Abstract Two different algorithms are presented to design lossless ladder filters. Both methods are developed from a characteristic equation of the filters. The first method defines a performance index J and, using the special properties of the formulation used, evaluates the gradient of J with respect to element values. Optimization routines are then used to obtain element values to give the desired response. The second method starts with the characteristic equation and obtains a set of algebraic equations to evaluate the errors in the element values. Using this information, element values are adjusted to obtain the desired filter.