Frequency conversion means output of the amplifier is at a frequency different from that of the input.
Yes there is. The circuit is called a heterodyne and is used in radio communications receivers to downconvert the high frequency radio signals to lower intermediate frequencies which are easier to process. The heterodyne principle starts by mixing the radio frequency signal with that of a lower frequency local oscillator which produces a spread of frequencies consisting of the original, the local oscillator frequency, and sum and difference frequencies. Everything except the difference frequencies is then filtered out. Radios in which only one heterodyne stage is used are called single-conversion receivers and up to three stages are used in triple conversion receivers.
Within each stage, frequency-selective circuits are used to focus on a narrow band of passed signals so the radio exhibits good selectivity or rejection of adjacent signals which would otherwise interfere with the signal frequency of interest. The tuning of each stage is synchronized so the bandpass of all the stages coincide throughout the heterodyning process regardless of what frequency the radio is tuned to receive.