Why Scharnhorst could not jam her way clear

Why could Scharnhorst not use electronic countermeasures to jam British radar during the fight with Duke of York?

Her exposed electronic systems were probably damaged early, and British optical fire control remained available even if radar were disrupted.

Scharnhorst's electronic equipment appears to have been damaged early, likely by 6-inch fire. Such guns may not penetrate enough armor to sink a battleship outright, but they can destroy exposed antennas and radars. That makes medium-calibre fire capable of a mission kill even when it cannot produce a sinking. British optical rangefinding also provided a fallback if electronic countermeasures affected radar. Radar remained faster and far less dependent on clear weather, so jamming it would help without making British fire control disappear.