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# How is trace math implemented within the Agilent Technologies Vector Network Analyzers?

Trace math within the Agilent Technologies Network Analyzers is applied to the complex real and imaginary data pairs. For all analyzers, as indicated in the data processing maps, trace math is implemented after error correction has been applied. Refer to the appropriate analyzer On-line Help or User’s Guide for additional details and block diagrams pertaining to the specific analyzer data processing map.

The two forms of trace math are ‘data/memory’ (data divided by memory) and ‘data – memory’ (data minus memory). ‘Data/memory’ is widely utilized as a normalization tool and is more commonly implemented versus ‘data – memory’.

### Details: ‘Data / memory’

Format: Linear Magnitude
For an analyzer display format of type linear magnitude the ‘data / memory’ trace math results in the division of two complex numbers. For division use the polar presentation of a complex number. The resulting magnitude is the ratio of the two amplitudes and the phase is difference of the two phases as described by the equation:

Where;
D = data trace magnitude,
α = data trace phase,
M =memory trace magnitude,
β = memory trace phase.

Format Logarithmic Magnitude
For an analyzer display format of type logarithmic magnitude ‘data / memory’ trace math results in the differences of the two original log magnitudes. The resulting magnitude is the ratio of the two amplitudes and the phase is difference of the two phases as described by the equation:

### Details: ‘Data - memory’

Data - memory is the vector subtraction of two complex numbers. This is used less often versus ‘data / memory’ trace math. An application of ‘data -memory’ would be the requirement to store data and then subtract a measured vector error such as directivity or any other interfering signal that can be measured separately. For ‘data - memory' the resulting magnitude and phase is not a simple subtraction of the magnitude and phases of the two numbers (for either linear or log formats). ‘Data - memory’ requires the following complex notation and equations:

Below is a sample of the ‘data - memory’ as applied to a pair of complex vector quantities and displayed geometrically: