UNIVERSITY OF CALIFORNIA, SAN DIEGO Department of Electrical and Computer Engineering Bang-Sup Song 1 ECE163 Lecture #2: Operational Amplifier (Opamp) Low-Frequency Small-Signal Model of Active Devices Electronic signal defined as a voltage at a circuit node moves from one circuit node to another after two voltage-to-current and current-to-voltage conversion processes. The voltage-to-current conversion is made possible by active devices like transistors or vacuum tubes. All active devices are non-linear by nature for large signals. In bipolar junction transistors (BJT), the collector current is an exponential function of the base-emitter voltage while in complementary metal-oxide-semiconductor (CMOS) transistors, the drain current is a square function of the gate-source voltage. Note that all active devices are three terminal devices. MOS device has a fourth terminal, which is called substrate or body normally tied to a constant voltage or its source. Vi + viIo + ioVi + viIo + ioVi + viIo + ioIo= f(Vi)gm= dI/dV= io/viVi Io= f(Vi)Slope = gmBiasPointIo = Isexp(Vi/VT)Io = K(Vi±Vth)2viioFig. 2.1: Generalized linear small-signal model of active device. Two among three terminals take the input voltage Vi, and the third terminal outputs the current Io. The large signal relations between Ioand Vifor BJT and MOS are non-linear functions as follows. BJT: Io=f(Vi)=IseViVT,Is±1fA,and VT±26mV@300oK.(2.1)MOS: Io=f(Vi)=μCox2WL(Vi±Vth)2,μnCox²200μA/V2,and Vth²0.4V.Assume that active devices are biased at an operating point (Io,Vi). The MOS device parameters such as NMOS mobility μn, gate capacitance per unit area Cox, and threshold voltage Vthvary depending on actual processes. If the bias point is perturbed by small amounts of ioand vi, the following still holds true as explained in Fig. 2.1.
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