PRODYN PASSIVE INTEGRATORS MODELS PI-1, 5, 10 & 100 The PI-1, 5, 10, and 100 series Integrators are passive resistor-capacitor integrators with standard RC time constants of 1, 5, 10 or 100 microseconds. They are available with standard connector types such as SMA (shown) or other styles can be specified. The unit and its idealized circuit (which is based on the AFWL RCI-1B integrator) is shown below: The transfer function of the Integrator is implicit in the Differential equation:   Rq    ____   +  ___  = V  in (t)           dt          C         where q is the charge on the capacitor. The integrator is designed to drive a >1 megohm, <10 pf load impedance. The voltage out is essentially the voltage across the capacitor, q/C, which is calculated by solving (integrating) the differential equation for q(t). This is most conveniently done by Laplace transforms, which yield the transfer function in the frequency domain:    Vout(s)       1 ______  =  _____ Vin(s)  sRC + 1     where s = j = Laplace operator. The transfer function is an integrator for sinusoidal inputs with frequencies large compared to 1/2pRC  ; or for transient inputs for times small compared to RC. Typical performance of the PI-100 integrating a 5ms square pulse is shown at the right. This pulse is integrated with an error of 2.5% over the 5ms duration.