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The yoke design is very complicated because it has to do several things:
1) converge the beams at the edges of the picture when the center is correct (eliminates the need for convergence circuits)
2) correct pincushion distortion (or produce a form of pincushion that is easlily correctible)
2a) have modified arctangent distortion that can be corrected by a simple "S" shaped horizontal deflection current component
3) maintain low astigmatism and therefore good focus from center to edge
4) have an apparent center of deflection that can be simulated by a light tower for deposition of the phosphor stripes, thereby having good purity from center to edge
5) have inductance and resistance that is amenable to solid state drive
and probably more that I can't recall
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