Round of 16. 4-Terminal Networks and Control Theory
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a. Supplementary on Filter Circuits
1. 2-Terminal Networks (2-terminal network)
⑴ Complex Angular Frequency
① Refers to (α + jω) which includes α in the existing angular frequency jω
② Represents an impedance Z(α + jω) as Z(s)
○ Example : Impedance of a coil is represented as sL, impedance of a capacitor is represented as 1/sC
○ Example : Impedance of a series circuit
○ Example : Impedance of a parallel circuit
③ Zero : Refers to the value of s that makes Z(s) = 0, indicating a short-circuit state of the circuit, represented as ‘O’
○ Example : Zero of a coil is s = 0, zero of a capacitor is s = ∞
④ Pole : Refers to the value of s that makes Z(s) = ∞, indicating an open-circuit state of the circuit, represented as ‘×’
○ Example : Pole of a coil is s = ∞, pole of a capacitor is s = 0
⑵ Feedback Circuit
⑶ Resistive Circuit
2. 4-Terminal Networks (4-terminal Network)
⑴ Overview
① Generally, an electrical network has two terminals each for input and output
○ Example : T-type, π-type, ladder-type, lattice-type, transformer, transmission line
② Active 4-Terminal Network, Passive 4-Terminal Network
○ Active 4-Terminal Network : A 4-terminal network that includes electromotive force within the circuit
○ Passive 4-Terminal Network : A 4-terminal network composed only of passive components
⑵ Impedance Parameters (Z Parameters)
Figure 1. Representation of Impedance Parameters
① Mathematical Expression : Provable by induction
② Impedance Matrix (Z Matrix) : Coefficient matrix of the right-hand side
○ Z11, Z12, Z21, Z22 have dimensions of impedance, hence called impedance parameters
○ Z11 : Open-circuit driving impedance at terminals 1-1’
○ Z21 : Forward transmission impedance in open-circuit condition
○ Z22 : Open-circuit driving impedance at terminals 2-2’
○ Z12 : Reverse transmission impedance in open-circuit condition
⑶ Admittance Parameters (Y Parameters)
Figure 2. Representation of Admittance Parameters
① Mathematical Expression : Provable by induction
② Admittance Matrix (Y Matrix) : Coefficient matrix of the right-hand side
○ Y11, Y12, Y21, Y22 have dimensions of admittance, hence called admittance parameters
○ Y11 : Short-circuit driving admittance at terminals 1-1’
○ Y21 : Forward transmission admittance in short-circuit condition
○ Y22 : Short-circuit driving admittance at terminals 2-2’
○ Y12 : Reverse transmission admittance in short-circuit condition
⑷ 4-Terminal Matrices (Transmission Parameters)
Figure 3. Representation of 4-Terminal Matrices
① Mathematical Expression : Provable by induction
② Parameters
○ A : Open-circuit reverse voltage gain (voltage ratio)
○ B : Short-circuit reverse transmission impedance
○ C : Open-circuit reverse transmission impedance
○ D : Short-circuit reverse current gain
○ AD - BC always holds : (Note) AD - BC represents the determinant of the matrix
⑸ Image Parameters
① Image Impedance : Denoted as Z01, Z02
Figure 4. Image Impedance
○ Impedance Matching : Process of connecting two image impedances
○ Well-organized image impedances lead to,
② Image Transfer Constant θ
3. Electric Control Theory
4. Filter Circuits
⑴ Overview
① Filter Circuit : A circuit that selects or blocks specific frequency ranges
② Passive Filter : A circuit made by connecting passive components (R, L, C)
③ Active Filter : A circuit made by connecting passive components and active elements like transistors, operational amplifiers
④ Resistance Filter Circuit : A filter circuit composed of R(≠0), L, and C combinations
○ Example : Low-pass filter, high-pass filter, band-pass filter, band-stop filter
⑤ L-C Type Filter : A pure reactance filter circuit composed only of L and C
○ Example : L-C Low-pass filter, L-C High-pass filter, L-C Band-pass filter
○ In L-type basic circuit, Z1 and Z2 should have a relationship in reverse, that is, Z1Z2 = K2, K : Nominal impedance
⑥ Pass-Band
⑦ Stop-Band
⑧ Transition Region
⑵ Low-Pass Filter
Figure 5. Bode Plot (Amplitude) for a Low-Pass Filter
Figure 6. Bode Plot (Phase) for a Low-Pass Filter
Figure 7. Low-Pass Filter with R, C (left) or R, L (right)
⑶ High-Pass Filter
Figure 8. Bode Plot (Amplitude) for a High-Pass Filter
Figure 9. Bode Plot (Phase) for a High-Pass Filter
Figure 10. High-Pass Filter with R, C (left) or R, L (right)
⑷ Band-Pass Filter
Figure 11. Normalized Plot for a Band-Pass Filter
Figure 12. Pass-Band Filter with Low-Pass and High-Pass Filters
① Center Frequency fc
② Quality Factor (Q-factor)
⑸ Band-Stop Filter
Figure 14. Band-Stop Filter
① Stop-Band
Input: 2017.07.24 13:01
Edited: 2018.01.13 20:26