5.3.1 Transfer Function in an Analog Circuit

The PLL transfer function can be used to evaluate the correlation between phase changes in the output and input. In Section 5.2.1, the transfer function was obtained for the simplest PLL, which consists of just a phase comparator and a controlled oscillator. This configuration represents a first-order loop since it has a linear function of s. The transfer function of the first-order loop is the ratio of the phase variation transferred from the input of the PLL to the output. In (5.21), the level of the phase variation ratio is obtained by calculating the absolute value of the transfer function.

In (5.21), the phase variation ratio approaches unity as ? approaches 0. Conversely, as ? is enlarged, the phase variation ratio becomes zero. It is shown that the PLL has a lowpass characteristic (see Figure 5.7), as only slow phase variations appear in the PLL output. The amplitude H( jw) becomes or drops by 3 dB when the angular frequency ? equals the loop gain K _o K _d. This can be considered as the PLL passband limit. In the frequency region where ? is sufficiently larger than the loop gain, the phase variation ratio decreases as ? increases. The rate of this decrease is 20 dB/decade, which is equivalent to 6 dB/octave.

Figure 5.7: The frequency response of a first-order...