Answer Happy

(a) Name four advantages of representing a signal in the form of time or frequency in the digital measurement systems. (marks 4) (b) The angular velocity (w), measured in revolutions per second (rps) of a wheel is to be measured. The angular velocity measurement is to be performed using the sprocket sensor assembly depicted in Figure Q1. Sketch a digital circuit using counters, digital logic gates and a timer that allows for the measurement of the angular velocity using the frequency measurement approach. (marks 4) electronic sensor Figure Q1. Sprocket sensor assembly mounted on a wheel. (c) Based on your sketch of the measurement circuit in sub-question Q1 (b) derive an equation that relates the number of counts in the counter (Nx) to the three variables measurement time (TM), the number of sprocket teeth Ny and w. (marks 4) (d) The design specification of the measuring circuit requires relative measurement errors (0) of 18 S 1% for angular velocities in the range of Irps SW s 100rps. Determine the minimal required number of sprocket teeth Nmin for 8 to stay within the specified limits when I'm = 100ms. Consider only the error due to counting in your calculation. (marks 4) (e) If instead of frequency measurement approach, time period measurement approach is used, under consideration of your findings in sub-question Q2 (d), determine the value of the frequency of frequency generator of the digital measurement circuit for the measurement the period of time, to give the same relative quantisation error as frequency measurement approach when the angular speed is w = 2.5rps. (marks 4)