Application of the Two Port Networks to the Transistor Circuits

We have seen how the six sets of network parameters can be used to characterize a wide range of two-port networks. Depending on the way two-ports are interconnected to form a larger network, a particular set of parameters may have advantages over others, as we noticed in Section 26.6 ( Interconnection of Networks ). In this section, we will consider two important application areas of two-port parameters: transistor circuits and synthesis of ladder networks

Transistor Circuits

The two-port network is often used to isolate a load from the excitation of a circuit. For example, the two-port in Fig. $ 1 $ may represent an amplifier, a filter, or some other network. When the two-port represents an amplifier, expressions for the voltage gain $ A_{v} $, the current gain $ A_{i} $, the input impedance $ Z_{\text {in }} $, and the output impedance $ Z_{\text {out }} $ can be derived with ease. They are defined as follows: Any of the six sets of two-port parameters can be used to derive the expressions in Eqs. (1) to (4). Here, we will specifically use the hybrid parameters to obtain them for transistor amplifiers.
The hybrid $ (h) $ parameters are the most useful for transistors; they are easily measured and are often provided in the manufacturer's data or spec sheets for transistors. The $ h $ parameters provide a quick estimate of the performance of transistor circuits. They are used for finding the exact voltage gain, input impedance, and output impedance of a transistor.
The $ h $ parameters for transistors have specific meanings expressed by their subscripts. They are listed by the first subscript and related to the general $ h $ parameters as follows: The subscripts $ i, r, f $, and $ o $ stand for input, reverse, forward, and output. The second subscript specifies the type of connection used: $ e $ for common emitter (CE), $ c $ for common collector (CC), and $ b $ for common base (CB). Here we are mainly concerned with the common-emitter connection. Thus, the four $ h $ parameters for the common-emitter amplifier are: These are calculated or measured in the same way as the general $ h $ parameters. Typical values are $ h_{i e}=6 \mathrm{k} \Omega, h_{r e}=1.5 \times 10^{-4}, h_{f e}=200 $, $ h_{o e}=8 \mu \mathrm{S} $. We must keep in mind that these values represent ac characteristics of the transistor, measured under specific circumstances. Figure $ 2 $ shows the circuit schematic for the common-emitter amplifier and the equivalent hybrid model. From the figure, we see that Consider the transistor amplifier connected to an ac source and a load as in Fig. 3. This is an example of a two-port network embedded within a larger network. We can analyze the hybrid equivalent circuit as usual with Eq. (7) in mind. Recognizing from Fig. 3 that $ \mathbf{V}_{c}=-R_{L} \mathbf{I}_{c} $ and substituting this into Eq. (7.b) gives or From this, we obtain the current gain as From Eqs. (7.b) and (8), we can express $ \mathbf{I}_{b} $ in terms of $ \mathbf{V}_{c} $ : or Substituting Eq. (9) into Eq. (7.a) and dividing by $ \mathbf{V}_{c} $ gives Thus, the voltage gain is Substituting $ \mathbf{V}_{c}=-R_{L} \mathbf{I}_{c} $ into Eq. (7.a) gives or Replacing $ \mathbf{I}_{c} / \mathbf{I}_{b} $ by the current gain in Eq. (8) yields the input impedance as The output impedance $ Z_{\text {out }} $ is the same as the Thevenin equivalent at the output terminals. As usual, by removing the voltage source and placing a $ 1-\mathrm{V} $ source at the output terminals, we obtain the circuit in Fig. 4, from which $ Z_{\text {out }} $ is determined as $ 1 / \mathbf{I}_{c} $. Since $ \mathbf{V}_{c}=1 \mathrm{~V} $, the input loop gives For the output loop, Substituting Eq. (10) into Eq. (11) gives From this, we obtain the output impedance $ Z_{\text {out }} $ as $ 1 / \mathbf{I}_{c} $; that is,