Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6 002 Circuits and Electronics Spring 2003 Handout S03 024 Homework 5 Issued Wed Mar 5 Due Fri Mar 14 Problem 5 1 A semiconductor diode can be used as a variable attenuator R I vD v i vD In this diagram the current source I establishes the steady DC current in the diode the operating point current while vi is the input to be attenuated R is sufficiently large to insure that the operating point current in the diode is approximately I iD I S qvD The i v characteristic of the diode is iD IS e kT 1 qvD A Derive an expression for the incremental conductance g of the diode Assume that e kT 1 That is the current I is large enough so that the diode is well into the forward or conducting region q B Show that g can be expressed as g I kT C Draw a complete incremental small signal model for the circuit above Explain why the current source does not appear in this model D Derive an expression for the attenuation of the circuit that is derive an expression for A A vd vi where vd is the incremental component of the diode voltage Assume R the attenuation is proportional to I 1 g and show that E If the magnitude of vd is too large this voltage will be distorted because the linear approximation implied in the definition of g becomes invalid What is a reasonable upper bound for vd Hint Think Taylor series expansion of iD f vD Problem 5 2 The Gizmo whose circuit symbol is shown below is an electronic valve The output characteristic of the Gizmo is shown as well iG GIZMO G vGC 6 vPC 4 0 1 2 3 4 C 1 iP mA P vG iP 2 C iG 0 0 10 20 30 40 vPC volts Values of vGC are in volts The Gizmo functions as an amplifier in the circuit shown below 40 volts iP RL 5 k P G GIZMO vPC vOUT vPC vIN vGC C A When no signal is present i e when vIN VIN the circuit is to have a current at P of iP 3mA That is the quiescent or operating point current is to be IP 3mA Specify the operating point value of VIN that will produce the desired operating point Hint Think load line B What is the value of VP C at the operating point C An incremental model for the Gizmo at any operating point in the output characteristics is shown below P G rp and are constants which can be derived directly from the output characteristics above vgc vgc C D Assume rp 1 5k and 15 These are not the correct values corresponding to the output characteristics above but will do for this part of the problem Draw a complete incremental model for the amplifier circuit shown above Label all component values E Calculate the incremental voltage gain of this amplifier Av vout vin Where vin and vout are the incremental components of the input and output voltages respectively F For extra credit determine the approximate correct values of r p and from the output characteristics Problem 5 3 A FET is used as the control valve in the amplifier circuit shown below V iD VI provides a steady or DC voltage to establish an operating point drain current of ID 50 A RL v i vi is the incremental input voltage vO vO is the total output voltage expressed as vO VO vo where vo is the incremental output voltage RS VI Note vi vgs for this circuit A Draw and label the complete incremental model of this amplifier B Derive an expression for the incremental voltage gain Av transconductance gm vo vi in terms of RS RL and the C Assume now that the source of the supply voltage V has been damaged and produces in addition to V a noise source vn The defective supply can be modeled as v n V Draw and label an incremental model for the amplifier which takes into account this noisy voltage source D Using that model determine the component of vo that results from vn Hint Think superposition
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