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BELL SYSTEM TECHNICAL JOURNAL 



case transducer are sorted* into voltage slices (the treads of the staircase), 

 and all signals within plus or minus half a step of the midvalue of a sUce are 

 replaced in the output by the midvalue. The corresponding output when 

 the input is a smoothly varying function of time is illustrated in Fig. 2. 

 The output remains constant while the input signal remains within the 

 boundaries of a tread and changes abruptly by one full step when the signal 

 crosses the boundary. It is not within the scope of the present paper to 

 discuss the internal mechanism of a staircase transducer, which may have 

 many different physical embodiments. We are concerned rather with the 

 distortion produced by such a device when operating perfectly. 



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The distortion or error consists of the difference between the input and 

 output signals. The maximum instantaneous value of distortion is half of 

 one step, and the total range of variation is from minus half a step to plus 

 half a step. The error as a function of input signal voltage is plotted in 

 Fig. 3 and a typical variation with time is indicated in Fig. 2. If there is a 

 large number of small steps, the error signal resembles a series of straight 

 lines with varying slopes, but nearly always extending over the vertical 

 interval between minus and plus half a step. The exceptional cases occur 

 when the signal goes through a maximum or minimum within a step. The 

 limiting condition of closely spaced steps enables us to derive quite simply 



