Solve exercise D7.18 with R =10 Ω, C = 100 nF and T = 10 ns. Justify whether or not this system will work?
Exercise 7.18
This problem addresses the issue of capacitive loading on a high-speed serial transmission line like SPI. The SPI ports of two 9S12s are connected with a VERY long cable. We will model this cable as a single resistor in series with a capacitor, as shown in Figure 7.63. For this question, assume an ideal transmitter (output impedance of 0) and an ideal receiver (input impedance of infinity). Let the resistance R be 1 Ω, and the capacitance C be 10 nF. Consider a 5-V 100-ns pulse (T = 100 ns) on the output of the transmitter (labeled as Vin) as might occur with a 5-Mbps SPI transmission. Derive an equation for Vout as a function of time for the first 100 ns. Show your work. Calculate values for Vout at time equals 0 and time equals 100 ns. Create a Vin versus time sketch similar to the right of Figure 7.63, and add a sketch of Vout on this same plot. Show both 0 to time T and time T to time 2T.
Figure 7.63
