Transcript class19
Speeding Things Up Resistors and Capacitors together Dr. Lu’s Guest Lecture Activity Work through today’s activity What Have We Learned About RC Circuits? When you decrease the capacitance in an RC circuit (using capacitor C in place of capacitor A in the activity), what happens to the rise time? Halving the capacitance resulted in what precise effect on the rise time? When you increase the resistance in an RC circuit (using 4.7 MW in place of 2.2 MW), what happens to the rise time? Slightly more than doubling the resistance resulted in what precise effect on the rise time? What Have We Learned About Rise Time? How did the rise time compare with the decay time for the first circuit? What were your rise times for Is this similar to what you observed in the keyboard activity? Capacitor A and 2.2 MW Resistor? Capacitor C and 2.2 MW Resistor? Capacitor C and 4.7 MW Resistor? Compare to t = RC = (0.10 mF)(2.2 MW) = 0.22 s t = RC = (0.05 mF)(2.2 MW) = 0.11 s t = RC = (0.05 mF)(4.7 MW) = 0.24 s The Relationship between Rise Time and Time Constant Rise time Dt defined by Dt = t90 – t10 = t(V=0.90V0) – t(V=0.10V0) Time constant t defined by V(t) = V0 (1 – e–t/t) (for charging circuit) So, 0.90 V0 = V0 (1 – e–t90/t) ln (e–t90/t) = ln (1 – 0.90) = ln (0.10) t90 = – t ln(0.10) t10 = – t ln(0.90) Dt = t ln(0.90) – t ln(0.10) = t ln(0.90/0.10) = t ln 9 Summary of RC Circuits For discharging, VC(t) = V0e-t/t For charging, VC(t) = V0 (1 - e-t/t) q(t) = C VC(t) in each case time constant t = RC = Dt/(ln 9) = Dt/2.20 At any time in charging circuit, V0 = VC(t) + VR = VC(t) + iR At any time in discharging circuit, 0 = VC(t) + VR = VC(t) + iR Why do we care about rise time? Rise time limits speed of signal processing/transfer Rise time limits speed of accessing electronic memory Rise time means that shrinking does not always result in faster processes Interconnects and capacitance Interconnects are “wires” (now strips of conductor) between circuit elements Interconnects run along edges of devices, separated by an insulator Charge carriers in interconnect attract opposite charges in device below them Voila! A capacitor Important notes from Turton and Lu Capacitors, resistors, and transistors are key components in modern electronic devices Challenge to create 2-dimensional circuits (or at least have all connections in 2D), so some (Lu) are moving toward 3D devices Shrinking devices saves $$ but poses problems like RC rise time, heat, new production methods, finite depletion regions, electromigration NO PHYSICAL LIMITS REACHED YET More notes from Turton and Lu Speed isn’t going to be drastically increased by shrinking components, due to RC complications We can, however, use materials with “faster” charge carriers Resistance due to collisions caused by imperfect crystal structure Materials with lower resistance may work better If fewer conduction states allowed to electron, it will be less likely to change direction