC Now, let us determine the transfer function of the circuit, say VL (s)/VS (s) Applying the voltage divider rule, we can write s2 + VL (s) s2 sL = = 1 R 1 VS (s) + R + sL s2 + s + sC L LC The denominator of this function, which determines the poles of the circuit, is identical to the characteristic equation of the circuit: The poles of the transfer function are identical to the roots of the characteristic equation! s1,2 = 1 L 2R 2 R L 4 LC
Comments: Describing a circuit by means of its transfer function is completely
equivalent to representing it by means of its differential equation However, it is often much easier to derive a transfer function by basic circuit analysis than it is to obtain the differential equation of a circuit CONCLUSION
In many practical applications it is important to analyze the frequency response of a circuit, that is, the response of the circuit to sinusoidal signals of different frequencies This can be accomplished quite effectively by means of the phasor analysis methods developed in 4, where the radian frequency, , is now a variable The frequency response of a circuit is then de ned as the ratio of an output phasor quantity (voltage or current) to an input phasor quantity (voltage or current), as a function of frequency One of the primary applications of frequency analysis is in the study of electrical lters, that is, circuits that can selectively attenuate signals in certain frequency 6
Frequency Response and System Concepts
regions Filters can be designed, using standard resistors, inductors, and capacitors, to have one of four types of characteristics: lowpass, highpass, bandpass, and bandreject Such lters nd widespread application in many practical engineering applications that involve signal conditioning Filters will be studied in more depth in s 12 and 15 Although the analysis of electrical circuits by means of phasors that is, steadystate sinusoidal voltages and currents is quite useful in many applications, there are situations where these methods are not appropriate In particular, when a circuit (or another system) is subjected to an abrupt change in input voltage or current, different analysis methods must be employed to determine the transient response of the circuit In this chapter, we have studied the analysis methods that are required to determine the transient response of rstand secondorder circuits (that is, circuits containing one or two energystorage elements, respectively) One method involves identifying the differential equation that describes the circuit during the transient period and recognizing important parameters, such as the time constant of a rstorder circuit and the damping ratio and natural frequency of a secondorder circuit A second method exploits the idea of complex frequency and the Laplace transform CHECK YOUR UNDERSTANDING ANSWERS
CYU 61 CYU 64 CYU 65 Z2 ZL + Z 2 0 = 2,0263 rad/s 1 R (a) 0 = (low); (b) 0 = (high); RC L HI (j ) = (c) 0 = CYU 66 1 R (high); (d) 0 = (low) RC L L/R H (j ) = 1 + ( L/R)2 (j ) = 90 + arctan CYU 67 CYU 68 CYU 69 CYU 610 CYU 611 CYU 612 CYU 613 CYU 614 CYU 615 CYU 616 CYU 617 CYU 618 CYU 619 CYU 620 0 = 3546 rad/s 0 648 rad/s = 37517 rad/s = 1,03049 rad/s = 51,878 rad/s = 69,032 rad/s 1 = 9995 rad/s; 2 = 2001 krad/s a 4; b j 2 ; c j ; d 2 j 3; e 3 and 3 j 4 a 2, 5 0 ; b 2 + j 4, 5 10 ; c j 2, 4 20 a 2e 2t ; b 12 cos(2t 30 ); c 6e 4t cos(3t + 10 ) a 6e t ; b 12 2e t cos(t + 45 ); c 6e 2t cos(t + 135 ) a 3e 4t cos(t + 165 ); b 8 2e 2t cos(2t 105 ) 1 1 a ; b 2 ; c 2 s s + 2 s (s + a) a ; b (s + a)2 + 2 (s + a)2 + 2 L R

