ECE201 Lect-23 1

Transient PSpice Analysis (7.4)

Dr. Holbert

April 26, 2006

ECE201 Lect-23 2

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 3

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?

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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).

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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.

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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

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Computer RAM-1 Bit

Q1

Q2 C

Precharge

Data

3.3V

Sense Amp

+

–

Vout

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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.

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RAM Discharge Equivalent Circuit

1M 1000pF

+

–

v(t)

The 1M 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.

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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?

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Capacitor Voltage

v(t) = 3Ve-t/RC

0

0.5

1

1.5

2

2.5

3

0 0.001 0.002 0.003 0.004 0.005

t

v(t)

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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?

0

0.5

1

1.5

2

2.5

3

0 0.001 0.002 0.003 0.004 0.005

t

v(t) t = 0.693ms

ECE201 Lect-23 15

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.

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RAM Precharge Equivalent Circuit

The 10 resistor models the “on” resistance of Q1.

10

1000pF3.3V

+

–

v(t)+–

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What is the time constant for this circuit?

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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?

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Capacitor Voltage

v(t) = 3.3V(1-e-t/RC)

00.51

1.52

2.53

3.5

0 1E-08 2E-08 3E-08 4E-08 5E-08

t

v(t)

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Precharge Time

Suppose we must precharge the capacitor to 3V. How long does this take?

t = 24.0ns0

0.51

1.52

2.53

3.5

0 1E-08 2E-08 3E-08 4E-08 5E-08

t

v(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) 50 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

+–

20

50

30 µF

6000 V

50 mHt=5ms t=5ms