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: I_j Q_j

and calibration data:

I & Q pedestals I_ped, Q_ped

Gains g_I, g_Q

Quadrature angle f_q

Channel Phase angle f₀

Define

· Quadrature angle error d = f_q – 90^o

· and

Correct for pedestals and gains: I’_j = g_I(I_j - I_ped) , Q’_j = g_Q(Q_j - Q_ped)

Adjust for quadrature error: V_jI = cI’_j + sQ’_j V_jQ = sI’_j + qQ’_j

Amplitude:

Phase: f_j = tan^-1(Q_j/I_j) - 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 I_ped, Q_ped

Gains g_I, g_Q

Quadrature angle f_q

Channel Phase angle f₀

Define

· Quadrature angle error d = f_q – 90^o

· and

· De-skewing matrix:

· Channel Phase rotation matrix:

· Gain Correction Matrix:

Transformation: