Download 305221, 226231 Computer Electrical Circuit Analysis

305221, 226231
Computer Electrical Circuit
Analysis
การวิเคราะห ์วงจรไฟฟ้าทาง
คอมพิวเตอร ์
ณรงค์3(2-3-6)
ชยั
มุ่งแฝงกลาง
คมกริ ช มาเที่ยง
สัปดาห์ที่ 10
Frequency Response
(First-Order circuits, Step response)
Outline
1
Objectives
2
First Order Circuit (RC)
3
First Order Circuit (RL)
4
Step Response of an RC
5
Step Response of an RL
Objectives
 เพื่อให้ นิสิตมีความรู้ ความเข้ าใจเกีย่ วกับวงจร(อนุพนั ธ์ )อันดับหนึ่ง
(First Oder
Circuit)
 A circuit comprising a resistor and capacitor (RC Circuit).
 A circuit comprising a resistor and an inductor (RL Circuit).
่
่
 เพือให้
นิสต
ิ มีความรู ้ความเข้าใจเกียวก
บ
ั ผลการตอบสนองแบบ
ทันทีทันใด(Step Response)
 Step Response of an RC Circuit.
 Step Response of an RL Circuit.
What is first order circuit ?
 A
first-order circuit is characterized by a first-order
differential equation.
Outline
1
Objectives
2
First Order Circuit (RC)
3
First Order Circuit (RL)
4
Step Response of an RC
5
Step Response of an RL
First Order Circuit (RC)
 A source-free RC circuit occurs when its dc source is
suddenly disconnected. The energy already stored in the
capacitor is released to the resistors.
+
DC
-
Example #1
Source-free RC Circuit
1. Initial condition :
Node
+
Vo
-
2. Apply KCL:
Source-free RC Circuit (cont.)
First-order differential equation :
Rearrange the in a terms as :
3. Integrating both sides :
Integration Constant
Source-free RC Circuit (cont.)
Rearrange the in a terms as :
4. Taking powers of ‘e’ produces:
By the initial conditions,
v(0)  A  Vo , Hence,
Natural Response
 The natural response of a circuit refers to the behavior (in
terms of voltages and currents) of the circuit itself, with no
external sources of excitation.
Time Constant
 The time constant (τ )of a circuit is the time required for
the response to decay to a factor of 1 / e or 36.8 percent of its
initial value.
Its implies that t =
τ:
τ
The voltage any time in the term of time constant ( ) :
Time Constant Table
Power & Energy Absorb
Example #2
1. Determine the equivalent resistances (Req):
2. Find the time constant (
τ ):
Example #2 (cont.)
v
3. Obtain ( c ) :
v
4. Obtain ( x ) :
i
5. Obtain ( x ) :
Outline
1
Objectives
2
First Order Circuit (RC)
3
First Order Circuit (RL)
4
Step Response of an RC
5
Step Response of an RL
First Order Circuit (RL)
 A source-free RL circuit occurs when its dc source is
suddenly disconnected. The energy already stored in the
capacitor is released to the resistors.
+
DC
-
Source-free RL Circuit
1. Initial condition :
2. Apply KVL:
Or
Source-free RL Circuit (cont.)
3. Rearrange and integrating gives:
Or
4. Taking powers of ‘e’ produces:
Current Response of RL Circuit
Time Constant :
The current any time in the term of
τ
time constant ( ) :
Voltage across resistor :
Power & Energy Absorb
Example #3
Example #3 (cont.)
Singularity/ Switching Functions
 Singularity functions are functions that either are
discontinuous or have discontinuous derivatives.
Singularity Functions (cont.)
Outline
1
Objectives
2
First Order Circuit (RC)
3
First Order Circuit (RL)
4
Step Response of an RC
5
Step Response of an RL
Step Response of an RC
 When the dc source of an RC circuit is suddenly applied,
the voltage or current source can be modeled as a step
function, and the response is known as “a step response”.
Step Response of an RC (cont.)
1. Initial voltage (V0) condition :
2. Apply KCL:
Or
Step Response of an RC (cont.)
Step Response of an RC (cont.)
Step Response of an RC (cont.)
Complete Response
Complete Response (cont.)
Complete Response (cont.)
Example #4
Example #4 (cont.)
Example #4 (cont.)
Outline
1
Objectives
2
First Order Circuit (RC)
3
First Order Circuit (RL)
4
Step Response of an RC
5
Step Response of an RL
Step Response of an RL
Step Response of an RL (cont.)
1. Let the response be the sum of the transient
response and the steady-state response,
2. The transient response is always a decaying
exponential, that is,
3. The steady-state response is the value of the current a long time
after the switch in Fig. 7.48(a) is closed.
Step Response of an RL (cont.)
Step Response of an RL (cont.)
Step Response of an RL (cont.)
Step Response of an RL (cont.)
Example #5
Example #5 (cont.)
Example #5 (cont.)