Laser-Based Measurements for Time and Frequency Domain Applications

70 Laser-based measurements for time and frequency domain applications

R

R

C

C

t

t

j

out

j

e

j

i

n

t

FIGURE 2.19

Low-pass (high- pass) behavior of the output-to-input ratio (error) in a PLL. (Adapted from

[87].)

ϕ

out

(s)

ϕ

in

(s)

=

K

s

= −i

K

ω

(2.193)

This equals the open-loop tr ansfer function, Equation 2.189. Thus, at low frequencies,

where the gain is high, the output follows the input faithfully, whereas, at high frequencies,

where the gain becomes low, the loop is essentially open and the response is as if ther e

were no loop (except that the low-frequency gain keeps it locked - otherwise none of these

equations would be valid). At the loop corner frequency, ω = K,