--- title: "Parallel connection of two-port networks" subject: "Filter Design" chapter: 4 key: "semester_5/filter_design:two-port-parallel-connection" source: https://www.bctengineer.com/q/semester_5/filter_design/two-port-parallel-connection site: BCT Engineering --- # Parallel connection of two-port networks Filter Design · Chapter 4: Properties and Synthesis of Passive Networks - Asked in: 2082 Baisakh, 1+4 marks - Video: [22.PARALLEL CONNECTION IN TWO PORT NETWORK ANALYSIS](https://www.youtube.com/watch?v=475ekeJ1Vwo) — Electrical Tutorial - Answer checked by Claude Sonnet 5.5 on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_5/filter_design/two-port-parallel-connection - Whole chapter: https://www.bctengineer.com/md/semester_5/filter_design/chapter-4 ## Question Define two port network. Describe the parallel connection of 2, two port networks with necessary figures and derivation. ## Short answer A two-port network has two terminal pairs with equal and opposite port currents. In a parallel connection, input ports are in parallel and output ports in parallel, so voltages are common and currents add. Using y-parameters, the overall admittance matrix is the sum of individual y-parameters: [Y] = [Ya] + [Yb], valid for common-ground networks or with isolation transformers. ## Answer A **two-port network** is a network with two pairs of terminals (an input port 1 and an output port 2), where the current entering one terminal of a port equals the current leaving the other. It is described by the four variables $V_1, I_1, V_2, I_2$ and a set of parameters (z, y, h, ABCD) that relate them. ```text I1 --> <-- I2 o-------+-------------+-------o + | | + V1 | Two-port | V2 - | network | - o-------+-------------+-------o ``` #### Parallel connection of two two-ports In a parallel connection, the input ports of networks $N_a$ and $N_b$ are connected in parallel, and the output ports are also connected in parallel. ```text I1 --> +--------+ <-- I2 o-----+-----| Na |-----+-----o | +--------+ | V1 | | V2 | +--------+ | +-----| Nb |-----+ +--------+ (both input ports joined in parallel, both output ports joined in parallel) ``` **Derivation.** Each network is best described by its short-circuit admittance (y) parameters: $$ \begin{bmatrix} I_{1a} \\ I_{2a} \end{bmatrix} = \begin{bmatrix} y_{11a} & y_{12a} \\ y_{21a} & y_{22a} \end{bmatrix} \begin{bmatrix} V_{1a} \\ V_{2a} \end{bmatrix}, \qquad \begin{bmatrix} I_{1b} \\ I_{2b} \end{bmatrix} = [Y_b] \begin{bmatrix} V_{1b} \\ V_{2b} \end{bmatrix} $$ Because the ports are in parallel, the **voltages are common**: $$ V_1 = V_{1a} = V_{1b}, \qquad V_2 = V_{2a} = V_{2b} $$ and the **port currents add** (KCL): $$ I_1 = I_{1a} + I_{1b}, \qquad I_2 = I_{2a} + I_{2b} $$ Substituting: $$ \begin{bmatrix} I_1 \\ I_2 \end{bmatrix} = \left([Y_a] + [Y_b]\right)\begin{bmatrix} V_1 \\ V_2 \end{bmatrix} $$ So the overall y-parameters are the sum of the individual ones: $$ y_{11} = y_{11a}+y_{11b}, \quad y_{12} = y_{12a}+y_{12b}, \quad y_{21} = y_{21a}+y_{21b}, \quad y_{22} = y_{22a}+y_{22b} $$ **Validity condition.** This addition rule holds only if the interconnection does not change the port currents of either network (the current entering one terminal of each port still leaves by the other). This is always true for three-terminal (common-ground) networks; otherwise it is checked by the Brune test, or an ideal 1:1 isolating transformer is used. **Use in filter design.** Parallel connection is used to realize transmission zeros: for example, the twin-T notch network is two T-sections in parallel whose $y_{21}$ terms cancel at the notch frequency. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. In a parallel connection of two two-ports: A. Both voltages and currents are common B. Port voltages are common and port currents add C. Currents are common and voltages add D. Currents add at port 1 only Answer: B. V1 = V1a = V1b, V2 = V2a = V2b, and I1 = I1a + I1b, I2 = I2a + I2b. (Key point: Parallel connection quantities) 2. For the parallel combination the overall matrix is: A. [Y] = [Ya][Yb] B. [Z] = [Za] + [Zb] C. [Y] = [Ya] + [Yb] D. [ABCD] = [ABCDa] + [ABCDb] Answer: C. y-parameters add: y11 = y11a + y11b, and so on. (Key point: Combined parameters) 3. A typical use of parallel connection in filter design is: A. Producing transmission zeros, as in the twin-T notch network B. Raising the cutoff of a Butterworth filter C. Converting a ladder to a lattice D. Cancelling private poles Answer: A. In twin-T, the y21 terms of the two T sections cancel at the notch frequency; validity needs the Brune test or isolating transformers. 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