Quadrature Detector Symbolic Model

Quadrature detectors (QD) are widely used in a radioelectronic devices as alternative to the synchronous detectors. There are many applications where there is necessary to measure the amplitude of input signal with specified frequency, but unknown or variable phase. For such cases the quadrature detectors are often used. The key advantage of quadrature detectors is that output signal is invariant to the phase of the input signal.

This paper is devoted to the symbolic model of the quadrature detector. The output signal is represented as a matrix contains the parameters of this signal frequency components (frequencies, amplitudes and phases). Proposed model is useful for analysis, optimization and statistical problems.

Proposed symbolic model of quadrature detector allows to obtain symbolic model once per given quadrature detector architecture and use this model many times for solving a lot of engineering problems like optimization or statistical analysis. The symbolic model can be used for quick output signal calculation. To do this the corresponding numerical values should be substituted instead of symbolic parameters.

The restriction of proposed model is that it allows to build the symbolic model in the frequency domain for all blocks of quadrature detector except SQRT block. But this model allows easily calculate SQRT output signal in time domain. To do this the matrix representation of SQRT input signal is converted to the time domain signal according to the given in paper equation and square root can be easily calculated.

The drawback of proposed model is that the case of complicated input signal, which contains a lot of frequency components, causes to the symbolic model complexity increase due the order of matrix model increase proportionally to the number of frequency components in the input signal.