Speeding Things Up
Resistors and Capacitors together
Dr. Lu’s Guest Lecture
Activity
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Work through today’s activity
What Have We Learned About
RC Circuits?
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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?
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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?
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How did the rise time compare with the decay
time for the first circuit?
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What were your rise times for
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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
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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
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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
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Important notes from Turton
and Lu
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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
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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