Lecture-2

Lecture-2 - 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 #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. V i + v i I o + i o V i + v i I o + i o V i + v i I o + i o I o = f(V i ) g m = dI/dV = i o /v i V i I o = f(V i ) Slope = g m Bias Point I o = I s exp(V i /V T ) I o = K(V i ± V th ) 2 v i i o Fig. 2.1: Generalized linear small-signal model of active device. Two among three terminals take the input voltage V i , and the third terminal outputs the current I o . The large signal relations between I o and V i for BJT and MOS are non- linear functions as follows. BJT: I o = f ( V i ) = I s e V i V T , I s ± 1 fA , and V T ± 26 mV @300 o K . (2.1) MOS: I o = f ( V i ) = μ C ox 2 W L ( V i ± V th ) 2 , n C ox ² 200 A / V 2 , and V th ² 0.4 V . Assume that active devices are biased at an operating point (I o ,V i ). The MOS device parameters such as NMOS mobility μ n , gate capacitance per unit area C ox , and threshold voltage V th vary depending on actual processes. If the bias point is perturbed by small amounts of i o and v i , the following still holds true as explained in Fig. 2.1.
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UNIVERSITY OF CALIFORNIA, SAN DIEGO Department of Electrical and Computer Engineering Bang-Sup Song 2 ECE163 I o + i o = f ( V i + v i ), where g m = i o v i = dI o dV i = ± f ( V i ) . ( 2 . 2 ) For small signals, the trans-conductance g m of any active device, which is defined as a ratio of the small-signal output current i o to the small-signal input voltage v i , is just a simple derivative of the I-V characteristic at the bias point. Therefore, the trans- conductance g m of the BJT and MOS transistors are defined as BJT: g m = I o V T ± 1 26 ² if I o = 1 mA . (2.3) MOS: g m = μ n C ox W L I o ± 1 224 ² if I o = 1 mA and W / L = 50. As noted, the g m of an NMOS transistor sized with W/L=50 and biased at 1mA is one order lower than that of a BJT at the same bias current. The g m of a PMOS transistor is even lower since its mobility is about 1/3 ~ 1/4 of the NMOS device mobility. v i i o v i i o v i r o g m v i ± + r i g m g m v i r o g m v i ± + Fig. 2.2: Low-frequency small-signal model of BJT and MOS.
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This note was uploaded on 09/10/2010 for the course ECE 107 taught by Professor Fullterton during the Spring '07 term at UCSD.

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Lecture-2 - UNIVERSITY OF CALIFORNIA, SAN DIEGO Department...

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