# zen barcode ssrs IMPULSE RESPONSE OF RC AND RL CIRCUITS in Software Paint QR Code in Software IMPULSE RESPONSE OF RC AND RL CIRCUITS

IMPULSE RESPONSE OF RC AND RL CIRCUITS
Recognize QR Code ISO/IEC18004 In None
Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications.
Print QR In None
Using Barcode maker for Software Control to generate, create QR-Code image in Software applications.
A narrow pulse can be modeled as an impulse with the area under the pulse indicating its strength. Impulse response is a useful tool in analysis and synthesis of circuits. It may be derived in several ways: take the limit of the response to a narrow pulse, to be called limit approach, as illustrated in Examples 7-11 and 7-12; take the derivative of the step response; solve the di erential equation directly. The impulse response is often designated by h t .
Scan QR Code JIS X 0510 In None
Using Barcode scanner for Software Control to read, scan read, scan image in Software applications.
Making Denso QR Bar Code In C#.NET
Using Barcode drawer for Visual Studio .NET Control to generate, create Quick Response Code image in .NET framework applications.
EXAMPLE 7.12 Find the limits of i and v of the circuit Fig. 7-17(a) for a voltage pulse of unit area as the pulse duration is decreased to zero. We use the pulse responses in (14) and (15) with V0 1=T and nd their limits as T approaches zero. From (14c) we have
QR Code 2d Barcode Printer In Visual Studio .NET
Using Barcode creation for ASP.NET Control to generate, create QR Code JIS X 0510 image in ASP.NET applications.
Draw QR Code JIS X 0510 In Visual Studio .NET
Using Barcode generator for .NET framework Control to generate, create QR Code JIS X 0510 image in .NET framework applications.
lim VT lim 1 e T=RC =T 1=RC
QR Encoder In Visual Basic .NET
Using Barcode creation for .NET framework Control to generate, create QR Code JIS X 0510 image in .NET applications.
Printing Bar Code In None
Using Barcode printer for Software Control to generate, create barcode image in Software applications.
From (15) we have: For t < 0; For 0 < t < 0 ; For t > 0; Therefore, hv t 1 t=RC u t e RC and hi t 1 1  t 2 e t=RC u t R R C
Drawing Code 3 Of 9 In None
Using Barcode generator for Software Control to generate, create Code 39 Extended image in Software applications.
Creating EAN13 In None
Using Barcode generation for Software Control to generate, create EAN-13 Supplement 5 image in Software applications.
and hi 0 1 1 and hi  t 0 hv RC R 1 t=RC 1 hv t and hi t 2 e t=RC e RC R C
Making UCC-128 In None
Using Barcode creation for Software Control to generate, create GS1-128 image in Software applications.
Generate UCC - 12 In None
Using Barcode printer for Software Control to generate, create GS1 - 12 image in Software applications.
hv 0
Code 2 Of 5 Encoder In None
Using Barcode printer for Software Control to generate, create 2 of 5 Industrial image in Software applications.
Recognizing UPC-A In Visual C#.NET
Using Barcode scanner for .NET Control to read, scan read, scan image in .NET framework applications.
EXAMPLE 7.13 Find the impulse responses of the RC circuit in Fig. 7-17(a) by taking the derivatives of its unit step responses. A unit impulse may be considered the derivative of a unit step. Based on the properties of linear di erential equations with constant coe cients, we can take the time derivative of the step response to nd the impulse response. The unit step responses of an RC circuit were found in (6) to be v t 1 e t=RC u t and i t 1=R e t=RC u t Thus
ECC200 Maker In Java
Using Barcode encoder for BIRT Control to generate, create DataMatrix image in Eclipse BIRT applications.
EAN 13 Maker In Java
Using Barcode printer for Java Control to generate, create EAN / UCC - 13 image in Java applications.
We nd the unit impulse responses by taking the derivatives of the step responses.
Encode Code-128 In None
Using Barcode generation for Online Control to generate, create Code128 image in Online applications.
Barcode Maker In .NET Framework
Using Barcode creator for Reporting Service Control to generate, create bar code image in Reporting Service applications.
CHAP. 7]
Decoding Code128 In Java
Using Barcode decoder for Java Control to read, scan read, scan image in Java applications.
USS Code 128 Reader In VS .NET
Using Barcode scanner for .NET framework Control to read, scan read, scan image in VS .NET applications.
FIRST-ORDER CIRCUITS
hv t
1 t=RC u t e RC
hi t
1 1  t 2 e t=RC u t R R C
EXAMPLE 7.14 Find the impulse responses hi t ; hv t ; and hi1 t of the RL circuit of Fig. 7-11(a) by taking the derivatives of its unit step responses. The responses of the circuit to a step of amplitude 9 were already found in Example 7.5. Taking their derivatives and scaling them down by 1/9, we nd the unit impulse responses to be 1 9 1 hv t 9 1 hi1 t 9 hi t d 200 800t u t 0:75 1 e 800t u t e dt 3 d 800 800t 1 3e 800t u t e u t  t dt  3 3  d 1 200 800t 1 800t 3 e e  t u t u t dt 4 9 18
SUMMARY OF STEP AND IMPULSE RESPONSES IN RC AND RL CIRCUITS
Responses of RL and RC circuits to step and impulse inputs are summarized in Table 7-1. Some of the entries in this table have been derived in the previous sections. The remaining entries will be derived in the solved problems.
RESPONSE OF RC AND RL CIRCUITS TO SUDDEN EXPONENTIAL EXCITATIONS
Consider the rst-order di erential equation which is derived from an RL combination in series with a sudden exponential voltage source vs V0 est u t as in the circuit of Fig. 7-18. The circuit is at rest for t < 0. By applying KVL, we get Ri L For t > 0, the solution is i t ih t ip t and i 0 0 17a di V0 est u t dt 16
Table 7-1(a) Step and Impulse Responses in RC Circuits RC circuit Unit Step Response Unit Impulse Response
vs u t ( v 1 e t=Rc u t i 1=R e t=Rc u t
vs  t ( hv 1=RC e t=RC u t hi 1=R2 C e t=RC u t 1=R  t
is u t ( v R 1 e t=RC u t i e t=RC u t
is  t ( hv 1=C e t=RC u t hi 1=RC e t=RC u t  t
FIRST-ORDER CIRCUITS
[CHAP. 7
Table 7-1(b) Step and Impulse Responses in RL Circuits RL circuit Unit Step Response Unit Impulse Response
vs u t ( v e Rt=L u t i 1=R 1 e Rt=L u t
vs  t ( hv R=L e Rt=L u t  t hi 1=L e Rt=L u t
is u t ( v Re Rt=L u t i 1 e Rt=L u t
is  t ( hv R2 =L e Rt=L u t R t hi R=L e Rt=L u t
Fig. 7-18
The natural response ih t is the solution of Ri L di=dt 0; i.e., the case with a zero forcing function. Following an argument similar to that of Section 7.4 we obtain ih t Ae Rt=L The forced response ip t is a function which satis es (16) for t > 0. ip t I0 est After substituting ip in (16), I0 is found to be I0 V0 = R Ls . boundary condition i 0 0 is also satis ed. Therefore, i t 17b The only such function is 17c By choosing A V0 = R Ls , the