A logarithmic amplifier (LDA) is described that includes an amplifier configured to oscillate a modulated input signal, a feedback establishing a 180 degree phase shift between the amplifier input and the output and maintaining oscillation of the input signal, a parallel resonant circuit connected to the amplifier output causing the amplifier to resonate at or around a center frequency, and a controller connected to the amplifier input cyclically terminating oscillation of the input signal each time a pre-determined threshold of current is detected, the controller including a low pass filter configured to generate a second output signal having a repetition frequency. The LDA may be used for AM with or without a PLL and/or a superhetrodyne. The LDA may be implemented as a mixer and used for phase demodulation. The LDA may be used for phase demodulation. The LDA may be used in place of a low noise amplifier.