Moments Based Computation of Intermodulation Distortion of Mixer Circuits

Computation of the 1-dB compression point in radio frequency amplifier circuits using moments analysis

“…In [2][3][4][5][6], the value of IP 3 was determined using numerical entries in specific locations of the moment vectors. These were shown to be equivalent to the numerical values of the required Volterra kernels evaluated at the frequencies of interest.…”

“…In this article, a new approach is presented to compute important distortion performance figures of merit that RF circuit engineers typically require. These are the 1-dB compression point with both single-tone and two-tone inputs, in addition to the values of IP 2 and IP 5 to complement the computation of IP 3 that was presented in earlier work [2][3][4][5][6]. These terms will be evaluated directly from the moment vectors.…”

“…(24), can be derived. Consider the system representation in terms of the Volterra series expression in (2). To determine the location of the kernels in the moment vectors, we substitute the expression for an input function with a single tone of amplitude a into (2), similar to the case of memoryless systems, which is given by:…”

“…The kernels of the Volterra series are then derived using the properties of multidimensional Laplace transforms of Volterra series [16], which would then allow for the substitution of the kernels into (2). The resulting expression is then rearranged by grouping equal powers of a together to obtain the following input-output relation The Volterra Series expression in (27) is similar to the expression shown in (23) and proves that the moment vectors essentially contain the numerical values of the Volterra series terms evaluated at the specified frequencies.…”

“…This is mainly due to the presence of multitone inputs and several harmonics which typically result in large systems of equations for the circuit simulator to process. Recently, a new method for computing the third-order intercept point (IP 3 ) in RF amplifier and mixer circuits was presented [2][3][4][5][6]. This new method is based on moments analysis [7] and was shown to present significant computation cost savings when compared to traditional distortion analysis using harmonic balance [8,9].…”