Amplitude & Phase Calibration

Rev. 2

S. Smith

27 Aug 2002

 

I&Q Measurement

Goal: Translate I&Q measurements from SIS digitizers to amplitude and phase using I&Q calibration parameters.

Given a vector of I and Q values from the waveform digitizers: Ij Qj

and calibration data:

I & Q pedestals Iped, Qped

Gains gI, gQ

Quadrature angle fq

Channel Phase angle f0

 

Define

        Quadrature angle error d = fq 90o

        and

Correct for pedestals and gains: Ij = gI(Ij - Iped) , Qj = gQ(Qj - Qped)

Adjust for quadrature error: VjI = cIj + sQj VjQ = sIj + qQj

Amplitude:

Phase: fj = tan-1(Qj/Ij) - f0


I&Q Control

Goal: Translate desired I&Q components to I&Q DAC values using calibration parameters.

Given a vector of I and Q values: I, Q

and calibration data:

I & Q pedestals Iped, Qped

Gains gI, gQ

Quadrature angle fq

Channel Phase angle f0

 

Define

        Quadrature angle error d = fq 90o

        and

        De-skewing matrix:

        Channel Phase rotation matrix:

        Gain Correction Matrix:

Transformation: