EECE 311 Homework, Spring 2008

American University of Beirut DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING EECE 311 – Electronic Circuits (Sections 1 & 2) Spring 2008 HOMEWORK 1 Due Friday February 29, 2008 at 1:00 PM Problem 1. Refer to Figure 6.4 in the textbook. Using VDD = 1.8 V and a pair of identical MOSFETs, design the current source in the figure to provide an output current of 50 μA, nominal. The nominal output current is obtained when the VO = VGS. The output voltage is required to operate in the range 0.3 V to 1.8 V, and it is also required that the change in the output current over this range be limited to 3% of the nominal value. a) Find the required values of R and all device dimensions (W and L). The technology parameters are: k’n = 360 μA/V2, V’An = 20 V/μm, and Vtn = 0.55 V. Do not neglect channel-length modulation in your design. b) Using PSpice, verify that the nominal value of IO is obtained at VO = VGS, and that the change in IO is limited to 3% of its nominal value, when VO changes from 0.3 V to VDD. Problem 2. Refer to Figure 6.18 (a) in the textbook. A common-source CMOS amplifier similar to the one shown in Fig. 6.18 (a) in the textbook uses a supply voltage VDD of 1.8 Volts, and a bias current IREF of 15 μA. The MOSFET parameters are: W/L = 40 for Q2, W/L = 5 for Q3, k’n = 360 μA/V2, k’p = 90 μA/V2, VAn = 1/λn = |VAp| = 1/|λp| = 6 V, Vtn = 0.55 V, and Vtp = –0.5 V. Do not neglect channel-length modulation in DC analysis. a) Find the value of VSG of Q2. b) Find the drain current of Q1 when vO = VDD/2. c) Find W/L for Q1 if the drain current found in part (b) corresponds to vI = VDD/2 and vO = VDD/2. d) Find the value of vO and the corresponding value of vI at which Q2 leaves the saturation region. e) Find the value of vO and the corresponding value of vI at which Q1 leaves the saturation region. f) Find the value of the small-signal voltage gain vo/vi around the DC bias point (VI = VDD/2, VO = VDD/2) g) Find the value of the output resistance Ro. h) Simulate the circuit in PSpice to derive the voltage transfer curve (vO versus vI) when vI varies between 0 V and 1.8 V. This is done as follows: vi input_node 0 DC 0V .DC vi 0V 1.8V 0.001V where input_node is the number you assigned to the input node. The .DC statement sweeps vI from 0 V to 1.8 V in 1 mV steps. Using the Probe trace of V(output_node), where output_node is the number you assigned to the output node, note that for a range of values of vI, the gain |dvO/dvI| is large and approximately constant. What is this range of values of vI? What is the corresponding range of values of vO? How do the values compare with the results of parts (d) and (e)? i) Bias the transistor at (VI = VDD/2, VO = VDD/2), and apply a sinusoidal input with an amplitude equal to 10 mV. Run a transient analysis using such a sinusoidal source (at a frequency of 1 KHz): vi input_node 0 SIN(DC_bias Amplitude 1KHz) .Tran 5us 8ms 5ms 5us DC_bias is VDD/2 and Amplitude is 10 mV. i.1) Verify, from the Probe plots of vO and vI, that the AC gain is close to the value calculated in part (f). i.2) Now change Amplitude to 50mV, and run the transient analysis. How do you explain the shape of the output waveform? j) Find the output resistance of the amplifier. This is done in SPICE as follows: Set the input source vI to VDD/2 (this is a zero-volt AC input source!), and connect an AC voltage source vx to the output node via a 1 F capacitor (this capacitance is needed in order not to disrupt the DC bias, and results in a negligible impedance of 0.16 mΩ at the AC frequency of 1 KHz): vx test_node 0 AC 1 cx test_node output_node 1 where test_node is the number you assigned to the test node to which vx is connected. Run an AC analysis at 1KHz using: .AC LIN 1 1KHz 1KHz .PRINT AC i(vx) The .PRINT statement will print the value of ix. After running PSpice, click on View -> Output File then scroll down to “**** AC ANALYSIS ” to read the value of ix = I(vx). Calculate the value of the output resistance from this value of ix. Compare with the value calculated in part (g). Problem 3. a) A direct-coupled amplifier has a low-frequency gain of 32 dB, poles at 11 KHz, 48 KHz, and 220 KHz, a zero at 96 KHz, and two more zeros at infinity. Express the amplifier gain function in the form: 1 2 1 2 (1 )(1 ) (1 ) (1 )(1 ) (1 ) z z zn M p p pn s s s A s s s ω ω ω ω ω ω + + + + + + � � . b) Sketch the Bode plot for the magnitude of the gain. c) Calculate the 3-dB frequency fH for this amplifier using: i) the dominant pole approximation ii) the definition of the 3-dB frequency (i.e. find the exact value of fH). What is the error (in %) in the value of fH due to the dominant pole approximation? d) Calculate the frequency ft at which the gain of the amplifier becomes unity (or 0 dB) using: i) the dominant pole approximation ii) the definition of ft. Comment on the usefulness of the dominant pole approximation in estimating ft. e) Verify using PSpice the values of fH and ft calculated above. Use Homework 1 Problem 3 .PARAM pi=3.141593 Vin 1 0 AC 1 Rin 1 0 1 Eamp 2 0 Laplace {V(1)}={ your gain function here } Rout 2 0 1 .AC DEC 20 1Hz 1000KHz .Probe .End and plot dB(v(2)).