Notes Midterm 1 – Tuesday Oct. 12, 2004, 12:40-2:00. Last names beginning with A-L in F295 Haas; M-Z in Sibley Auditorium, Bechtel Center. Covers through Ch. 3, topics of HW4, concepts of first 3 labs. GSIs will review material in discussion sections this week. Bring photo-ID, no books, no cell phones, you may bring one 8-1/2 by 11 sheet of notes, you may bring a calculator, and you don’t need a blue book.
EECS40, Fall 2004
Lecture 12, Slide 1
Prof. White
Lecture #12 • • • • • •
OUTLINE Op-Amp circuits continued: examples Inverting amplifier circuit Summing amplifier circuit Non-inverting amplifier circuit Differential amplifier circuit Current-to-voltage converter circuit Reading Chapter 14. (Also, amplifiers are discussed in great detail in Ch. 11)
EECS40, Fall 2004
Lecture 12, Slide 2
Prof. White
Review: Negative Feedback • Negative feedback is used to “linearize” a high-gain differential amplifier. With feedback
+
V V+
V0
+
Without feedback
VIN
A 105
V0(V)
V0
V0
5
50μV
A 105
V V
5 4 3 2 1 1 2345
VIN
5 EECS40, Fall 2004
Lecture 12, Slide 3
Prof. White
Application of Voltage Follower: Sample and Hold Circuit
EECS40, Fall 2004
Lecture 12, Slide 4
Prof. White
Inverting Amplifier Circuit in + – +
vs
vn + vp – –
+
Rs
if
vo
–
is
Rf
+ vo –
Rf Rs
vs
in = 0 is = -if vp = 0 vn = 0 EECS40, Fall 2004
Lecture 12, Slide 5
Prof. White
Analysis using Realistic Op Amp Model • In the analysis on the previous slide, the op amp was assumed to be ideal, i.e. Ri = ; A = ; Ro = 0 • In reality, an op amp has finite Ri, finite A, nonzero Ro, and usually is loaded at its output terminals with a load resistance RL.
EECS40, Fall 2004
Lecture 12, Slide 6
Prof. White
Summing Amplifier Circuit Ra ib
+
– +
ic vc
– +
vb
in
Rc
vn + vp – –
in = 0 ia + ib + ic = -if
+
– +
va
Rb
Rf
if
–
ia
+ vo –
superposition !
Rf Rf Rf vo va vb vc Rb Rc Ra
vp = 0 vn = 0 EECS40, Fall 2004
Lecture 12, Slide 7
Prof. White
Application: Digital-to-Analog Conversion A DAC can be used to convert the digital representation Binary Analog number output of an audio signal into an analog voltage that is then (volts) used to drive speakers -- so that you can hear it! 0000 0 “Weighted-adder D/A converter” S4
20K 40K
S2
80K
+ -
S1
4-Bit D/A (Transistors are used as electronic switches) EECS40, Fall 2004
5K
+
+
S3
8V
10K
V0
S1 closed if LSB =1 S2 " if next bit = 1 S3 " if " " = 1 S4 " if MSB = 1 Lecture 12, Slide 8
0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111
MSB
.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5
LSB Prof. White
Analog Output (V)
Characteristic of 4-Bit DAC 8 7 6 5 4 3 2 1 0
0000
0
2 0001
EECS40, Fall 2004
4 0100
6
8
10
1000
12
14
16
1111
Digital Input Lecture 12, Slide 9
Prof. White
Noninverting Amplifier Circuit
+ vn vg
Rg +
– +
–
ip
+
in
vo
–
Rs
Rf
vp
+ vo –
Rs R f Rs
vg
–
i p = 0 vp = vg vn = vg in = 0 Rs & Rf form a voltage divider EECS40, Fall 2004
Lecture 12, Slide 10
Prof. White
Differential Amplifier Circuit Ra in
– +
Rc – +
vb
ip vn Rd –
+ vp –
vn va vn vo 0 in = 0 Ra Rb Rd ip = 0 v p R R vb vn c d EECS40, Fall 2004
+
+
–
va
Rb
+ vo –
Rd ( Ra Rb ) Rb vo vb va Ra ( Rc Rd ) Ra Ra Rc Rb vb va If , then vo Rb Rd Ra
Lecture 12, Slide 11
Prof. White
Differential Amplifier (cont’d) More usual version of differential amplifier (Horowitz & Hill, “Art of Electronics”, p. 184-5 (part of their “smorgasbord” of op-amp circuits): Let Ra = Rc = R1 and Rb = Rd = R2 Then v0 = (R2 / R1)(vb – va) To get good “common-mode rejection” (next slide) you need well-matched resistors (Ra and Rc, Rb and Rd), such as 100k 0.01% resistors
EECS40, Fall 2004
Lecture 12, Slide 12
Prof. White
Differential Amplifier – Another Perspective Redefine the inputs in terms of two other voltages: 1. differential mode input vdm vb – va 2. common mode input vcm (va + vb)/2 so that va = vcm – (vdm/2) and vb = vcm + (vdm/2) Then it can be shown that vo Acm vcm Adm vdm Ra Rd Rb Rc Rd ( Ra Rb ) Rb ( Rc Rd ) where Acm and Adm Ra ( Rc Rd ) 2 Ra ( Rc Rd ) “common mode gain” EECS40, Fall 2004
“differential mode gain”
Lecture 12, Slide 13
Prof. White
Differential Amplifier (cont’d)
Ra Rc Rb If , then vcm 0 and vdm Rb Rd Ra • An ideal differential amplifier amplifies only the differential mode portion of the input voltage, and eliminates the common mode portion. – provides immunity to noise (common to both inputs)
• If the resistors are not perfectly matched, the common mode rejection ratio (CMRR) is finite:
Adm 1 Rb / Ra Ra Rc CMRR if (1 ) Acm Rb Rd EECS40, Fall 2004
Lecture 12, Slide 14
Prof. White
Op-Amp Current-to-Voltage Converter
EECS40, Fall 2004
Lecture 12, Slide 15
Prof. White
Summary • Voltage transfer characteristic of op amp: vo
Vcc slope = A >>1
~10 V
vp–vn
-Vcc ~1 mV
• A feedback path between an op amp’s output and its inverting input can force the op amp to operate in its linear region, where vo = A (vp – vn) • An ideal op amp has infinite input resistance Ri, infinite open-loop gain A, and zero output resistance Ro. As a result, the input voltages and currents are constrained: vp = vn and ip = -in = 0 EECS40, Fall 2004
Lecture 12, Slide 16
Prof. White
EECS40, Fall 2004
Lecture 12, Slide 17
Prof. White
EECS40, Fall 2004
Lecture 12, Slide 18
Prof. White
EECS40, Fall 2004
Lecture 12, Slide 19
Prof. White
Differentiator (from Horowitz & Hill)
EECS40, Fall 2004
Lecture 12, Slide 20
Prof. White
Op-Amp Imperfections Discussed in Hambley, pp. 651-665 (of interest if you need to use an op-amp in a practical application!) Linear range of operation: Input and output impedances not ideal values; gain and bandwidth limitations (including gain-bandwidth product); Nonlinear limitations: Output voltage swing (limited by “rails” and more; output current limits; slew-rate limited (how fast can the output voltage change); full-power bandwidth DC imperfections: Offset current (input currents don’t sum exactly to zero); offset voltage;
EECS40, Fall 2004
Lecture 12, Slide 21
Prof. White