What is the spurious analysis methodology for a complex RF signal chain with multiple mixing stages?

The spurious analysis methodology for a complex RF signal chain with multiple mixing stages systematically identifies all unwanted spectral products (spurs) that can appear at the output of the signal chain, determining which spurs fall within the desired output band and evaluating their power level relative to the desired signal. The methodology involves: identifying all mixing stages in the signal chain (each mixer, frequency multiplier, and nonlinear amplifier generates mixing products; for a two-stage superheterodyne: mixer 1 converts RF to IF1, mixer 2 converts IF1 to IF2 or baseband; each stage generates products at m x f_input ± n x f_LO for all integer m and n), computing the spurious frequencies (for each stage: calculate all products up to at least order 5x5 (m,n up to 5); for cascaded stages: the output spurs of stage 1 become the input signals for stage 2, creating cross-products that multiply the number of potential spurs; the total number of spurs to check grows as (2M+1)^(2N) for M maximum order and N stages), evaluating the spur power level (the amplitude of each mixing product at order (m,n) is approximately: P_spur = P_input x (gain of the mixer at that order); for a typical double-balanced mixer: the (m,n) product is suppressed by approximately 20-30 dB per unit increase in (m+n) from the fundamental (1,1) product; a 3rd-order spurious product is approximately 40-60 dB below the fundamental, while 5th-order is approximately 60-100 dB below), filtering between stages (bandpass filters at each IF stage remove many spurious products before they reach the next mixer; the filter bandwidth and rejection determine which spurs are eliminated; the spur analysis must account for the filter's frequency response at each spur frequency), and creating a spur chart (a graphical representation showing all significant spurs within and near the output band as a function of LO frequency or RF input frequency; spur charts help identify 'spur-free' operating regions).