On the Mixing Properties of Non-Linear Condensers

The theory of a mixer circuit, containing a non-linear condenser as a mixing element, is developed. It is shown that such a condenser has an imaginary conversion transconductance and a capacitive input and output impedance. It is found that the circuit has widely different properties, depending upon the choice of the frequency, ωm, of the local oscillator, the i-f frequency, ω0, and the input frequency, ωi. The following three cases are considered: (a) ωm = ωi+ω0, (b) ωm = ωi−ω0, and (c) ωm = ω0−ωi. A non-linear condenser in a mixing circuit acts as a transformer; in the cases (b) and (c) the mixing condenser transforms an i-f impedance into a positive input load; in case (a) an i-f impedance is transformed into a negative input load, so that oscillations may even occur. In case (c) the power gain is larger than unity, the power delivered to the circuit by the antenna is smaller than the power dissipated by the output load, and the difference is due to the power delivered by the local oscillator. In case (b) the power gain is smaller than unity, because in this case power is dissipated by the local oscillator. In case (c) instability may occur; the circuit is then capable of splitting the local-oscillator signal into two signals of frequencies, ωi and ω0, respectively. The band width and the noise factor of the circuit are also discussed; it is shown that the circuit might have a very low noise factor. A few experiments are given which show qualitative agreement with theory.