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The theory of the two-electrode nonlinear mixer for superheterodyne use is developed so as to include the effect of resistive impedance at image frequency. The general theory is applied to the calculation of conversion loss under optimum conditions of matching the intermediate-frequency circuit to the mixer stage. Even when the intermediate-frequency circuit is not matched to the mixer, this matched-impedance conversion loss is important in the determination of the over-all signal-to-noise ratio of a receiver. This loss is computed for an idealized diode with different operating conditions, for various values of image-frequency impedance, and for different values of radio-frequency circuit losses. Although the chief effect of different image-frequency impedances is a change in the optimum operating conditions and in the required local-oscillator power, there is also an effect on the minimum conversion loss. Very low impedances or very high impedances result in smallest conversion loss. The impedances often encountered at ultra-high frequency (image-frequency impedance approximately the same as signal-frequency impedance) result in an increase in conversion loss which may be between 0 and 3 decibels, depending on the circuit losses.