By Donald R. Stephens

ISBN-10: 1461376181

ISBN-13: 9781461376187

ISBN-10: 1461557178

ISBN-13: 9781461557173

This ebook is meant for the graduate or complicated undergraduate engineer. the first motivation for writing the textual content used to be to offer an entire instructional of phase-locked loops with a constant notation. As such, it may well function a textbook in formal school room guide, or as a self-study advisor for the working towards engineer. A former colleague, Kevin Kreitzer, had advised that I write a textual content, with an emphasis on electronic phase-locked loops. As modem designers, we have been consistently receiving requests from different engineers soliciting for a definitive reference on electronic phase-locked loops. There are numerous reliable papers within the literature, yet there has been now not a great textbook for both lecture room or self-paced research. From my very own event in designing low section noise synthesizers, I additionally knew that third-order analog loop layout used to be passed over from so much texts. With these requisites, the fabric within the textual content looked as if it would circulate certainly. bankruptcy 1 is the early heritage of phase-locked loops. i think that old wisdom provides perception to the advance and development of a box, and phase-locked loops are not any exception. As mentioned in bankruptcy 1, patron electronics (color tv) triggered a speedy development in phase-locked loop conception and functions, very like the instant communications progress this present day. xiv Preface even supposing all-analog phase-locked loops have gotten infrequent, the continual time nature of analog loops permits an exceptional advent to phase-locked loop theory.

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**Example text**

With the substitution, the filter's transfer function is 1 w F(s) =- 2- - - = _---::~n-2 S ~s -+,,2-+1 2 Wn Compare s2+J2wns+Wn2 2-69 Wn Ho ,1 (s) (Equation 2-61) or ~ ,2 (s) (Equation 2-64) to the Butterworth filter transfer function in Equation 2-69. If ( = 1/J2, Ho ,1 (s) is exactly a Butterworth filter response. If (= 1/J2 , the denominator of ~ ,2 (s) has the form of a Butterworth filter. The different parameters of the filters will be discussed in a later chapter, but the value (= 1/J2 yields excellent performance, and is used in many PLL designs.

E(1) = ~e, where ~e is constant. The Laplace transform of this input is OJ (s) = ~O/ S . Gardner's Filter From Equations 2-52 and 2-86, The steady-state time response, obtained from the Final Value Theorem, is Lim ~ e (t)} = O. The time response is obtained from the inverse Laplace t-+«> Transform of Equation 2-94, but is too lengthy to placed in the text. J2PKd 1'1 S2 S 1'I1'3S3+1'IS2 +~2PKoKd1'2S+~2PKoKd e As with Gardner's filter, the steady-state time 2-96 response is Lim{Oe (t )} = O. The inverse Laplace transform of Equation 2-95 yields the t-+«> time response, but again, the time response is too long to place on the page.

If the pole (root of s +a + j ~ = 0) has a positive real A simple pole like component, the exponential will increase with time, causing an unbounded response. The term e-jPt indicates the time response will be oscillatory, with the frequency established by the imaginary component of the pole, ~ . We will show later that the time response and stability of a phase-locked loop are opposing values. A phase-locked loop with the damping factor ~ > 1 is much more stable than a loop with ~ < 1.

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