# Electronics II. Final Examination

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1 f3fs_elct7.fm - The University of Toledo EECS:3400 Electronics I Section Student Name Electronics II Final Examination Problems Points Total 40 Was the exam fair? yes no

2 Analog Electronics f3fs_elct7.fm - Problem points Equation (-) specifies the expression of amplification transfer function of a given feedback amplifier. A f (s) = K f (s + )(s + 0 ) K f = -4π 0 [rad/s] = π 0 3 rad/s (-) For the given amplification transfer function of equation (-), demonstrate an ability to:. determine the midband gain A Of in db,. determine the values of the lower and upper angular cutoff frequencies, L and H, of the magnitude A f () of A f (s), 3. determine the bandwidth of the amplifier whose amplification transfer function is given by (-). 4. Prepare an asymptotic Bode plot of the magnitude A f (). Hint # For full credit, give answers to all questions, prepare all required circuit diagrams and all equations in the space reserved for them; include all symbolic and numerical expressions whose evaluation produces shown numerical results. Solution An explicit demonstration of understanding the following solution steps is expected.. Determine the numerical values of zeros and poles of the amplification transfer function given as equation (-). Show your work and the results in the space reserved for equation (-). p = - = -π 0 3 rad/s p = - = -0 = -0 π 0 3 = -π 0 5 rad/s (-). Determine the value of the magnitude of amplifier s midband gain, A OF, in db. Show the necessary calculations in the space reserved for equation (-3). K f K A f (s) = = f (s + )(s + ) s s = (+ )(+ ) K f A Of = = A Of = A Of = -0 4 = 0 4-4π 0 π 0 3 π 0 5 = -0 4 A Of [db] = 0lg A of = 0 lg0 4 = 0 4 = 80 db A Of (+ s s )(+ ) (-3).3 Prepare the expression of the amplification/gain A f (s) when s=j, and following this, prepare the 8//4

3 Analog Electronics f3fs_elct7.fm - 3 expression for the magnitudes A f (j) and A f () = A f (j). Show the necessary calculations in the space reserved for equation (-4). A f (s) = A s=j f (j) = (+ j ) A O (+ j ) (-4) A f () = A f (j) = + ( ) A O + ( ).4 Prepare the expression for calculating the db value of the magnitude A f () of the given transfer function (-). Show the necessary calculations in the space reserved for equation (-5). A f () [db] = 0lgA f () = 0lgA Of -0lg + ( -0lg.5 Based on the determined values of poles of A f (s), and the expressions (-4) and/or (-5), determine ) (-5) lower and upper angular cutoff frequencies, L and H, of the magnitude A f () of the given transfer function (-). Show the necessary calculations in the space reserved for equation (-6). + ( ) L = 0 rad/s H = = π 0 3 rad/s (-6).6 Prepare the expression and calculate the bandwidth of the feedback amplifier whose transfer function is given in (-). Show in the space reserved for equation (-7), the necessary calculations for expressing the bandwidth in the Hz frequency unit. BW = f = H - L π = π π = 0 3 Hz (-7) 8//4

4 Analog Electronics f3fs_elct7.fm Using the prepared expression (-5), prepare the asymptotic Bode Plot of the amplitude characteristic A f () of the given transfer function (-). Show the prepared Bode plot in the space reserved for Figure.. A f ()[db] 80 H lg Figure. Asymptotic Bode Plot of the magnitude Af() of the given transfer function A f (s). 8//4

5 Analog Electronics f3fs_elct7.fm - 5 Problem 3 points Given is the electric circuit model of a MOSFET differential amplifier shown in Figure.(a). R D I D M I S v d v d I S M +V DD R D ID + - v I v I - + R D =40kΩ I SS =400µA k n =400µA/V V TN =V V DD =5V V SS =5V λ = 0.0V - R D I D M I S v d v d I S M +V DD R D ID + - 0V 0V - + I SS I SS +V SS +V SS (a) 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). (b) 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 model of the MOSFETs, and the MOSFET small signal model s parameters. Hint # For full credit, give answers to all questions, prepare all required circuit diagrams and all equations in the space reserved for them; include all symbolic and numerical expressions whose evaluation produces shown numerical results. Solution An 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 SS = -(I S + I S ) I S = I S } I S = I S = -I SS (-) I D =I D = -I S I SS = = 0-4 A 8//4

6 Analog Electronics f3fs_elct7.fm Calculate the indicated gate-to-source voltage, V GS, of the transistors in the amplifier s circuit model of Figure.. Show your calculation in the space reserved for equation (-). V GS = V TN + I D k n = = V (-).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). V DS = R D I D +V DD + 0V + V GS = = 9V (-3).5 In the space reserved for Figure., show the small signal circuit model of the n-channel unipolar transistor. G D v gs g m v gs S r o Figure. Small signal electric circuit model of the unipolar transistor..6 Using the given circuit element parameter values, 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 TN = = 400 µa/v (-4).7 Using the given circuit element parameter values, determine the value of the small signal output resistance, r o, of the transistors in the given amplifier circuit. Show your calculation in the space reserved for equation (-5). r o = V DS + I D λ = 0-4 = = 545kΩ (-5) 8//4

7 Analog Electronics f3fs_elct7.fm - 7 Problem 3 5 points Given is a feedback amplifier circuit model of Figure 3.. V i Σ V A fw V o V 4 β A f (j) = V o V i A = fw - Afw β Figure 3. An operational circuit voltage amplifier model. It is necessary to design a physical feedback amplifier which will satisfy the following criteria: (a) its DC gain A of ought to have the value of A of = 0dB, (b) its phase margin should have the value PM=45 o, (c) its reverse amplification module should have a frequency-independent transfer function β, (d) it ought to be built using the, currently under design, forward gain amplifier whose voltage amplification transfer function A fw (j) is given by equation (3-). A fw (j) = ( A ofw = j ) j j j 0 4 (+ 0 8 ) (+ p ) (+ p3 ) (3-) For the given feedback amplifier s circuit model of Figure 3., demonstrate an ability to determine:. a frequency-independent value of the reverse gain amplification β,. a suggested way of compensation of the given forward gain amplifier s transfer function of equation (3- ) so that the feedback amplifier s criteria can be satisfied. Hint # For full credit, give answers to all questions, prepare all required circuit diagrams and all equations in the space reserved for them; include all symbolic and numerical expressions whose evaluation produces shown results. Solution An 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 ofw in db, - dominant pole s frequency p, - other poles frequencies p3. A ofw = A fw (0) = 0 db p = 0 Krad/s p3 = 00 Mrad/s 8//4 (3-)

8 8//4 3. Prepare the asymptotic Bode plots of the forward gainamplifier s amplitude and phase characteristics. Show the prepared characteristics in the space reserved for Figure A fw ()[db] T o =70db K 0K 00K M 0M 00M G K 0K 00K M 0M 00M G lg θ fw ()[ o ] A fw ( u )=A f ( u )=50db>0dB (a) A ofw = A of + T o PM=45 o u 80 lg A fw ()[db] nd =0.rad/s A of =0dB GM=40dB A fw - unaltered A fw - altered K 0K 00K M 0M 00M G θ fw (),θ f ()[ o ] u = p PM=45 o 3 80 = p+decade Figure 3. Asymptotic Bode plots of the amplitude an phase characteristics. (a)forward gain amplifier. (b)forward gain amplifier (blue) and feedback amplifier of Figure (3-) (red). (b) lg Notes on Analog Electronics f3fs_elct7.fm - 8

9 Analog Electronics f3fs_elct7.fm Calculate the frequency-independent value of the reverse gain amplification β. Show your calculation in the space reserved for equation (3-3). β = 0. β Aof = 0 (3-3) 3.4 Determine the degree value of θ T ( u ), (which is the loop-gain s phase shift θ T at the unity gain frequency u ) that will satisfy the phase margin requirement. Show your calculation in the space reserved for equation (3-4). θ T ( u ) = PM - 80 o = 45 o - 80 o = - 35 o (3-4) 3.5 Determine the degree value of θ f ( u ), (which is the feedback amplifier s phase shift θ f at the unity gain frequency u ) that will satisfy the phase margin requirement. Show your calculation in the space reserved for equation (3-5). Since the reverse amplification module has a frequency-independent transfer function β, the phase characteristics of all three transfer functions: θ fw ( u ), θ f ( u ), and θ T ( u ) must be identical. θ f ( u ) = θ T ( u ) = - 35 o (3-5) 3.6 In the Bode plot of the phase characteristic in Figure 3.(a), show the way to graphicaly determine the unity loop-gain frequency u. Show the determined value of u in the space reserved for equation (3-6) u = 45 Mrad/s (3-6) 3.7 Using the determined value of u, and the asymptotic Body plot of amplitude characteristic A fw ()[db], determine graphically the db values of A fw ( u )=A f ( 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 ( u ) = 50 db A f ( u ) = 50 db (3-7) 3.8 Compare the determined value of A f ( u )=A f (0)=A of with the value specified for A of by criterion (a), and for full credit, mark your answers yes, no, or not applicable for all given choices. yes no not applicable x A f ( u ) > A of x A f ( u ) = A of, x A f ( u ) < A of. 8//4

10 Analog Electronics f3fs_elct7.fm When in part 3.8 a determination has been made that A f ( u )> A of, use the compensation method that adds a new dominant pole to the voltage amplification transfer function A fw (j) of the forward-gain amplifier, in order to adjust the feedback amplifier s DC amplification to the required value of 0 db, while maintaining the required phase margin of 45 o. Show in Figure 3.(b), the details of the graphical construction method that determins the location of the new dominant pole nd. Hint # In Figure 3.(b): - use dashed-lines in blue-pencil to draw the amplitude and phase characteristics of the forward-gain amplifier when it has the new dominant pole added to its transfer function; - use a red-pencil to draw the amplitude and phase characteristics of the feedback amplifier when it uses the forward-gain amplifier that has the new dominant pole added to its transfer function. 3.0 Determine from Figure 3.(b), the location of the new dominant pole nd, and write the determined frequency in the space reserved for equation (3-8) nd = 0. rad/s (3-8) 8//4

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