University:
Kentucky State University
Course:
PHY 212 | General Physics II
Academic year:

2022
Views:

260

Pages:

34
Author:

Arielle Armstrong

Chapter #12: Two-Port Networks: Cascading: two twoport networks connected in cascade • Parameters: Single-Port Network: singleport network with current i flowing into port a and current i flowing out of port b ia = -ib singleport network with a resistor Two-Port Network: twoport network with input port a,b and output port c,d ia = i1 ic = i2 → Multi-port Network: [Image of a multi-port network] ← we won't deal with it! → back to the single-port network: • Mesh Analysis: (N) # of equations Z11I1 + Z12I2 + ... + Z1NI_N = V1 Z21I1 + Z22I2 + ... + Z2NI_N = V2 ... ZN1I1 + ZN2I2 + ... + ZNNI_N = VN Zij (s) is the impedance. → Coefficients Matrix: Z11 Z12 ... Z1N Z21 Z22 ... Z2N ... ... ... ... ZN1 ZN2 ... ZNN → determinant: Δz = |Z| = |Z11 Z12 ... Z1N| |Z21 Z22 ... Z2N| |... ... ... ...| |ZN1 ZN2 ... ZNN| No independent source. I1 = |0 -40 -10| |-1 45 -5| |0 -5 35| = -0.1115 A y₁₂ = ΔI₁/V₂|V₁=0 = I₁/1 = -0.1115 S Note: When y₁₂ = y₂₁, it's called a "bilateral CKT". I₂ = |50 0 -10| |-40 -1 -5| |-10 0 35| = -0.1269 A y₂₂ = ΔI₂/V₂|V₁=0 = I₂/1 = 0.1269 S [Image of a circuit with admittances] * Another method to find Y (for simple CKTS only): * Using Nodal analysis: * Convert impedances to admittances Nodal equations: ``` 0.15V₁ - 0.05V₂ - 0.1V₃ = I₁ -0.05V₁ - 0.25V₂ + 0.2V₃ = I₂ -0.1V₁ - 0.2V₂ + 0.325V₃ = 0 ``` 3 eq → 2 eq From V₃ = 0.31V₁ + 0.2V₂