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Round of 16. 4-Terminal Networks and Control Theory

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1. 2-Terminal Networks

2. 4-Terminal Networks

3. Electric Control Theory

4. Filter Circuits


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

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