11/17/2009 Reading Chapter 11 of Hambley Chapter 14.8 of Hambley

Transcription

1 EE40 Lec 21 Amplifiers Prof. Nathan Cheung 11/17/2009 eading Chapter 11 of Hambley Chapter 14.8 of Hambley Slide 1

2 OUTLINE Amplifier Models with dependent sources Efficiency Input and Output Impedance Effects Pulse esponse Linear and Nonlinear Distortions Differential Amplifier Common Mode ejection Instrumentation Amplifier Bias Current, Offset Voltage, Offset Current Slide 2

3 Voltage Amplifier Model Voltage Gain A = o / i Parameters: Current Gain A i= i o/i i = A ( i/ L L) Input impedance i Power Gain G = A A i = (A ) 2 ( i / L ) Output impedance o Open-circuit oltage gain A oc * Impedance is complex in general. is used here for simplicity Slide 3

4 Cascade Amplifiers Simplification i = i of first stage o = o of flast stage A oc has to include loading effect of each stage Slide 4

5 Amplifier Efficiency Power to load (P o ) Efficiencyi η 100% Power from power sup ply(p ) s Slide 5

6 Example : Amplifier Efficiency Power Supply A Source Amplifier Power Supply B Amplifier Efficiency η = 8/22.5 =36% Slide 6 Source P i = (10-3 V) 2 /10 5 Ω =10-11 W Load P 0 = (8V) 2 /8Ω =8 W Power Supplies P s = 15W+7.5W =225W 22.5 Amplifier P -11 d = 22.5W+10 W-8W = 14.5 W Load

7 Current Amplifier Model Parameters: Input impedance i Output impedance o Current Gain A i = i o /i i Voltage Gain A = o/ i= A i i( ( L/ i i) Power Gain G = A A i = (A i ) 2 ( L / i ) Short-circuit current gain A isc * Impedance is complex in general. is used here for simplicity Slide 7

8 Voltage Amplifier and Current Amplifier Models Conersion Same Input impedance i Same Output impedance o A isc = i i osc i = A oc i o Slide 8

9 Transconductance Amplifier Model Short-Circuit Transconductance Gain [ in Siemens] G msc = i osc / i This model is used for the MOSFET small signal model, with i = Slide 9

10 Example: NMOS Small-Signal Equialent Circuit oltage gain = g out m gs ( r ) out A = = g m o in How can we increase the gain, A? Slide 10 o D ( r ) D

11 Transresistance Amplifier Model Open-Circuit Transresistance Gain [ in ohms] moc = ooc /i i Slide 11

12 Input Impedance Effects Desire in >> s for in s Desire in << s for i in i s Desire in s to minimize transmission line reflection Slide 12

13 Source and Load esistance Effects Example: MOSFET Small Signal Model Oerall transconductance is degraded by the source resistance s and load resistance L i out s in g m in + s L + out = out Slide 13

14 ac Couplng Slide 14

15 Pulse esponse: ise time, inging, and Tilt ise Time Slide 15

16 ise Time (estimate only) For f H =1/C, tr~ln(9)/f H Slide 16

17 inging (qualitatie only) Amplifier has a peaked response at f r 1/f r Slide 17

18 Tilt (estimate only) For f L ~1/C Slide 18

19 Linear Waeform Distortion Let the Phasor Amplifier Gain be H(ω)=A(ω)e j θ(ω) With in (t) = o cos[ωt+θ]= e{ o e j(ωt+θ) } out (t) = e{a(ω) o e j(ωt+θ+ θ(ω) } =A(ω) o cos[ωt+θ+ θ(ω)] Therefore, zero waeform distortion if A(ω) independent of ω and θ(ω)=0 or A(ω) independent of ω and θ(ω)=kω out (t) =A(ω) o cos[ω(t+k)+θ] - just a time shift Slide 19

20 Linear Waeform Distortion Amplitude Distortion A(ω) depends on ω Slide 20

21 Linear Waeform Distortion Phase Distortion θ(ω) depends on ω Example: (ω)=45 = o for all ω Slide 21

22 Conditions for zero Linear Waeform Distortion Slide 22

23 Non-Linear Waeform Distortion Harmonic Distortion i =Kcos(ωt) Polynomial expansion of o =f( i ) o =A o +A 1 i +A 2 ( i ) 2 +A 3 ( i ) 3 + = Vo+ V 1 cos(ωt)+ V 2 cos(2ωt)+ Total Harmonic Distortion 2nd harmonic THD = 2 V 2 V V 3 4 V + 1 V + 1 V Slide 23

24 Differential Amplifier Slide 24

25 Differential Signal and Common Mode Signal edefine the inputs in terms of two other oltages: 1. differential mode input id i1 i2 2. common mode input icm ( i1 + i2 )/2 so that i1 = icm + ( id /2) and i2 = icm - ( id /2) + o = A d id Acm icm differential mode gain common mode gain Slide 25

26 Common Mode ejection atio Example CM (in db) = 20log A d A cm Differential signal from sensor = 1mV (peak). We want outputs signal > 1V implies A d > 1000 Common mode signal =100V (from power line). We want common mode signal < 0.1V implies A cm <10-4 Therefore CM needs to be > 20log(10 7 )= 140dB Slide 26

27 A cm Measurement Measurement of CM A d Measurement Slide 27

28 Example: Differential Amplifier OpAmp Circuit b i + a + + i n + + a c i p + o + + p n b d a b b b a d o + = ) ( ) ( p = 0 + b o n a a n d a a b d c a o + ) ( i n = 0 ( ) b h If Slide 28 n b d c d p = + = i p = 0 ( ) a b a b o d c b a = = then, If

29 Differential Amplifier (cont d) If a b = CM= c d, then A cm = 0 and If the resistors are not perfectly matched, o 0 een when a = b. The common mode rejection ratio is finite: A d = b a CM A A d cm 1 + b ε / a if a b = (1 ε) c d *To get good common-mode mode rejection, you need well-matched resistors ( a and c, b and d ), such as 100kΩ 0.01% resistors Slide 29

30 Instrumentation Amplifier Sensor applications frequently requiring a differential amplifier with ery large input resistance for both the inerting and non inerting inputs. An instrumentation amplifier employs two non inerting amplifiers to buffer the input signal, followed by an inerting stage that forms the difference. Slide 30

31 Instrumentation Amplifier CMM does not depend on internal resistances of 1 and 2 Slide 31

32 Offset Voltage, Offset Current, and Bias Current For direct coupled amplifiers, unbalanced internal components can cause a nonzero output een input sources are zero. Three current sources and one oltage sources are added to model this imperfection V off =offset oltage source I off =offset current source I B = Bias current Slide 32

33 Example Calculation Gien V off =2mV I B = 100nA I off = 20nA A cm =1 A d =100 Both input terminals to ground through 100kΩ resistors Use superposition Vo = A d (V off +V Ioff )+ A cm icm = 1000( )+1(0.01)=3.343V Slide 33