Lecture Electric circuit theory: First-order crcuits - Nguyễn Công Phương

Lecture Electric circuit theory: First-order crcuits include all of the following: Introduction to transient analysis, initial conditions, the source-free RC circuit, the source-free RL circuit, step response of an RC circuit, step response of an RL circuit, the classical method, first-order Op Amp circuits

Electric Circuit Theory

First-Order Circuits

Nguy ễ n Công Ph ươ ng

I Basic Elements Of Electrical Circuits

II Basic Laws

III Electrical Circuit Analysis

IV Circuit Theorems

V Active Circuits

VI Capacitor And Inductor

VII First-Order Circuits

VIII.Second Order Circuits

IX Sinusoidal Steady State Analysis

X AC Power Analysis

XI Three-phase Circuits

XII Magnetically Coupled Circuits

XIII.Frequency Response

XIV.The Laplace Transform

XV Two-port Networks

First-Order Circuits

1 Introduction to Transient Analysis

2 Initial Conditions

3 The Source-free RC Circuit

4 The Source-free RL Circuit

5 Step Response of an RC Circuit

6 Step Response of an RL Circuit

7 The Classical Method

8 First-order Op Amp Circuits

Introduction to Transient Analysis (1)

+ –

0

+ –

t v

Introduction to Transient Analysis (2)

Open-circuit Not open-circuit Open-circuit

Old steady-state Transient New steady-state

-state

Old steady-state Transient New steady-state

-state

Introduction to Transient Analysis (3)

First-Order Circuits

1 Introduction to Transient Analysis

2 Initial Conditions

3 The Source-free RC Circuit

4 The Source-free RL Circuit

5 Step Response of an RC Circuit

6 Step Response of an RL Circuit

7 The Classical Method

8 First-order Op Amp Circuits

Initial Conditions (2)

• 1 st switching rule/law: the current (magnetic flux) in an

inductor just after switching is equal to the current (flux) in the same inductor just prior to switching

i L (0 + ) = i L (0 – )

λ(0 + ) = λ(0 – )

• 2 nd switching rule/law: the voltage (electric charge) in a

capacitor just after switching is equal to the voltage (electric charge) in the same capacitor just prior to switching

v C (0 + ) = v C (0 – )

q(0 + ) = q(0 – )

Initial Conditions (3)

Ex 1

The switch has been at A for a long time,

and it moves to B at t = 0; find I0?

The switch has been at A for a long time,

and it moves to B at t = 0; find I0?

+ –

20 V

A

B

Initial Conditions (4)

Ex 3

The switch has been at A for a long time,

and it moves to B at t = 0; find V0?

The switch has been at A for a long time,

and it moves to B at t = 0; find V0?

+ –

20 V

0.1 mF V0

+ –

A

B

First-Order Circuits

1 Introduction to Transient Analysis

2 Initial Conditions

3 The Source-free RC Circuit

4 The Source-free RL Circuit

5 Step Response of an RC Circuit

6 Step Response of an RL Circuit

7 The Classical Method

8 First-order Op Amp Circuits

The Source-free RC Circuit (1)

0 0

→ =

0 0

(0)

t

t RC t

The Source-free RC Circuit (2)

C

C

+ –

The Source-free RC Circuit (3)

Ex 2

E = 24 V; R1 = 8 Ω; R2 = 12 Ω; C = 0.01F;

the switch has been closed for a long time,

and it is opened at t = 0; find vC for t ≥ 0? R1 C

R2

vC

+ –

t C

First-Order Circuits

1 Introduction to Transient Analysis

2 Initial Conditions

3 The Source-free RC Circuit

4 The Source-free RL Circuit

5 Step Response of an RC Circuit

6 Step Response of an RL Circuit

7 The Classical Method

8 First-order Op Amp Circuits

The Source-free RL Circuit (1)

0 0

→ =

0 0

The Source-free RL Circuit (2)

Ex.

E = 24 V; R1 = 5 Ω; R2 = 4 Ω; R3 = 12 Ω;

L = 0.01H; the switch has been closed for

a long time, and it is opened at t = 0;

First-Order Circuits

1 Introduction to Transient Analysis

2 Initial Conditions

3 The Source-free RC Circuit

4 The Source-free RL Circuit

5 Step Response of an RC Circuit

6 Step Response of an RL Circuit

7 The Classical Method

8 First-order Op Amp Circuits

Step Response of an RC Circuit (1)

E2

R

t = 0

+ –

+ –

E1

C

v

+ –

0

t

v t V

Step Response of an RC Circuit (2)

E2

R

t = 0

+ –

+ –

E1

C

v

+ –

Forced response/steady-state response

Natural response/transient-state response

First-Order Circuits

1 Introduction to Transient Analysis

2 Initial Conditions

3 The Source-free RC Circuit

4 The Source-free RL Circuit

5 Step Response of an RC Circuit

6 Step Response of an RL Circuit

7 The Classical Method

8 First-order Op Amp Circuits

Step Response of an RL Circuit (1)

t L

t = 0

+ –

+ –

E1

Step Response of an RL Circuit (2)

Forced response/steady-state response

Natural response/transient-state response

E2

R

L i

t = 0

+ –

+ –

E1

i

1 0

E I

v

10

E I

R

=

2

E R

First-Order Circuits

1 Introduction to Transient Analysis

2 Initial Conditions

3 The Source-free RC Circuit

4 The Source-free RL Circuit

5 Step Response of an RC Circuit

6 Step Response of an RL Circuit

7 The Classical Method

8 First-order Op Amp Circuits

The Classical Method (1)

E2

R

L i

t = 0

+ –

+ –

E1

2 1 2

( )

R t L

E I

R t L

The Classical Method (2)

E2

R L i

L

→ = −

R t L n

+ –

E1

The Classical Method (3)

t RC

v = E + Ae−

1 0

R

C vn

+ –

The Classical Method (4)

E2

R L i

+ –

E1

v

+ –

i = Ae−

2 0

1 Write the general form

2 Find the initial

5 Find the integration

constant

6 Write the complete

response

The Classical Method (5)

Ex 1

The switch has been at A for a long time,

and it moves to B at t = 0; find v for t ≥ 0?

t RC

1 Write the general form

2 Find the initial condition

3 Find the forced response

4 Deactivate source(s), find the

natural response (with the unknow integration

constant)

5 Find the integration constant

6 Write the complete response

The Classical Method (6)

0

36V 12V

100 Ω 0.05 mF

The Classical Method (7)

Ex 2

The switch has been at A for a long

time, and it moves to B at t = 0;

t RC

1 Write the general form

2 Find the initial condition

3 Find the forced response

4 Deactivate source(s), find the

natural response (with the unknow integration

constant)

5 Find the integration constant

6 Write the complete response

The Classical Method (8)

Ex 3

The switch has been at A for a long time,

and it moves to B at t = 0; find i for t ≥ 0?

1 Write the general form

2 Find the initial condition

3 Find the forced response

4 Deactivate source(s), find the

natural response (with the unknow integration

constant)

5 Find the integration constant

6 Write the complete response

f

20

400.5

R

t t

t L

The Classical Method (9)

0

6A 5A

The Classical Method (10)

Ex 4

The switch has been at A for a long time,

and it is opened at t = 0; find i for t ≥ 0? 5 A

0.25 H

40 Ω 30 Ω

t = 0 i

R

t t

t L

First-Order Circuits

1 Introduction to Transient Analysis

2 Initial Conditions

3 The Source-free RC Circuit

4 The Source-free RL Circuit

5 Step Response of an RC Circuit

6 Step Response of an RL Circuit

7 The Classical Method

8 First-order Op Amp Circuits

First-Order Op Amp Circuits (1)

Ex 1

The switch has been at A for a long time,

and it moves to B at t = 0; find vo for t ≥ 0?

First-Order Op Amp Circuits (2)

Ex 1

The switch has been at A for a long time,

and it moves to B at t = 0; find vo for t ≥ 0?

20

5 t V

3 3

First-Order Op Amp Circuits (3)

First-Order Op Amp Circuits (5)

1 µF