My first thought was gypsy moths, which favor birch trees, but they would have eaten the leaves, not turned them brown. Sounds more like leaf scorch, which is caused by a lack of water in the leaves. This can happen in drought, or in extreme heat and wind, or if roots are damaged. Birch like moist soil, so drought is your most likely cause. Mulch the trees and keep them watered. If you have water restrictions, please think about getting a rain barrel and collecting your own irrigation water.
Luke Miller, editor
Garden Ideas & Outdoor Living magazine