(Review) The principle of superposition (Cont.)

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Prof. Dong‐Weon Lee

MEMS & Nanotechnology Laboratory School of Mechanical Systems Engineering

Chonnam National University

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MEMS@chonnam.ac.kr

(Review) The principle of superposition (Cont.)

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(Review) The principle of superposition: Ex.

Known quantities:

Resistance value, voltage source Find:

Determine the voltage across resistor R

1

2

^R‐V

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(Review) The principle of superposition: Ex.

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(Review) The principle of superposition: Ex. (Cont.)

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(Review) The principle of superposition: Ex.

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(Review) The principle of superposition: Ex. (Cont.)

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(Review) The principle of superposition: Ex. (Cont.)

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One‐port network and equivalent circuits: Network Thévenin equivalent circuits:

Any combination of voltage sources, current sources, and resistors with two terminals is electrically equivalent to a single voltage source V

_T

and a single series resistor R

_T

. For single frequency AC systems the theorem can also be applied to general impedances, not just resistors.

Norton equivalent circuits:

Any collection of voltage sources, current sources, and resistors with two

terminals is electrically equivalent to an ideal current source, I, in parallel with a single resistor, R. For single‐frequency AC systems the theorem can also be

applied to general impedances, not just resistors.

Things to do: Equivalent resistance, Thévenin voltage, Norton current

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Computation of Thévenin and Norton equivalent resistance Methodology

1. Remove load resistor (R

_L

)

2. Remove all independent voltage & current sources

3. Calculate the total resistance between load terminals, with the load removed

①

② ③

②’

It has no relationship to the load

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Thévenin equivalent resistor

Known quantities:

resistance value, source current and voltage Find:

Thévenin equivalent resistance R

_T

V=5V; I=1A; R

₁

=2, R

₂

=2, R

₃

=1, R4=2

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Thévenin equivalent resistor Find:

Thévenin equivalent resistance R

_T

seen by the load R

_L

2 W

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Computing the Thévenin voltage Thévenin voltage:

Open circuit voltage when a load(R

_L

) was removed

개방단자에서 v

_T

=v

_oc

By the KVL

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Computing the Thévenin voltage

Expression by equivalent resistance and voltage Methodology

1. Remove the load, leaving the load terminals open circuited.

2. Define the open‐circuit voltage v

_OC

across the open load terminals.

3. Apply any preferred method (e.g.: nodal analysis) to solve for v

_OC

.

4. The Thévenin voltage is v

_T

= v

_OC

.

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Computing the Thévenin voltage: Ex. open‐circuit voltage Known quantities:

resistance value, source voltage Find:

Thévenin voltage v

_oc

v=12V; R

₁

=1, R

_2 and 3

=10, R

₄

=20

Apply KCL

v

_a

‐ v

_b

= 7.059V = v

_oc

1. Remove the load, leaving the load terminals open circuited.

2. Define the open‐circuit voltage v_OCacross the open load terminals.

3. Apply any preferred method (e.g.: nodal analysis) to solve for v_OC. 4. The Thévenin voltage is v_T= v_OC.

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Computing the Norton current Norton current:

Short circuit current when a load(R

_L

) is replaces with short circuit

Methodology

1. Replace the load with a short circuit.

2. Define the short‐circuit current i

_SC

to be the Norton equivalent current.

3. Apply any preferred method (e.g.: nodal analysis) to solve for i

_SC

.

4. The Norton current is i

_N

= i

_SC

.

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Computing the Norton current Known quantities:

resistance value, source voltage Find:

Norton current i

_cc

24 V

3 A

4 W 12 W

6 W

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Thévenin resistance, voltage and Norton current

Methodology (remind) 1. Remove a load resistance(R_L)

2. Remove all independent voltage and current sources 3. Calculation of total resistance when the load is removed

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Thévenin resistance, voltage and Norton current (Cont.)

Methodology (Remind)

1. 부하를 제거하여 부하 단자를 개방회로로 설정 2. 개방된 부하 단자에 걸리는 개방 전압 v_OC를 정의 3. v_OC를 구하기 위해 node voltage 등의 방법 이용 4. v_T=v_OC

‐ 방법 및 절차

1. 부하를 단락회로로 대체

2. 단락 전류 i_SC를 Norton 등가 전류로 정의 3. 노드 전압법 등을 이용하여 i_SC를 구함 4. i_N=i_SC

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Thévenin equivalent: Ex

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Source transformation

v

_T

=v

_oc

R

_L

=0 Refer a current divider

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Measurement of open‐circuit voltage and short‐circuit current:

Experimental determination

유한 크기의 meter resistance: r

_m

Ideal voltmeter?

Ideal ammeter?

This is very useful technique when we know internal

resistance of measurement system

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Focus on measurements: Experimental determination Known quantities:

resistance value, source current and voltage Find:

Thévenin equivalent resistance R

_T

of an unknown circuit from measurements of open‐circuit voltage and short‐circuit current

measured v

_oc

=6.5V; measured i

_sc

=3.75mA; r

_m

=15W

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Maximum power transfer

Matching

Assumption: v

_T

and R

_T

are fixed

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Maximum power transfer

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