One class of transfer functions with monotonic step response

The paper describes the transfer functions with monotonic step response. These functions required in design of wide-band pulse amplifiers were synthesized using the first semi-period of the sin² (πt/τ)function as an approximation to the impulse response. For this class of transfer functions the delay-to-rise-time ratio is equal to π/τ. The order of transfer function is found from one of two inequalities defining whether the transfer function is even or odd. To simplify the design the delay-to-rise-time ratio and the corresponding poles are given for the transfer functions from the forth to tenth order. The delay-to-rise-time ratio of the proposed transfer functions is better than that of Bessel or Gaussian filter functions by fifteen to twenty five percents.