Waveform Comparison
C H Gough
Intoduction
This Note is one of a series, documenting the development of the five Storage Ring Kicker systems for the SLS. The magnetic field is a half-sine pulse of about 6s. The field in these magnets should track in time to at least 0.5% of each other, and preferably much better.
Shape Comparison
To resolve small details on large waveforms, it is possible to use the difference between two large signals of nearly the same form.
This greatly increases resolution, but requires more effort to get clear results. To aid this process for the Storage Ring kickers, perfect half-sine waveforms were compared using the circuit Pspice circuit "Pulse Shape Comparison". The results are shown in Fig.1-5. In general:
an even function with small start and finish transients shows amplitude error only;
an even function with equal start and finish transients in the same direction, after trigger shifting, shows frequency error only;
an odd function shows frequency/phase error;
for a reasonable 0.5% total system error budget, amplitude error should be <0.1%, frequency error <0.5% (L=0.5%
simultaneous and independant with C=0.5%) and trigger error <1.7ns.
Present measurement results show L(magnet)=0.1% and C=0.2%, and the charging voltage is taken as stable to 16 bits. Thus the turn-on and turn-off transients (where both effective trigger delay and effective amplitude are determined) are more troublesome.
A nasty observation is that the four kickers must operate with fixed trigger offsets to account for the finite speed of the electron beam passing through. Thus dynamic adjustment of trigger time requires dynamic time adjustment of the measured signals to compensate.
Fig.1 Amplitude error only, 0.1%
Fig.2 Frequency error 0%, trigger point shifted 2.5ns.
Fig.3 Frequency error 0.1%, trigger point adjusted for minimum start transient, then shifted 2.5ns.
Fig.4 Frequency error 0.1%, trigger point adjusted for symmetric waveform, then shifted 2.5ns.
Fig.5 Frequency error +0.1%, trigger point adjusted for symmetric waveform, amplitude adjusted from -0.2% to 0% in steps of 0.05% (the flattest waveform corresponds to -0.15%)
