The applet compares the common methods of digital vector thresholding to that of the perfect threshold case.
RF amplifier I/Q mixer, detector-video, and vector-video receiver types can be compared.
The upper display simulates the voltage vector with base noise (no signal) and signal vector rms noise circles against various thresholding schemes on a linear power scale.
The display is normalized to the Equivalent Threshold-to-Noise Ratio (ETNR = SNR when the signal is equal to the threshold level).
The large red circle represents the perfect True Vector threshold, where the vector detection level is vector angle invariant.
The green box represents the simplest implementation of the Cartesian Box threshold where the vector x and y components are each compared to equal, fixed positive, and negative thresholds.
The orange corner cutouts represent the Dual Box, dual threshold implementation; the lower-to-upper threshold ratio Tl/T is adjustable with the relevant scrollbar.
The blue hexagonal plot simulates the improved Greatest Sum variant, where the x and y vector components are combined by an adjustable k-factor to better approximate the true vector threshold.
The vector angle is adjustable using the Vector Angle scrollbar.
The lower displays show the threshold detection probability as a function of input signal power and angle, respectively. The latter is useful for determining the optimum factors for the Dual Box and Greatest Sum schemes.
Two practical vector demodulation cases, selectable from the drop-down menu, are modeled. The RFA + I/Q demodulator is relevant to IFM and DF/phase measurement systems using RF preamplifiers, whereas, the vector-video I/Q receiver can be adapted for coherent/FFT phase measurement analyzers. Note that the SNR/TNR scrollbars in the vector-video case, for scaling convenience, are modified from power ratios to voltage ratios.
All data values may be modified and the display may be updated using scrollbars.

User Notes:
The triggering probability versus power display is automatically updated when varying the vector angle.
At low SNR, the vector noise smooths the threshold variation.
The RFA + I/Q demodulator vector peak noise is elliptical, due to the correlated signal x noise component. In this case, the I/Q demodulator is modeled as an IFM discriminator with the two inputs fed from a common source via direct and delayed paths. The delay is the reciprocal of the IFM unambiguous bandwidth determined by a scrollbar (IFM Band).
By reducing the unambiguous band to zero, the corresponding delay is infinity, removing all correlation between noise from the two paths. The noise contour now becomes circular and the configuration is useful for evaluating RF amplified phase measurement or interferometer systems.
Increasing the IFM unambiguous bandwidth and adjusting the RF bandwidth such that B_u/B_r >>1, maximises the noise correlation in the two paths and so reduces the noise circles to straight in-phase lines, simulating the square-law detector.
Tabled to the right of the vector display are the signal power level equivalent to the scrollbar receiver parameters and the SNR setting, the SNR and TNR in dB, and the triggering probabilities of the four schemes at the vector phase set by the vector phase angle scrollbar.
When investigating vector detection around a threshold setting, note that significant noise levels, up to about three times the rms noise circle, can affect the triggering probability.