ESE 271 / Spring 2013 / Lecture 10
Ideal linear passive circuit elements.
Does not store energy, i.e. has no memory
Resistor
Capacitor
p
p
Dissipates power:
Does not dissipate power.
Stores energy in the form of electric field.
Voltage drop across capacitor can not be changed abruptly.
I d
Inductor
Does not dissipate power.
Stores energy in the form of magnetic field
form of magnetic field.
Current through inductor can not be changed abruptly.
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ESE 271 / Spring 2013 / Lecture 10
Transient response ‐ Resistive circuit.
Resistor does not store energy and, thus, gy
,
,
has no memory. Current and voltage in resistor can be changed abruptly.
There are no transients, circuit containing id l i t i
ideal resistor immediately assumes new di t l
steady‐state condition. 2
ESE 271 / Spring 2013 / Lecture 10
Transient response ‐ Capacitor.
Voltage across capacitor can not be changed abruptly.
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ESE 271 / Spring 2013 / Lecture 10
Transient response ‐ Inductor.
Current through inductor can not be changed abruptly.
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ESE 271 / Spring 2013 / Lecture 10
Transient response – Charging capacitor.
“Force”
1. Solve unforced equation and find natural solution:
2. Plug natural solution with A(t) into complete equation and use initial condition:
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ESE 271 / Spring 2013 / Lecture 10
Transient response – Charging capacitor.
Solve forced equation using functional form of the natural solution.
Find B from initial conditions:
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ESE 271 / Spring 2013 / Lecture 10
Transient response – Charging capacitor.
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ESE 271 / Spring 2013 / Lecture 10
Response of RC–circuit to square pulse
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ESE 271 / Spring 2013 / Lecture 10
Response of RC–circuit to square pulse
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ESE 271 / Spring 2013 / Lecture 10
Response of RC–circuit to square wave input
Period of square wave
Period of square wave
Time constant
Capacitor can be fully charged and discharged during half period
duty cycle is shown
Capacitor is never fully charged/discharged – some kind of new steady‐state condition (AC).
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ESE 271 / Spring 2013 / Lecture 10
Response of RC–circuit to sine wave input
Amplitude
Period
Angular frequency
Frequency
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ESE 271 / Spring 2013 / Lecture 10
Sine wave voltage and current in resistor.
No energy storage, no delays, no transients.
Current repeats voltage.
Current repeats voltage.
What about power?
N it i i t t
Now it is instant power:
Frequency doubled
Power dissipated
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ESE 271 / Spring 2013 / Lecture 10
Sine wave voltage and current in capacitor.
Energy storage in capacitor leads to delay between current and voltage waveforms.
Current is leading by:
Voltage is lagging by quarter period.
“need current to get voltage”
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ESE 271 / Spring 2013 / Lecture 10
Sine wave voltage and current in inductor.
Energy storage in inductor leads to delay between current and voltage waveforms.
Voltage is leading by:
Current is lagging by quarter period.
“need voltage to get current”
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ESE 271 / Spring 2013 / Lecture 10
Phase of harmonic (sine wave) signal
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ESE 271 / Spring 2013 / Lecture 10
AC power in capacitor.
Instant power:
No power dissipated
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ESE 271 / Spring 2013 / Lecture 10
AC power in inductor.
Instant power:
No power No
power
dissipated
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ESE 271 / Spring 2013 / Lecture 10
Series connection of C and L under harmonic excitation.
Out of phase
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ESE 271 / Spring 2013 / Lecture 10
Series connection of R, C and L under harmonic excitation.
Energy dissipation
Note that when
Note that when
there is
there is Energy exchange
hence
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