ESE 271 / Spring 2013 / Lecture 14
Last time: Phasor analysis with sources of different frequencies
Case 1:
Then we know what to do: build phasor circuit and find
then
Case 2:
Now we can not build phasor circuit containing both sources since impedances depend on frequency but we can use superposition principle and treat one source at a time.
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ESE 271 / Spring 2013 / Lecture 14
Transfer function.
Specifies response of linear circuit to sine wave signal of certain frequency. Linear circuit
Transfer function
‐ Phasor of input signal
‐ Phasor of output signal
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ESE 271 / Spring 2013 / Lecture 14
Transfer function of RC circuit.
Phasor circuit
‐ Magnitude of transfer function
‐ Phase of transfer function
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ESE 271 / Spring 2013 / Lecture 14
Magnitude frequency response of RC circuit.
Decibel (dB) scale.
‐ dB scale
Let’s introduce corner (3dB, cutoff) frequency:
‐ dB scale
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ESE 271 / Spring 2013 / Lecture 14
Magnitude frequency response of RC circuit.
Bode plot.
Sine wave with frequency:
Goes through the circuit almost unchanged
Gets attenuated
This circuit is passive low pass filter of the first order
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ESE 271 / Spring 2013 / Lecture 14
Phase frequency response of RC circuit.
Bode plot.
3dB frequency
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ESE 271 / Spring 2013 / Lecture 14
Example.
Almost unchanged
Amplitude decreased 100 times
Time delay between input and output signal becomes T/4.
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ESE 271 / Spring 2013 / Lecture 14
Transfer function of RL circuit.
Phasor circuit
Corner frequency
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ESE 271 / Spring 2013 / Lecture 14
Magnitude frequency response of RL circuit.
Bode plot.
This circuit is passive high pass filter of the first order.
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ESE 271 / Spring 2013 / Lecture 14
Phase frequency response of RL circuit.
Bode plot.
3dB frequency
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ESE 271 / Spring 2013 / Lecture 14
Example.
Amplitude decreased 100 times
Time delay
Almost unchanged
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ESE 271 / Spring 2013 / Lecture 14
Magnitude and Phase frequency response of:
1.
2.
3.
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ESE 271 / Spring 2013 / Lecture 14
Power delivered to complex impedance Z
Assume that there were no energy stored at
Then the energy delivered by time t is:
where
‐ instantaneous power
Energy delivered during period will be:
Average power delivered:
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ESE 271 / Spring 2013 / Lecture 14
Average Power delivered to Z
zero
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ESE 271 / Spring 2013 / Lecture 14
Average Power delivered to Z
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ESE 271 / Spring 2013 / Lecture 14
Root Mean Square (RMS)
Let’s consider resistor
Case 1:
Case 2:
Periodic signals (not necessarily sine waves)
Case 2a:
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ESE 271 / Spring 2013 / Lecture 14
Complex Power
Let’s introduce RMS phasors:
Definition of complex power
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ESE 271 / Spring 2013 / Lecture 14
Power absorbed by Z
Resistive part of total impedance
Reactive component of complex impedance does not absorb any power on average.
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