19.10 Summary

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19.10 Summary

• 1. A two-port network is one with tw o ports (or tw o pairs of access terminals), known as input and output ports.
• 2. The six parameters used to model a two-port network are the impedance [z], admittance [y], hybrid [h], inverse hybrid [g], transmission [T], and inverse transmission [t] parameters.
• 3. The parameters relate the input and output port variables as

$$\begin{bmatrix} \mathbf{V}_1 \\ \mathbf{V}_2 \end{bmatrix} = [\mathbf{z}] \begin{bmatrix} \mathbf{I}_1 \\ \mathbf{I}_2 \end{bmatrix}, \qquad \begin{bmatrix} \mathbf{I}_1 \\ \mathbf{I}_2 \end{bmatrix} = [\mathbf{y}] \begin{bmatrix} \mathbf{V}_1 \\ \mathbf{V}_2 \end{bmatrix}, \qquad \begin{bmatrix} \mathbf{V}_1 \\ \mathbf{I}_2 \end{bmatrix} = [\mathbf{h}] \begin{bmatrix} \mathbf{I}_1 \\ \mathbf{V}_2 \end{bmatrix}$$ $$\begin{bmatrix} \mathbf{I}_1 \\ \mathbf{V}_2 \end{bmatrix} = [\mathbf{g}] \begin{bmatrix} \mathbf{V}_1 \\ \mathbf{I}_2 \end{bmatrix}, \qquad \begin{bmatrix} \mathbf{V}_1 \\ \mathbf{I}_1 \end{bmatrix} = [\mathbf{T}] \begin{bmatrix} \mathbf{V}_2 \\ -\mathbf{I}_2 \end{bmatrix}, \qquad \begin{bmatrix} \mathbf{V}_2 \\ \mathbf{I}_2 \end{bmatrix} = [\mathbf{t}] \begin{bmatrix} \mathbf{V}_1 \\ -\mathbf{I}_1 \end{bmatrix}$$

• 4. The parameters can be calculated or measured by short-circuiting or open-circuiting the appropriate input or output port.
• 5. A two-port network is reciprocal if z12 = z21, y12 = y21, h12 = −h21, g12 = −g21, ∆T = 1 or ∆t = 1. Networks that have dependent sources are not reciprocal.
• 6. Table 19.1 provides the relationships between the six sets of parameters. Three important relationships are

$$[y] = [z]^{-1}, \qquad [g] = [h]^{-1}, \qquad [t] \neq [T]^{-1}$$

• 7. Two-port netw orks may be connected in series, in parallel, or in cascade. In the series connection the z parameters are added, in the parallel connection the y parameters are added, and in the cascade connection the transmission parameters are multiplied in the correct order.
• 8. One can use PSpice to compute the tw o-port parameters by con straining the appropriate port v ariables with a 1-A or 1-V source while using an open or short circuit to impose the other necessary constraints.
• 9. The network parameters are specifically applied in the analysis of transistor circuits and the synthesis of ladder LC networks. Network parameters are especially useful in the analysis of transistor circuits because these circuits are easily modeled as tw o-port networks. LC ladder networks, important in the design of passive low-pass filters, resemble cascaded T networks and are therefore best analyzed as two-ports.

Review Questions

19.1 For the single-element two-port network in Fig. 19.64(a), z11 is:

(a) 0 (b) 5 (c) 10 (d) 20 (e) undefined

Figure 19.64

For Review Questions.

• 19.2 For the single-element two-port network in Fig. 19.64(b), z11 is:
  • (a) 0 (b) 5 (c) 10
  • (d) 20 (e) undefined
• 19.3 For the single-element two-port network in Fig. 19.64(a), y11 is:
  • (a) 0 (b) 5 (c) 10
  • (d) 20 (e) undefined
• 19.4 For the single-element two-port network in Fig. 19.64(b), h21 is:
  • (a) −0.1 (b) −1 (c) 0 (d) 10 (e) undefined
• 19.5 For the single-element two-port network in Fig. 19.64(a), B is:

(a) 0	(b) 5	(c) 10
(d) 20	(e) undefined

19.6 For the single-element two-port network in Fig. 19.64(b), B is:

(a) 0	(b) 5	(c) 10
(d) 20	(e) undefined

19.7 When port 1 of a two-port circuit is short-circuited, I1 = 4I2 and V2 = 0.25I2. Which of the following is true?

(a) y11 = 4	(b) y12 = 16
(c) y21 = 16	(d) y22 = 0.25

19.8 A two-port is described by the following equations:

V1 = 50I1 + 10I² V2 = 30I1 + 20I²

Which of the following is not true?

(a) z12 = 10 (b) y12 = −0.0143 (c) h12 = 0.5 (d) A = 50

19.9 If a two-port is reciprocal, which of the following is not true?

(a)

$$\mathbf{z}_{21} = \mathbf{z}_{12}$$

\n(b) $\mathbf{y}_{21} = \mathbf{y}_{12}$
\n(c) $\mathbf{h}_{21} = \mathbf{h}_{12}$
\n(d) $AD = BC + 1$

19.10 If the two single-element two-port networks in Fig. 19.64 are cascaded, then D is:

(a) 0 (b) 0.1 (c) 2 (d) 10 (e) undefined

Answers: 19.1c, 19.2e , 19.3e , 19.4b, 19.5a, 19.6c, 19.7b, 19.8d, 19.9c, 19.10c.