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z -L<br />

FIGURE 34.27 Linearized model: (a) second-order DPLL loop filter, (b) timing loop with phase detector modeled<br />

by its average signal gain.<br />

FIGURE 34.28 Closed loop frequency response of SLT DPLL for low p g and f g update gains.<br />

The open loop DPLL transfer function, G(z), incorporating the loop filter L(z) and clock update gain is<br />

Referring to the timing loop model of Fig. 34.27(b), the closed loop transfer functiont (T out/T in) = H(z) is<br />

© 2002 by CRC Press LLC<br />

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(34.28)<br />

Note that K p has dimensions of LSB/T, K V and G(z) have dimensions of T/LSB and H(z) is a transfer<br />

function with respect to two time quantities. The effective noise bandwidth is then,<br />

An example of a closed loop transfer function for the SLT DPLL is shown in Fig. 34.28 for LOW update<br />

gains. To find the effect of AWG noise, n(k), first convert the σ n to an effective timing noise by dividing<br />

by the rms slope, σ s, of the signal that is obtained during the numerical generation of the signal slopes<br />

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