Download Transient PSpice Analysis (7.4)

Transient PSpice Analysis (7.4)
Dr. Holbert
April 26, 2006
ECE201 Lect-23
1
Typical Transient Problems
• What is the voltage as a capacitor discharges to
zero?
• What is the voltage as a capacitor charges from
one voltage (often zero) to another constant
voltage?
• How does the current through an inductor increase
from zero to a final value?
• How does the current through an inductor
decrease from an initial value to zero?
ECE201 Lect-23
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More Typical Problems
• What are the transient and AC steady-state
responses of an RC circuit to a sinusoidal
source?
• What are the transient and AC steady-state
responses of an RL circuit to a sinusoidal
source?
ECE201 Lect-23
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Solutions
• Changes in capacitor voltages and inductor
currents from one value to another are
easily solved.
• Changes in other voltages or currents in the
circuit may or may not be easy to solve
directly; they are all easy to solve using
Laplace transforms (EEE 302).
ECE201 Lect-23
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More Solutions
• Steady-state responses to sinusoidal sources
are easy to find using AC steady-state
analysis.
• Transient responses to sinusoidal sources
are hard to find directly; they are easier to
find using Laplace transforms.
ECE201 Lect-23
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Example Problems:
Changes from one value to another
• Computer RAM
– Refresh time
– Write time
• Stator coil on a motor
– Response to a step in current
ECE201 Lect-23
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Computer RAM-1 Bit
3.3V
Precharge
Data
Q1
Q2
Sense Amp
C
+
Vout
–
ECE201 Lect-23
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How the RAM Works
• When the Precharge line is high (> 3V) and
the Data line is low (~0V), transistor Q1 is
on and the capacitor charges up to 3V.
• If the Data line goes high after the capacitor
is charged, then Q2 turns on and the
capacitor discharges.
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RAM Discharge
• With Q1 and Q2 off, the capacitor holds a
charge that represents the stored data bit.
• This charge leaks through Q2, the input of
the sense amplifier, and the capacitor.
• To determine the time before a refresh is
necessary, we can use a simple equivalent
circuit.
ECE201 Lect-23
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RAM Discharge Equivalent Circuit
+
1MW
1000pF
v(t)
–
The 1MW resistor models the parallel
combination of the off resistance of Q2, the
input resistance of the sense amplifier, and the
leakage resistance of the capacitor.
ECE201 Lect-23
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What is the time constant for this
circuit?
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The RAM Discharge Time
• The RAM discharge time is the time
required for the capacitor to discharge to a
given voltage from an initial voltage of 3V.
• What is the initial voltage?
• What is the DC steady state (final) voltage?
• What does the capacitor voltage v(t) look
like?
ECE201 Lect-23
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Capacitor Voltage
v(t) = 3Ve-t/RC
3
v(t)
2.5
2
1.5
1
0.5
0
0
0.001
0.002
0.003
0.004
0.005
t
ECE201 Lect-23
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Refresh Rate
Suppose we must refresh before v(t) drops
below 1.5V. How long can we wait before a
refresh?
3
v(t)
2.5
2
t = 0.693ms
1.5
1
0.5
0
0
0.001
0.002
0.003
0.004
0.005
t
ECE201 Lect-23
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RAM Precharge
• With Q2 off, Q1 is turned on to charge the
capacitor.
• The current to charge the capacitor comes
through Q1.
• To determine the time necessary to
precharge the capacitor, we use a simple
equivalent circuit.
ECE201 Lect-23
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RAM Precharge Equivalent
Circuit
10W
3.3V
+
–
+
v(t)
1000pF
–
The 10 W resistor models the “on” resistance
of Q1.
ECE201 Lect-23
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What is the time constant for this
circuit?
ECE201 Lect-23
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The RAM Precharge Time
• The RAM precharge time is the time
required for the capacitor to charge to a
voltage of 3V from an initial voltage of 0V.
• What is the initial voltage?
• What is the DC steady state (final) voltage?
• What does the capacitor voltage v(t) look
like?
ECE201 Lect-23
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Capacitor Voltage
v(t)
v(t) = 3.3V(1-e-t/RC)
3.5
3
2.5
2
1.5
1
0.5
0
0
1E-08
2E-08
3E-08
4E-08
5E-08
t
ECE201 Lect-23
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Precharge Time
v(t)
Suppose we must precharge the capacitor to
3V. How long does this take?
3.5
3
2.5
2
1.5
1
0.5
0
t = 24.0ns
0
1E-08
2E-08
3E-08
4E-08
5E-08
t
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PSpice Defibrillator Example
•
•
•
•
•
Start PSpice and enter circuit diagram
Set capacitor and inductor initial conditions
Setup Transient analysis, 0.01 ms step to 15 ms end
Run simulation; Probe starts automatically
Plot: (1) 50W resistor voltage, (2) capacitor voltage,
and (3) clockwise inductor current
• Find peak heart voltage and current
• Determine charging time constant ()
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Heart Defibrillator Circuit
t=5ms
t=5ms
50 mH
20 W
30 µF
+
–
6000 V
50 W
ECE201 Lect-23
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