 In this paper Floyd M. Gardner derived a linear mathematical model of CP-PLL and, based on its analysis, conjectured that transient response of practical charge-pump PLL's can be expected to be nearly the same as the response of the equivalent classical PLL.Floyd M. Gardner introduced "a lock-in range concept" for PLLs and posed the problem on its formalization (known as the Gardner problem on the lock-in range).In the 1st edition of his book he introduced a lock-in frequency concept for the PLL in 
the following way