Physics 111 – BSC Lecture 9 Page 1 of 7 Jim Siegrist Phone: 486-4397 Email: [email protected] Room (at LBL): 50-4055 Advice: Today: lec 9 OP AMP III lec 10 TH Mar 15 lec 11 TH Mar 22 lec 12 TUE Apr 3 Last Lecture!! Final project proposals (< ½ page) due Monday, March 19. I sign off, talk to TA’s first. Problems 8.12, 8.13 → supplementary. Circuit Analyses Frequency Response, General Circuit Substitute the op-amp model: (A = A(ω) → small at large ω) Node equations at v− and vout: (1) 01=+−+−−−−iFoutinRvZvvZvv (2) ()00=−−+−−−ooutFoutRvAvZvv vinvoutZ1ZFvinvoutZ1ZFA( )vv+−−RiRo()+()−Physics 111 – BSC Lecture 9 Page 2 of 7 inoutvvA =′ Solve (2) for v− in terms of vout ⇒ From (1), ()⎟⎟⎠⎞⎜⎜⎝⎛−=⇒=⎟⎟⎠⎞⎜⎜⎝⎛−+⎟⎟⎠⎞⎜⎜⎝⎛+−−oFoFoutFooFoutRAZRZvvZRAvRZv1||0111()()()⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎣⎡++−=⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎣⎡⎟⎟⎠⎞⎜⎜⎝⎛++−=→∞→→⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎣⎡−+⎟⎟⎠⎞⎜⎜⎝⎛++−−=⎥⎥⎥⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎢⎢⎢⎣⎡⎟⎟⎠⎞⎜⎜⎝⎛−⎟⎟⎠⎞⎜⎜⎝⎛+⎟⎟⎠⎞⎜⎜⎝⎛++−−==′⇒=⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎣⎡−⎟⎟⎠⎞⎜⎜⎝⎛−⎟⎟⎠⎞⎜⎜⎝⎛++⇒=−⎟⎟⎠⎞⎜⎜⎝⎛++−111121111111111111,0lim1111111111111111||1111111ZZAAZZAZZZZZRRAZRZZRRZZZZRAZZRZRZZZZvvAZvZRAZRZRZZvZvZvRZZvFFFFFioFoFFoiFFoFFoFiFFinoutinFoFoFiFoutinFoutiFPhysics 111 – BSC Lecture 9 Page 3 of 7 As gain gets small, Also, just rearranging terms, Stability Instability most often occurs when output appears for no input → oscillations. Signal suffers a phase shift passing through amp. Typically, ~ 0 at low frequency increases at higher frequencies → −1 at 180° ⇒ negative feedback at low ν becomes positive at high ν General form for gain ~ ()()()()ωωωωfAAcA+=′1 c(ω) depends on form of circuit f(ω) is called feedback coefficient if A(ω)f(ω) = −1 (for some ω), instability results Turns out, if | Af | ≥ 1 for ω whose phase shift is −180°, instability occurs (Nyquist Criterion) For voltage follower, (last time) for inverter (see previous pg) 0~~1111→+−+−′ZZAZZZZZAZAFFFF⎟⎟⎠⎞⎜⎜⎝⎛++⎟⎟⎠⎞⎜⎜⎝⎛+−=⎟⎟⎠⎞⎜⎜⎝⎛+⎟⎟⎠⎞⎜⎜⎝⎛++⎟⎟⎠⎞⎜⎜⎝⎛+⎟⎟⎠⎞⎜⎜⎝⎛−=′FFFFFFFZZZAZZZAZZZZZZAZZZZZAA11111111111FFFZZZfZZZcfcAAA+=+−=⇒==⇒+=′111&11Physics 111 – BSC Lecture 9 Page 4 of 7 Suppose: (follower) −180° ⇒ ω ~ 107 A = gain ~ 104 at 107 ⇒ | Af | >> 1 ⇒ oscillations Op-Amp design: ω ~ 107, |A| ~ +10−1 ⇒ stable Obtain by putting RC filter someplace in op-amp (rolloff at |A| 20db/decade, phase shift of 90°) More phase shifts from stray capacitance at higher ν, but |A| already < 1 emphasize ⇒ why leads must be short, circuits neat |A|ω1051041031106107108ω107010−90θA−180|A|ω10510107ω1070−90θA−18010600Physics 111 – BSC Lecture 9 Page 5 of 7 Summary of Op-Amp • Op amps are cheap, versatile, and form building blocks for circuits • Ideal op-amp: 0=∞=∞=oiRRA • Offsets • MSR • Negative feedback provides de-sensitivity of op-amp characteristics • Limited frequency response – pass band with negative feedback much larger • Improper feedback ⇒ oscillations Instruments & Devices Transistors Transistors are control elements Take a small input signal & amplify it, with the power to do so coming from the external DC sources. Bipolar: current-operated, 3-terminal device consisting of one forward & one reverse biased diode, with base region in common Emitter-Base is forward biased by (−)VBE ⇒ Majority carriers (hole) are injected into base where they drift to collector. ()+I (diffusion gradient) Electron current ()−I from base to emitter is made small by construction (doping – emitter much more heavily doped) Total emitter current −++== IIIE controlelementpowersupplyRLvSEmitter−VBEV CB+CollectorJEJCPI +I −N(I I ) +−PCPICOIBBaseI +COIPCI −COIEICPhysics 111 – BSC Lecture 9 Page 6 of 7 Some holes reach collector, rest are recombined in the base. pcII −+ go out though base Ipc go to collector Reverse current Ico from collector to base +coI = holes moving from N to P across Jc −coI = electrons moving from P to N across JC −++=−cococoIII − sign convention so Ico in direction Ic Holes generated thermally within the base Total collector current: EcopccocIIIIIα−≡−= or EcocIII −−≡α large-signal current gain α always > 0, ranges from .90 − .998, varies with IE, VCB, temperature Also, ααβ−≡1; in CE configuration, Ic ~ β Ibase ⇒ β is current gain of the device; current operated device!! Circuit Symbols: Identical, arrow opp. [Current in emitter is positive in the direction of the arrow on the emitter lead] 3 terminals ⇒ 6 ways to connect N-P-NVCBICVCEVBEIBIEbceP-N-PIEIBVCEVBEICbcePhysics 111 – BSC Lecture 9 Page 7 of 7 Closing Comments: * VCE > 0, collector more positive than emitter * * max power dissipation, etc. limits on IC, IB, VCE Pmax = (IC VCE)max * VB ~ VE + .6 in active gain region (when ‘on’) = VE + VBE * IC ≈ βIB current operated device detailed use of this in lecture 11 – push-pull case