Yii: How to Search a HAS_MANY relation using CDbCriteria Compare()

Using Yii's implementation of ActiveRecord makes querying a database much easier for simple queries. For more complex situations, you will still find yourself having to write some straight SQL on occasion. In this case, using a custom query was not necessary. I was trying to add another search parameter, using the AR compare() method, to search a relation with a HAS_MANY relationship, and it was displaying an "unknown column" error. Without a proper example, it wasn't clear at first how to get this work...