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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?.
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Speeding Things Up Resistors and Capacitors together
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? • Is this similar to what you observed in the keyboard activity? • What were your rise times for • 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