Download 07.Circuits and Systems - Analog and Digital Signal by John G. Webster (Editor) PDF

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Extra resources for 07.Circuits and Systems - Analog and Digital Signal Processing

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To devise a first-order, real, stable, all-pass transfer function, we place a zero outside the unit circle in the z plane on the real axis at z = (1/r1 ) corresponding to a pole at z = r1 , |r1 | < 1. The resulting transfer function is given by or Evaluating H(z) in Eq. (68) for z = ejωT , where T is the sampling interval, we obtain and has a phase characteristic that can be expressed as Thus, the phase and delay characteristics are the same as for the low-pass prototype transfer function except for the factor of two.

Only one capacitor is needed. ALL-PASS CIRCUIT REALIZATIONS Voltage-mode Realizations where K1 is the gain factor associated with the transfer function of the first-order all-pass filter. If C1 R1 = CR, K1 = 1, and R2 = R3 , then Eq. (35) reduces to the transfer function of a standard second-order bandpass filter given by The Q and ω0 of the poles in Eq. (36) are Although the circuit requires the matching of elements and several operational amplifiers, including, possibly, a buffer at the input, it demonstrates that all-pass filters can be employed in the realization of filters having frequencyselective magnitude characteristics.

Second-order bandpass filter realized by incorporating a first-order all-pass filter in a feedback path. Figure 11. Input voltage vi (t), delayed input voltage vA (t), and comparator output voltage vo (t) for the slope-polarity detector shown in Figure 10 when the input voltage is a sine wave. fer function of the circuit is Figure 13. Passive circuit that can be used to realize a first-order all-pass filter. Only one capacitor is needed. ALL-PASS CIRCUIT REALIZATIONS Voltage-mode Realizations where K1 is the gain factor associated with the transfer function of the first-order all-pass filter.

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