ELECTRIC CIRCUITS ECSE2010 Spring 2003 Class 28

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ELECTRIC CIRCUITSECSE-2010Spring 2003Class 28

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ASSIGNMENTS DUE

• Today (Thursday)
• Activities 28-2, 28-1 (In Class)
• Next Monday
• Homework 10 Due
• Activities 29-1, 29-2 (In Class)
• Next Tuesday/Wednesday
• Activity 30-1 (In Class)

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REVIEW

• Ideal Transformers
• Primary and Secondary Windings No Loss
• Turns Ratio, N N2 / N1
• Dot Convention N gt - N if opposite
• Transformer Rules V2 N V1
• I2 I1 / N
• Refer to Primary ZL gt ZL / N2
• Refer to Secondary VS gt N VS
• ZS gt N2 ZS

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IDEAL TRANSFORMER
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IDEAL TRANSFORMER
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IDEAL TRANSFORMER
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IDEAL TRANSFORMER
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IDEAL TRANSFORMER
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IDEAL TRANSFORMER CKT
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REFERRAL TO PRIMARY
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EXAMPLE
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EXAMPLE
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REFERRAL TO SECONDARY
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EXAMPLE
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EXAMPLE
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POWER TRANSFER
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POWER TRANSFER

• General AC Circuit
• Source Network gt Vs in series with Zs
• Thevenin Equivalent Circuit
• Load Network gt ZL
• For PMAX to ZL
• Want ZL Zs
• Often Helps to Use Transformer
• Provides another Knob

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ACTIVITY 28-2
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ACTIVITY 28-2

• Two Transformers
• Refer to Middle Section
• T1 Refer from Primary to Secondary
• T2 Refer from Secondary to Primary
• Vs,RMS 640 Volts (RMS)
• Find I, gt Calculate V1, V2
• Calculate I1, I2, I4, V3, V4
• Find Ptotal and Efficiency

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ACTIVITY 28-2
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ACTIVITY 28-2
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ACTIVITY 28-2
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ACTIVITY 28-2
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ACTIVITY 28-2
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ACTIVITY 28-2
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ACTIVITY 28-2
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ACTIVITY 28-2
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ACTIVITY 28-2
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ACTIVITY 28-2
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ACTIVITY 28-2
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ACTIVITY 28-2
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ACTIVITY 28-2
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ACTIVITY 28-2
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ACTIVITY 28-2
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MUTUAL INDUCTANCE

• Consider 2 Inductors, L1, L2
• Inductors can be in the same Circuit, or in
  different Circuits
• Magnetic Field of L1 can link with L2 and vice
  versa
• If Magnetic Field changes with time gt Creates
  voltages in linked coils L1, L2
• Refer to this as Mutual Inductance, M
• M is also measured in Henries
• Can show that M 0 lt k lt 1

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MUTUAL INDUCTANCE
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MUTUAL INDUCTANCE
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MUTUAL INDUCTANCE
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MUTUAL INDUCTANCE

• Consider Circuit Model
• v1 L1 di1 / dt M di2 / dt
• v2 L2 di2 / dt M di1 / dt
• Note direction of i1, i2
• Dot convention If Current goes IN to Dot
  Voltage due to Mutual Inductance is Positive
• Replace M with (- M) if dots are on opposite ends
  of Inductors

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TEE MODEL

• Consider a Circuit That Looks Like a Tee
• 3 Ideal inductors
• No mutual inductance

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TEE CIRCUIT
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TEE MODEL
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TEE MODEL

• For a Tee Circuit
• Ideal inductors, no mutual inductance
• Same equations as before
• gt Can Replace Inductors exhibiting Mutual
  Inductance with Tee Model and then do AC Steady
  State Circuit Analysis

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TEE MODEL
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ACTIVITY 28-1
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ACTIVITY 28-1

• Always Wise to Label Nodes
• Can get lost otherwise
• Look for Common Node
• Node a for this circuit
• Replace with Tee Model

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ACTIVITY 28-1
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ACTIVITY 28-1

• Replace with Tee Model
• L1 - M 2.5H j (L1 - M) j 50 ohms
• L2 - M - .4 H j (L2 - M) - j 8 ohms
• (Negative Inductances are not Uncommon when using
  the Tee Model)
• M .5H j M j10 ohms
• Put Back in Original Circuit
• Be Careful!!

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ACTIVITY 28-1
i2
i1
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ACTIVITY 28-1
I2
I1
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ACTIVITY 28-1
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ACTIVITY 28-1