ECE3204 Microelectronics II Bitar / McNeill. ECE 3204 / Term D-2017 Problem Set 7

Transcription

1 EE3204 Microelecronics II Biar / McNeill Due: Monday, May 1, 2017 EE 3204 / Term D-2017 Problem Se 7 All ex problems from Sedra and Smih, Microelecronic ircuis, 7h ediion. NOTES: Be sure your NAME and EE MAILBOX NUMBER are prominenly displayed on he upper righ corner of wha you hand in. When appropriae, indicae answers wih a box or underline Work as nealy as possible You mus show all work o receive credi. Answers alone are no sufficien. These problems have been used before. Soluions are ou here. Be sure you know how o do hese problems ON YOUR OWN, since you will be esed in each area. 1. [Qualiaive s-plane pracice] Skech he pole locaions in he s-plane ha correspond o he following ime-domain impulse responses. Superimpose he locaions on he same plo, o show he relaive locaions corresponding o he various waveforms. A B D E F G H

2 EE3204 Microelecronics II Biar / McNeill 2. [Sabiliy analysis pracice] An op-amp has a D gain of 10 5 = 100,000 and wo poles: one a 100Hz, and one a 100 khz. a) Deermine he expression for A(s), he op-amp open-loop gain ransfer funcion. Skech he magniude and phase Bode plos A(f) and A(f) for he op-amp open-loop gain. Or, if you prefer, A(ω) and A(ω) The op-amp is o be used in he uniy gain configuraion: IN OUT b) Deermine he feedback facor β, he fracion of he op-amp oupu ha is fed back o he op-amp invering inpu. c) Skech A, β, and Aβ, and use his plo o esimae he frequency a which he magniude of he loop gain is equal o uniy: when Aβ = 1. d) onfirm your graphical esimae in (c) by using he expression in (a) o calculae a numerical value for he frequency a which Aβ = 1. e) Skech Aβ and use his plo o esimae he phase shif around he loop Aβ a he frequency a which Aβ = 1. Wha is he esimaed phase margin? Indicae he phase margin on your plo. f) onfirm your esimae in (e) wih a calculaion of he phase shif a he frequency from (d). Wha is he calculaed phase margin? g) Is his closed loop circui sable?

3 EE3204 Microelecronics II Biar / McNeill 3. [Sabiliy analysis pracice] The same op-amp from he previous problem (D gain of 10 5 = 100,000 and poles a 100Hz and 100kHz) is conneced closed loop wih a noninvering gain of a) Skech he circui configuraion. b) Deermine he feedback facor β, he fracion of he op-amp oupu ha is fed back o he op-amp invering inpu (boh symbolic and numerical expressions). c) Skech A, β, and Aβ, and use his plo o esimae he frequency a which he magniude of he loop gain is equal o uniy: when Aβ = 1. d) onfirm your graphical esimae in (c) by using he expression in (a) o calculae a numerical value for he frequency a which Aβ = 1. e) Skech Aβ and use his plo o esimae he phase shif around he loop Aβ a he frequency a which Aβ = 1. Wha is he esimaed phase margin? Indicae he phase margin on your plo. f) onfirm your esimae in (e) wih a calculaion of he phase shif a he frequency from (d). Wha is he calculaed phase margin? g) Is his closed loop circui sable? Hin: You should have found ha he uniy gain configuraion for his op-amp in (2) was unsable, bu he configuraion wih closed loop gain of 1000 was sable. The poin of hese wo problems is ha sabiliy is no a propery of only he op-amp depending on he feedback, a paricular op-amp may give sable or unsable performance wih he feedback loop closed.

4 EE3204 Microelecronics II Biar / McNeill 4. [Pracice wih sabiliy, op-amp ransfer funcions] A high performance op-amp has an open loop ransfer funcion s ( 30,000)1+ 2π( 100kHz) A(s) = s 1+ 2π( 3kHz) 1+ s 2π( 10kHz) a) Deermine numerical values for all pole(s) and/or zero(s) for A(s) b) Plo he pole-zero consellaion for he open-loop A(s) in he s-plane. c) AREFULLY skech he magniude and phase ( A(ω) and A(ω), or, if you prefer, A(f) and A(f)) Bode plo of he open-loop ransfer funcion. Be sure o label and dimension your axes, and indicae any ineresing poins on your plo! The op-amp is o be used in he uniy gain configuraion: d) Deermine he phase margin φ M. IN OUT e) Indicae wheher he closed-loop circui will be sable or unsable.

5 EE3204 Microelecronics II Biar / McNeill 5. [Oscillaors] Figure 7-5a shows a phase-shif oscillaor: a cascade of hree idenical buffered R lowpass sages, followed by an invering amplifier. (For he purposes of his problem, he op-amps use ±10 supplies; assume he op-amps o be oherwise ideal.) A colleague is having rouble wih he design and asks you for help. 56kΩ R F OUT Figure 7-5a. Your colleague expecs a pure sine wave a he oupu bu insead sees he clipped sine wave in Figure 7-5b: To analyze he oscillaor, you break he loop and injec a sinusoidal es signal as shown in Figure 7-5b. IN 56kΩ RF OUT Figure 7-5b. a) A wha frequency f f=0 will he oal phase shif from IN o OUT equal zero? (Or, equivalenly, a wha frequency f f=0 will IN o OUT be exacly in phase?) b) Wih an inpu sine wave a f f=0, wha will be he gain magniude from IN o OUT? (Or, equivalenly, wih an inpu sine wave a f f=0, wha is he magniude of he ransfer funcion v ou /v in?) c) Explain wha is wrong: why is he oupu waveform a clipped sine wave, raher han a pure sine wave wih a sable ampliude?

6 EE3204 Microelecronics II Biar / McNeill 6. [Analysis echniques] To deermine he oscillaion frequency f OS of he Wien bridge oscillaor used in Lab 6, our analysis akes place in he frequency domain and considers (among oher hings) ransfer funcions, he s-plane, and phase shif as a funcion of frequency. To deermine he oscillaion frequency of he Schmi rigger oscillaor used in Lab 3 (and shown below in figure 7-6 o refresh your memory), our analysis ook place in he ime domain o find he oscillaion period T = 4R 2 R R 1 The oscillaion frequency was hen deermined as f OS = 1 T = R 1 4R 2 R Figure 7-6. The quesion is: an he same frequency domain echniques used for he Wien bridge oscillaor be used o deermine he oscillaion frequency for he circui of Figure 7-6? If so, use he frequency domain echnique o perform he analysis and verify he expression for he oscillaion frequency f OS. If no (frequency domain echniques canno be used), explain why no.

7 EE3204 Microelecronics II Biar / McNeill 7. [Advanages of feedback] An audio power amplifier oupu sage is found o have an inerfering 60Hz "hum" corruping is oupu. This can be modeled as shown in Figure 7-7. The power sage is modeled as wo volage sources in series: a dependen source equal o he inpu volage represening he desired behavior, and an independen signal source represening he inerfering signal hum. An op-amp wih open loop gain A buffers he audio signal as shown in Figure 7-7. a) When he op-amp feedback is aken from volage P a he op-amp oupu as shown by connecion (a) in he figure: deermine an expression for v OUT as a funcion of AUDIO, hum, and he op-amp gain A. b) When he op-amp feedback is aken from volage OUT a he load as shown by connecion (b) in he figure: deermine an expression for v OUT as a funcion of AUDIO, hum, and he op-amp gain A. c) In boh cases, skech he approximae OUT if AUDIO is a 600Hz, 100m peak sine wave, hum is a 60Hz, 1 peak sine wave, and A= v hum R + v in - + v in MODEL OF POWER OUTPUT STAGE v AUDIO A (a) v P POWER OUTPUT STAGE vout (b) R L Figure 7-7.