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Lecture #19 amplifier examples: comparators, op amps. Reminder: MIDTERM coming up one week from today (Monday October 18 th ) This week: Review and examples. Midterm. Monday, October 18, In class One page, one side of notes. Topics. Today: Amplifier examples Comparator Op-Amp. V IN.
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Lecture #19 amplifier examples: comparators, op amps. Reminder: MIDTERM coming up one week from today (Monday October 18th) This week: Review and examples EE 42 fall 2004 lecture 19
Midterm • Monday, October 18, • In class • One page, one side of notes EE 42 fall 2004 lecture 19
Topics Today: • Amplifier examples • Comparator • Op-Amp EE 42 fall 2004 lecture 19
VIN + + V0 Amplifier V+rail V+rail V0=AVIN Output is referenced to “signal ground” V0 cannot rise above some physical voltage related to the positive power supply VCC (“ upper rail”) V0 < V+RAIL V0 cannot go below most negative power supply, VEE i.e., limited by lower “rail” V0 > V-RAIL EE 42 fall 2004 lecture 19
VIN + + V0 WHAT ARE I-V CHARACTERISTICS OF AN ACTUAL HIGH-GAIN DIFFERENTIAL AMPLIFIER ? Circuit model gives the essential linear part The gain may be 100 to 100,000 or more But V0 cannot rise above some physical voltage V0 < V+RAIL And V0 cannot go below the lower “rail” V0 > V-RAIL CMOS based amplifiers can often go all the way to their power supplies, perhaps ± 5 volts EE 42 fall 2004 lecture 19
+ + High gain Amplifier VIN VIN V0 We can make very high gain amplifiers by cascading lower gain amplifiers. For example, if we have two amplifiers, each with a gain of 100, then when the output of the first is feed into the input of the second, the total gain is 10,000. With a very high gain amplifier, a very small change in the input causes a large change in the output voltage, so the range of voltages over which the input results in a linear output is very narrow. EE 42 fall 2004 lecture 19
Differential Amplifier Circuit Model in linear region V0 V+ + A AV1 Ri V + + + V1 V0 But if A ~ , is the output infinite? “Very high gain” OP-AMPS AND COMPARATORS A very high-gain differential amplifier can function either in extremely linear fashion as an operational amplifier (by using negative feedback) or as a very nonlinear device – a comparator. “Differential” V0 depends only on difference (V+ V-) EE 42 fall 2004 lecture 19
(a) V-V near origin (b) V-V over wider range upper “rail” V0 (V) V0 (V) 3 0.2 2 0.1 1 VIN(V) VIN(V) 1 3 3 2 1 2 10 30 30 20 10 20 1 lower “rail” 2 .2 3 I-V Characteristics of a real high-gain amplifier Example: Amplifier with gain of 105, with max V0 of 3V and min V0 of 3V. EE 42 fall 2004 lecture 19
(c) Same V0 vs VIN over even wider range V0 (V) 3 2 (b) V-V over wide range 1 upper “rail” 1 V0 (V) 2 VIN(V) 3 3 2 1 VIN(V) 1 3 3 2 1 2 10 30 30 20 10 20 lower “rail” 1 2 3 I-V CHARACTERISTICS OF AN ACTUAL HIGH-GAIN DIFFERENTIAL AMPLIFIER (cont.) Example: Amplifier with gain of 105, with upper rail of 3V and lower rail of 3V. We plot the V0 vs VIN characteristics on two different scales EE 42 fall 2004 lecture 19
(c) V-V with equal X and Y axes V0 (V) 3 2 1 1 VIN(V) 2 3 1 3 3 2 1 2 I-V CHARACTERISTICS OF AN ACTUAL HIGH-GAIN DIFFERENTIAL AMPLIFIER (cont.) Now plot same thing but with equal horizontal and vertical scales (volts versus volts) Note: • (a) displays linear amplifier behavior • (b) shows limit of linear region – (|VIN| < 30 V) • (c) shows comparator function (1 bit A/D converter centered at VIN = 0) where lower rail = logic “0” and upper rail = logic “1” EE 42 fall 2004 lecture 19
V0 VIN V0 2 If VIN > 1.010 V, V0 = 2V = Logic “1” 1 1V VIN 0 1 2 If VIN < 0.99 V, V0 = 0V = Logic “0” + VIN + V0 Comparator EXAMPLE OF A HIGH-GAIN DIFFERENTIAL AMPLIFIER OPERATING IN COMPARATOR (A/D) MODE Simple comparator with threshold at 1V. Design lower rail at 0V and upper rail at 2V (logic “1”). A = large (e.g. 102 to105 ) NOTE: The actual diagram of a comparator would not show an amplifier with “offset” power supply as above. It would be a simple triangle, perhaps with the threshold level (here 1V) specified. EE 42 fall 2004 lecture 19
pulses out comparator transmission regenerated pulses pulses in We set comparator threshold at a suitable value (e.g., halfway between the logic levels) and comparator output goes to: +rail if VIN > VTHRESHOLD and to rail if VIN < VTHRESHOLD. Conversion from signals to digital data Signals are conveyed as voltages, but signal levels must be converted into digital data. ( 1 bit A/D) The rails of the comparator are the logic levels, for example +rail = “1” or “true” and -rail→”0” or “false” EE 42 fall 2004 lecture 19
R1 R2 R1 R2 V0 VIN AV1 Ri + EXAMPLE VIN Circuit Model + - V0 V1 + - + OP-AMPS A very high-gain differential amplifier can function in extremely linear fashion as an operational amplifier by using negative feedback. Negative feedback Stabilizes the output We will show that that for A (and Ri 0 for simplicity) Stable, finite, and independent of the properties of the OP AMP ! EE 42 fall 2004 lecture 19
Example: R1 R2 9K 1K V0 VIN Circuit (assume R1 R2 V0 1K 9K () (+) VIN + - + OP-AMPS – “TAMING” THE WILD HIGH-GAIN AMPLIFIER KEY CONCEPT: Negative feedback First of all, notice that if the input resistance of the amplifier is so large that the current into it is negligible, then R1 and R2 form a voltage divider to give the input to the negative terminal EE 42 fall 2004 lecture 19
OP-AMP very high gain →predictable results Analysis: Lets solve for V- then find Vo from Vo = A (V+ - V-) EE 42 fall 2004 lecture 19
OP-AMP very high gain →predictable results EE 42 fall 2004 lecture 19
Example: R2 R1 VIN 9K 1K V0 + - + OP-AMPS – Another Basic Circuit Now lets look at the Inverting Amplifier When the input is not so large that the output is hitting the rails, we have a circuit model: R1 R2 VIN V0 1K 9K () (+) EE 42 fall 2004 lecture 19
Inverting amplifier analysis Analysis: Solve for V- then find VO from VO = - AV- EE 42 fall 2004 lecture 19
Solving Op-Amp circuits We can take a very useful short-cut for OP-Amp circuits with high gain if we notice that if the circuit is in the linear range, then (V+-V-) must be very small, and it goes to zero as the gain goes to infinity. The shortcut is just to assume (V+-V-) =0, and then to check later to make sure that the amplifier is truly in the linear range. EE 42 fall 2004 lecture 19
+ - + Capacitor in the feedback Now lets look at the Inverting Amplifier Example: R1 VIN 1K V0 In the linear range, the circuit model: R1 VIN V0 1K () (+) EE 42 fall 2004 lecture 19
Integrator • Since the positive terminal is grounded, the negative terminal will be near zero volts • The input terminal also takes in no current EE 42 fall 2004 lecture 19