Lecture-1 - UNIVERSITY OF CALIFORNIA SAN DIEGO Department...

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UNIVERSITY OF CALIFORNIA, SAN DIEGO Department of Electrical and Computer Engineering Bang-Sup Song 1 ECE163 Lecture #1: Feedback Amplifier Stability v i i i Network v i i i Network v o i o One-port network Two-port network Fig. 1.1: Driving-point and transfer concepts. Driving-Point and Transfer Functions Consider any networks with one port or two ports as shown in Fig. 1.1. On each port, we can define its terminal voltage and the current flowing into the terminal. In the one- port case shown on the left side, the ratio of the terminal voltage to the current can be defined. R s ( ) = v i s ( ) i i s ( ) , and G s ( ) = i i s ( ) v i s ( ) . (1.1) The former is driving-point resistance, and the latter one is driving-point conductance. Their units are ± and 1/ ± , respectively. That is, if the input and output are referred to the same port, the term “driving-point” is used. On the other hand, in the two-port case shown on the right side, the following four ratios can be defined. A v s ( ) = v o s ( ) v i s ( ) , A i s ( ) = i o s ( ) i i s ( ) , R s ( ) = v o s ( ) i i s ( ) , and G s ( ) = i o s ( ) v i s ( ) , (1.2) where A v (s) and A i (s) are unit-less transfer functions defined as voltage and current gains, respectively. The latter two definitions are the same as in (1.1) for the one-port network, but they are called as trans-resistance and trans-conductance, respectively. The term “trans” is now used since the input and output ports are different. In steady-state small-signal analysis, impedances of reactive components such as inductor and capacitor are frequency-dependent as sL and 1/sC, where s is the complex frequency of j ² . The unit of ² is rad/sec. Note that the angular frequency ² is defined as the amount of angle rotation per second, while the ordinary frequency unit in Hertz (Hz) is defined as the number of rotations per second. Since one rotation of a vector covers an angle of 2 ³ radian, there is a 2 ³ difference between ² and f like ² = 2 ³ f. In general, all these transfer functions can be represented as a ratio of two polynomial functions N(s) and D(s) in steady state. Let’s consider a general transfer function H(s) as follows.
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