It is shown that a weak threshold network (in particular, threshold network) of width w and depth d cannot be constructed from balancers of width p 0, p 1,…, p m − 1 , if w does not divide P d , where P is the least common multiple of p 0, p 1,…, p m − 1 . This holds regardless of the size of the network, as long as it is finite, and it implies a lower bound of log p w on its depth. More strongly, a lower bound of log p max w is shown on the length of every path from an input wire to any output wire that exhibits the threshold property, where p max is the maximum among p 0, p 1,…, p m − 1 .