Page1 Name ES 330 Electronics II Homework # 2 (Fall 2016 Due Wednesday, September 7, 2016) Problem 1 (15 points) You are given an NMOS amplifier with drain load resistor R D = 20 k. The DC voltage (V RD ) appearing across resistor R D = 1.5 volts with an applied gate-to-source voltage (V GS ) of 0.7 volt. Small-signal AC measurements ) give a voltage gain A v = -10 V/V. (a) Find the threshold voltage V t of the N-channel MOSFET. (b) The process transconductance parameter k n = 200 A/ V 2 ; what is the MOSFET s gate width-to-length ratio (in symbols, W/L)? Problem 2 (20 points) Suppose you are given the common-emitter bipolar amplifier as shown schematically below. (Note: This is Figure 7.6 (on page 377) of Sedra and Smith, 7 th edition)
Page2 The power supply voltage V CC = +5 volts and the load resistor R C = 1 k. For the range of collector bias currents, I C = 0.5 ma, 1 ma, 2.5 ma, 4 ma and 4.5 ma, determine the corresponding collector-to-emitter voltages V CE and voltage gains A v for each of the collector currents. Place answers in the table below. I C (ma) V CE (volts) A v (V/V) 0.5 ma 1 ma 2.5 ma 4 ma 4.5 ma Problem 3 Bipolar Transistor Operation (10 points) The essence of transistor operation is that for change in v be, represent it by v be, results in a change in collector current i c, represented by i c. The small-signal approximation means keeping v be small enough to allow i c to be linearly related to v be by the relationship, i c = g m v be. The parameter g m is the transconductance of the transistor. When passing i c through resistor R C, a chanage in output voltage v o is generated.
Page3 (a) Using the expression, A v = - [I C /V T ]R C, where V T is the thermal voltage kt/q = 0.026 volt (not MOSFET threshold voltage), derive a simple expression for transconductance g m. (b) Calculate the value of g m when I C = 0.5 ma. Problem 4 Using Grahical Analysis (20 points) You are presented with the NPN bipolar transistor circuit shown below: In this problem you are to construct a graphical drawing of the i C v CE characteristic of the BJT, with base current values of i B = 10 A, 20 A, 30 A, 40 A and 50 A, to estimate amplifier parameters. To simplify the problem we ignore the Early effect ; meaning the output resistance is infinite (i.e., horizontal lines on the i C v CE characteristic) and take the BJT s current gain = 100 at all current levels. Given: V CC = +5 volts and R C = 1 k ; these two parameters allow you to construct and draw the load line upon the BJT s i C v CE characteristic curve.
Page4 (a) Draw the collector current lines on the graph and then draw the load line established by the collector load resistor R C. (b) Estimate the peak-to-peak collector voltage swing resulting from driving the base current i B over the range of 10 A (minimum) to 40 A (maximum). Use the drawing above to estimate this peak-to-peak voltage swing. (c) Assuming the BJT biased at V CE = ½V CC, find the values of I C and I B at this Q-point (i.e., Q is the quiesent point). (d) Assuming the currrent value at bias point Q from part (c), given that V BE = 0.700 volt and R B = 100 k, find the required value of power supply V BB.
Page5 Problem 5 Transconductance of NMOS Transistor (15 points) We have an NMOS transistor with k n = 10 ma/v 2. The overvoltage V OV parameter is set at V OV = 0.2 volt so that the transistor is in its saturated mode of operation. (a) What is the DC bias drain current I D? (b) Next, we superimpose a small voltage upon the DC bias gate voltage, V GS, with amplitude v gs = + 0.02 volt. Find the corresponding incremental collector current i D by evaluating the total collector current i D and then subtracting the DC bias current I D. (c) Repeat the calculation from part (b) but now with v gs = - 0.02 volt. (d) Use the results from parts (b) and (c) to estimate the value of the transconductance g m of the transistor. (e) Calculate the transconductance using Equation (7.33) in Sedra and Smith (from page 384). [Note: Equation (7.33) reads g m = k n V OV.] Compare this result with what you obtained in part (d) above. [In other words, how well do they agree?]
Page6 Problem 6 Using the T-equivalent Model (20 points) For the NMOS transitor embedded within the schematic circuit, you are to use the T- equivalent model (but assume that = 0 which means that the output resistance is infinite and can be ignored) to derive equations for its small-signal voltage gain behavior. (a) Draw the circuit with the T-equivalent model substituted for the MOSFET symbol and in the format to be used for performing a small-signal analysis. Label all elements.
Page7 Problem 6 continued.... (b) Derive a voltage gain expression for v s /v i. (c) Derive a voltage gain expression for v d /v i.