Editing Costas loop (section)

==Frequency acquisition==
{| style="float:center; margin:auto"
|[[File:Costas loop before sync.png|340px|thumb|Costas loop before synchronization]]
|[[File:Costas loop after sync.png|290px|thumb|Costas loop after synchronization]]
|}

{| style="float:center; margin:auto"
|[[File:Costas loop signals before sycnhronization.svg|290px|thumb|Carrier and VCO signals before synchronization]]
|[[File:Costas loop trainsient process.svg|160px|thumb|VCO input during synchronization]]
|[[File:Costas loop after synchronization.svg|290px|thumb|Carrier and VCO signals after synchronization]]
|}

The classical Costas loop will work towards making the phase difference between the carrier and the VCO become a small, ideally zero, value.<ref>{{harvnb|Costas|1956}} states, "The local oscillator must be maintained at proper phase so that the audio output contributions of the upper and lower sidebands reinforce one another. If the oscillator phase is 90° away from the optimum value, a null in audio output will result, which is typical of detectors of this type. The actual method of phase control will be explained shortly, but for the purpose of this discussion, maintenance of correct oscillator phase shall be assumed."</ref><ref>Using a loop filter with an integrator allows a steady-state phase error of zero. See {{section link|PID controller|Integral term}}.</ref><ref>{{cite book |last=Best |first=Roland E. |title=Phase-Locked Loops |edition=third |location=New York |publisher=McGraw-Hill |date=1997 |pages=44–45 |isbn=0-07-006051-7}}</ref> The small phase difference implies that frequency lock has been achieved.