Fast Hopping Frequency Generation in Digital CMOS by Mohammad Farazian Lawrence E. Larson & Prasad S. Gudem

Author:Mohammad Farazian, Lawrence E. Larson & Prasad S. Gudem
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

(4.17)

After substituting the values of and into (4.17), it can be rewritten as

(4.18)

A similar equation can be obtained for the second delay cell, as follows.

(4.19)

Fig. 4.3Schematic of the two-stage CMOS ring-oscillator when an external signal is injected at the output of the first delay cell

To further simplify our analysis, we define and as follows

(4.20a)

(4.20b)

By separating the real and imaginary parts of (4.18) and (4.19) we obtain

(4.21a)

(4.21b)

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