DAC and Vector Modulator DC offset calibration

Transcription

1 DAC and Vector Modulator DC calibration Zheqiao Geng March 9, 9 Introduction This is the algorithm to calibrate the DC of the DAC of the LLRF controller. The goals are Calibrate the DAC/VM DC automatically Study the possibility to calibrate onle (with terrupt operation) Phenomena Fig1 DC at FLASH klystron 5 Problems: Problems to set zero gradient DC is added to the feed forward signals, make difficulties to defe the feed forward tables Cause error for applications that take the decay data (assumg there is no power at the end of the RF pulse) Error Model V = I + jq V = I + jq Fig Drivg cha of the cavities Copyright 1 by MSK. Publication of any part of this document should be agreed by the authors

2 Fig3 Error model of the drivg cha Calibration Unknown parameters: I, Q : The of the I/Q channels, which have the same scale with feed forward table K i + j*k q : The complex ga from the feed forward signal to pick up signal (both are expressed by the sampled values) g, φ: The ga imbalance and phase imbalance of the vector modulator (potato effect the first order approximation) Known parameters: I, Q : The put signal generated by feed forward table I, Q : The put signal measured from the pick up pot (see Fig) ω: The RF signal frequency, which will not appear the calibration, only for better understandg of the Fig3 Calibration strategy: Lear fittg The formula for fittg is worked as below: The base band equation [( I + I ) + j( Q + Q )]( K jk ) I + jq = + (1) I = Ki Q = K ( I + I ) Kq( Q + Q ) ( I + I ) + K ( Q + Q ) q i And because of the put signal at the pick up pot is ( RF band) V () t = I cos( ωt) + gq s( ωt + ϕ) = I cos( t) + gq s( ωt) cos( ϕ) + gq cos( ωt) s(ϕ ω ) So, with the demodulation, the base band put signal can be written as I Q = I + gq = gq cos s( ϕ) ( ϕ) Put equation () to (4), we get the formula between put and put i q () (3) (4) Copyright 1 by MSK. Publication of any part of this document should be agreed by the authors. - -

3 where I Q = ai = ci + bq + dq + k + l a = Ki + Kq c = Kqg cos e = ai, f = bq m = ci, n = dq k = e + f, l = m + n g s( ϕ), b = Kq + Kig s( ϕ) ( ϕ), d = K g cos( ϕ) i From equation (5), there are 6 unknown parameters: a, b, c, d, k and l. So, we need 3 put/put vectors for calculatg these parameters. But the normal way is to generate more put vectors, measure the correspondg put vectors, and use lear fittg for better estimation of the unknown parameters. After gettg a, b, c, d, k and l, the of I/Q channels can be calculated from the equation below k = ai l = ci + bq + dq Also, from a, b, c, d, the complex ga, phase and amplitude imbalance can be estimated as (5) (6) (7) 1 cb Ki = a c d 1 + d c Kq = Ki d c g cos( ϕ) = Kq b + Kq g s( ϕ) = Ki (8) Matlab Code function [ki,kq,ioff,qoff,pha_imbalance,amp_imbalance] = nfun_cal_dac(i,q,i,q) %=================================================== % function to calibrate the DC %=================================================== pno = length(i); A = zeros(*pno, 6); B = zeros(*pno, 1); for ii = 1:pno Copyright 1 by MSK. Publication of any part of this document should be agreed by the authors

4 A(*ii-1, 1) = I(ii); A(*ii-1, ) = Q(ii); A(*ii-1, 3) = ; A(*ii-1, 4) = ; A(*ii-1, 5) = 1; A(*ii-1, 6) = ; A(*ii, 1) = ; A(*ii, ) = ; A(*ii, 3) = I(ii); A(*ii, 4) = Q(ii); A(*ii, 5) = ; A(*ii, 6) = 1; B(*ii-1) = I(ii); B(*ii) = Q(ii); end; X = A\B; a = X(1); b = X(); c = X(3); d = X(4); k = X(5); l = X(6); A1 = [a b; c d]; B1 = [k;l]; X1 = A1\B1; Ioff = X1(1); Qoff = X1(); % calculate other parameters ki = (a - c*b/d) / (1 + (c/d)^); kq = ki * c/d; gcosf = c / kq; gsf = (b + kq) / ki; pha_imbalance = atan(gsf / gcosf) * 18 / pi; amp_imbalance = abs(complex(gcosf, gsf)); Copyright 1 by MSK. Publication of any part of this document should be agreed by the authors

5 Test Results Fig4 Workg status of ACC1 Table1 Calibration results of different pot number I Q K i K q g φ / deg Gradient / MV/m 3 pots e e pots e e pots e e pots e e pots e e IQ put from the feed forward table, set pot gradient = 1 MV/m IQ put from the klystron forward signal measurement, set pot gradient = 1 MV/m Fig5 3 pots put and put IQ put from the feed forward table, set pot gradient = 1 MV/m IQ put from the klystron forward signal measurement, set pot gradient = 1 MV/m Copyright 1 by MSK. Publication of any part of this document should be agreed by the authors

6 Fig6 8 pots put and put x 1 4 IQ put from the feed forward table, set pot gradient = 5 MV/m IQ put from the klystron forward signal measurement, set pot gradient = 5 MV/m x Fig7 16 pots put and put x 1 4 IQ put from the feed forward table, set pot gradient = 5 MV/m IQ put from the klystron forward signal measurement, set pot gradient = 5 MV/m x Fig8 3 pots put and put IQ put from the feed forward table, set pot gradient = 1 MV/m IQ put from the klystron forward signal measurement, set pot gradient = 1 MV/m Fig9 64 pots put and put Future plan DC can be calibrated durg normal operation by troducg small calibration pulse after the ma RF pulse, see the Fig1. Copyright 1 by MSK. Publication of any part of this document should be agreed by the authors

7 5 x 14 Calibration pulse after the normal RF pulse by feed forward table Feed forward signal for normal RF pulse Amplitude / arbitrary unit Calibration pulse Time / μs Fig1 Calibration pulse References [1]. Personal discussion with Stefan Simrock Copyright 1 by MSK. Publication of any part of this document should be agreed by the authors