The noise in dark and illuminated Schottky barrier and diffused PIN non-guard-ring photodiodes has been measured between 0.1 Hz and 10 kHz and compared to theory with an excellent fit. It is shown that diodes used photovoltaically are free of 1/f noise in the dark. It is also demonstrated that there is an optimum bias (ca. 100 mV) for minimum noise equivalent power. When only a resistive load is used with a detector, it often determines the frequency response and noise of the detector circuit. We develop and demonstrate equations for the major improvements in both noise and frequency response that can be obtained using a current mode (inverting) operational amplifier.