Fiqh-us-Sunnah Volume 1, Purification and Prayer, Fiqh 1.102.

The azhan is to be made exactly at the beginning of the prayer time, except for the morning prayer, when it may be said before dawn (provided that the people are able to distinguish between the early azhan and that of the proper time). ‘Abdullah ibn ‘Umar related that the Prophet, upon whom be peace, said, “Bilal makes the azhan during the night, so eat and drink until you hear the azhan of Ibn Umm Maktum.” (Related by al-Bukhari and Muslim.) The wisdom behind allowing the morning azhan a little earlier is made clear in a hadith recorded by Ahmad and others from Ibn Mas’ud: “None of you should let Bilal’s azhan prevent you from the pre-dawn meal, as he is making the azhan for those who are praying to stop and for those who are sleeping to get up.” But Bilal made his azhan in exactly the same way as the regular azhan. At-Tahawi and an-Nasa’i relate that the time difference between Bilal’s azhan and that of Ibn Umm Maktum was the time it took for one to come down from the minaret and for the others to get up to it.

Enough time should be left between the azhan and iqamah for people to prepare themselves for prayer and get to the mosque. The hadith that state the time difference are weak. Al-Bukhari has a section entitled How Much Time Is There Between the Azhan and Iqamah?, but no specific length of time has been confirmed therein. Ibn Batal said, “There is no time limit set, except that of the time beginning and the people gathering for the prayer.” Jabir ibn Sumra said, “The callers to prayer of the Prophet would make the azhan and then leave some time, making the iqamah only when they saw the Prophet, upon whom be peace, coming (to the place of prayer). (Related by Ahmad, Muslim, Abu Dawud, and at-Tirmizhi.)