Electronics II. Final Examination

Transcription

1 The University of Toledo f6fs_elct7.fm - Electronics II Final Examination Problems Points Total 40 Was the exam fair? yes no

2 The University of Toledo f6fs_elct7.fm - Problem 5 points Given is the linear two-port circuit model shown in Figure.(a). = 45 kω R s = 80 kω C p = 90 pf C s = 350pF C s R s Z s vi C p v o V i Zp V o (a) (b) Figure. A two-port linear circuit model. (a) Time domain model. (b)phasor domain model. Problem Statement For the given two-port circuit model of Figure.(a), demonstrate an ability to:. determine the phasor domain voltage transfer function A v (s) of the given time domain circuit model,. prepare the factorized form of the transfer function A v (s), 3. determine the pole(s) and zero(s) of the transfer function A v (s), 4. Prepare an asymptotic Bode plot of the magnitude A v (ω) of A v (s). Hint # For full credit: all equations, all answers to questions, all circuit models and other graphical representations are expected to be entered into the space designated for them; all shown numerical results must be preceded by the symbolic and numeric expressions whose evaluation produces the shown results. Problem Solution For full credit, explicit demonstration of understanding the following solution steps is expected.. Prepare the phasor domain circuit model of the time domain model shown in Figure.(a). Show the prepared phasor domain model in the space reserved for Figure.(b). /8/4

3 The University of Toledo f6fs_elct7.fm - 3. Prepare the symbolic expressions of impedaces shown in Figure.(b), and show them in the space reserved for equations (-). Z s = R Z Rs Z s Cs sc s Z Rs + Z = = Cs R s + sc s Z p = + srp C p R s + sr s C s (-).3 For the two-port circuit of Figure., prepare the phasor domain expression of the voltage transfer function A V (s). Show the result of your work in the space reserved for equation(s) (-). By the voltage divider formula, A V (s) = Z p Z p + Z s = + sc p + sc p R s + + scs R s = Rp + R s +R s C s s + R s (C s + C p ) + R s s (-) 3.4 Using the expression for A V (s) obtained in section.3, determine the asymptotic expressions of A V (s) when s 0, and when s and calculate their numerical values in magnitude and decibel scales. Show your work and the obtained asymptotic expressions in the space reserved for equations (-3). a R =A v (s) = = s = R s a R [db] = 0lg (0.05) = db C s a C =A v (s) = = s = C s + C p (-3) a C [db] = 0lg (0.54) = -.5dB -5.3 db /8/4

4 The University of Toledo f6fs_elct7.fm Manipulate the expression for A V (s) prepared in section.3 into the factorized form, and show the obtained factorized form in the space reserved for equations (-4). Show additionally in the same reserved space the symbolic expressions, and calculate the values of the zero and the pole which appear in the factorized form. Show your work in the space reserved for equations (-4). The voltage transfer function A v (s) can be written in factorized form as, s+ Rs C A V (s) = a s R ω z s+ Rs C s C p ω p s - s = a z C s - s p with, s z = - ω z (-4) = - 0 = - R = - 5 s C s 8.7 = krad/s a = - ω C z a = R 0.54 s p = - ω p 0.05 = - 36 krad/s 4.6 Using the prepared values of constants a R, ω z, and ω p, shown in (-3 and -4), prepare the asymptotic Bode Plot of the amplitude characteristic A v (ω) of the two-port circuit model of Figure.. Show the prepared Bode plot in the space reserved for Figure A v (ω)[db] lg ω ω p ω p ω z -40 Figure. Asymptotic Bode Plot of the magnitude A v (ω) of the given two-port circuit model of Figure.. /8/4

5 The University of Toledo f6fs_elct7.fm - 5 Problem 0 points Given is the electric circuit model of a MOSFET differential amplifier shown in Figure 3.(a). +V DD R D =4kΩ +V DD v G + - R D R D V I OD D I D M M I S I S + - V TN =.V R D R D I SS =0mA k n = 50µA/V I D I D V DD =5V M M v G I S I S v G =0 v G = V GS I SS V GS V GS I SS V GS (a) (b) Figure. A MOSFET differential amplifier circuit model. (a) The circuit model with connected signal sources. (b)equivalent DC circuit model. for determining the quiescent operating points of the transistors in the circuit of Figure.(a). Problem Statement For the given amplifier s circuit model of Figure.(a), demonstrate an ability to determine:. operating point of the matched transistors in the circuit of a differential amplifier,. small signal parameters of the transistors, Hint # For full credit: all equations, all answers to questions, all circuit models and other graphical representations are expected to be entered into the space designated for them; all shown numerical results must be preceded by the symbolic and numeric expressions whose evaluation produces the shown results. Problem Solution For full credit, explicit demonstration of understanding the following solution steps is expected.. In the space reserved for Figure.(b), prepare the DC equivalent circuit model for determining the quiescent operating points of the transistors in the circuit of Figure.(a).. Calculate the drain current values of the transistors in the amplifier s circuit model of Figure.(b). Show your calculation in the space reserved for equation (-). I D = -I S = - -I SS = I SS =0 0-3 = A (-) /8/4

6 The University of Toledo f6fs_elct7.fm Calculate the indicated gate to source voltage, V GS, of the transistor(s) in the amplifier s circuit model of Figure.. Show your calculation in the space reserved for equation (-) V GS = V TN + I D (-) = k =. + = 4.V n 00.4 Calculate the common value of the drain to source voltages, V DS and V DS, of the transistors in the amplifier s circuit model of Figure -. Show your calculation in the space reserved for equation (-3). KVL: V DS = - I D R D + V DD + V GS = - I SS = = 9.V R D + V DD + V GS = (-3).5.5 In the space reserved for Figure., show the unilateral low-frequency small-signal circuit model of the MOSFET transistor. G i d D v gs g m v gs r o v ds S.5.6 Using the given values of circuit element parameters and currents, determine the value of the small signal transconductance, g m, of the transistors in the given amplifier circuit. Show your calculation in the space reserved for equation (-4). I D g m = V GS -V = = A/V TN 4.-. (-4) /8/4

7 The University of Toledo f6fs_elct7.fm - 7 Problem 3 5 points Given is a feedback amplifier circuit model of Figure 3.. The design specifications of the amplifier V i Σ V A fw V o V 4 β A F (jω) = V o V i A = fw - Afw β Figure 3. An operational circuit voltage amplifier model. include the following requirements: (a) its DC gain A Fo ought to have the value of A Fo = 5dB, (b) its phase margin should have the value PM=45 o, (c) its reverse amplification module s transfer function β should have a real value, (d) it ought to be built using as the forward-gain amplifier an off-the-shelf integrated circuit amplifier whose voltage amplification transfer function A fw (jω) is given by equation (3-). A fw (jω) = ( A fwo = jω ) jω jω jω 0 4 (+ 0 7 ) (+ ωp ) (+ ωp3 ) (3-) Problem Statement For the given feedback amplifier s circuit model of Figure 3., demonstrate an ability to determine:. the frequency-independent value of the reverse gain amplification β,. the way of compensation of the given forward gain amplifier s transfer function of equation (3-) so that the feedback amplifier s design criteria will be satisfied. Hint # For full credit: all equations, all answers to questions, all circuit models and other graphical representations are expected to be entered into the space designated for them; all shown numerical results must be preceded by the symbolic and numeric expressions whose evaluation produces the shown results. Problem Solution For full credit, explicit demonstration of understanding the following solution steps is expected. 3. In the space reserved for equation(s) (3-), prepare the values of forward-gain amplifier s parameters:. magnitude of the DC amplification A fwo in db,. dominant pole s angular frequency ω p, 3. other poles angular frequencies ω p3. A fwo = A fw (0) = 00 db (3-) ω p = 0 Krad/s ω p3 = 0 Mrad/s /8/4

8 3 8/3/7 3. Prepare the asymptotic Bode plots of the forward-gain amplifier s amplitude and phase characteristics. Show the prepared characteristics in the space reserved for Figure 3.(a) A fw (ω)[db] A F (ω)[db] A fwo = A Fo + T o A fw (ω u )=A F (ω u )=50db lgw K 0K 00K M 0M 00M G K 0K 00K M 0M 00M G lgw θ fw (ω)[ o ] PM=45 o (a) ω u ω lgw K 0K 00K M 0M 00M G K 0K 00K M 0M 00M G lgw A fw - unaltered A fw - altered A fwo =0 db A Fo =5dB GM=0dB θ F (ω)[ o ] ω u PM=45 o ω 80 (b) The University of Toledo Section

9 The University of Toledo f6fs_elct7.fm Calculate the frequency-independent value of the reverse gain amplification β. Show your calculation in the space reserved for equation (3-3). A Fo [db] = 0lg A Fo = 5dB lg A Fo = A Fo = 7.78 β = 7.78 A Fo = =.5 (3-3) 3.4 Determine the degree value of θ T (ω u ), (which is the loop-gain s phase shift θ T at the unity gain frequency ω u ) that will satisfy the phase margin requirement. Show your calculation in the space reserved for equation (3-4). θ T (ω u ) = PM - 80 o = 45 o - 80 o = - 35 o (3-4) 3.5 Determine the degree value of θ F (ω u ), (which is the feedback amplifier s phase shift θ F at the unity gain frequency ω u that will satisfy the phase margin requirement. Show your calculation in the space reserved for equation (3-5). Since the reverse amplification module s transfer function β, has constatant real value, all three phase characteristics: θ fw (ω u ), θ F (ω u ) and θ T (ω u ) are identical. θ F (ω u ) = θ T (ω u ) = - 35 o (3-5) 3.6 In the Bode plot of the phase characteristic in Figure 3.(a), show the way to graphically determine the unity loop-gain frequency ω u. Show the determined value of ω u in the space reserved for equation (3-6) ω u = 4.5 Mrad/s (3-6) 3.7 Using the determined value of ω u, and the asymptotic Body plot of amplitude characteristic A fw (ω)[db], determine graphically the db values of A fw (ω u ) and A F (ω u ). Show in Figure 3.(a) the details of the applied graphical process, and show the determined values in the space reserved for equation (3-7). A fw (ω u ) = 50 db A F (ω u ) = 50 db (3-7) /8/4

10 The University of Toledo f6fs_elct7.fm Compare the obtained value of A F (ω u )=A F (0)=A Fo with the value specified for A Fo by requirement (a), and mark, for full credit, your answers yes, no, or not applicable for all given choices. yes no not applicable x A F (ω u ) > required A Fo x A F (ω u ) = required A Fo x A F (ω u ) < required A Fo When in part 3.8 a determination has been made that A F (ω u )>A Fo, apply the compensation method that modifies the DC gain value of the forward-gain amplifier, so that the difference between A F (ω u ) and A Fo is compensated, while the required phase margin is maintained. Show the details of the applied graphical construction method in the space reserved for Figure 3.(b),. Hint # Fore clarity in Figure 3.(b): - use dashed-lines in blue-pencil to draw the amplitude and phase characteristics of the forward-gain amplifier before the modification has been applied to its transfer function; - use a red-pencil to draw the amplitude and phase characteristics of the feedback amplifier after the modification has been applied to its transfer function. 3.0 After the application of graphical construction method has been completed, determine from Figure 3.(b) the value of the reduction to be applied to the forward-gain amplifier s DC gain. Show the determined modification s value in the space reserved for equations (3-8). Reduction of the forward-gain amplifier s DC gain: A fwo = 0 db (3-8) /8/4