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Announcements • Assignment 3 due now, or by tomorrow 5pm in my mailbox • Assignment 4 posted, due next week – Thursday in class, or Friday 5pm in my mailbox • mid-term: Thursday, October 27th Lecture 11 Overview • • • • • Amplifier impedance The operational amplifier Ideal op-amp Negative feedback Applications – Amplifiers – Summing/ subtracting circuits Impedances • Why do we care about the input and output impedance? • Simplest "black box" amplifier model: ROUT VIN RIN AVIN VOUT • The amplifier measures voltage across RIN, then generates a voltage which is larger by a factor A • This voltage generator, in series with the output resistance ROUT, is connected to the output port. • A should be a constant (i.e. gain is linear) Impedances • Attach an input - a source voltage VS plus source impedance RS RS VS ROUT VIN RIN AVIN • Note the voltage divider RS + RIN. • VIN=VS(RIN/(RIN+RS) • We want VIN = VS regardless of source impedance • So want RIN to be large. • The ideal amplifier has an infinite input impedance VOUT Impedances • Attach a load - an output circuit with a resistance RL RS VS ROUT VIN RIN AVIN • Note the voltage divider ROUT + RL. • VOUT=AVIN(RL/(RL+ROUT)) • Want VOUT=AVIN regardless of load • We want ROUT to be small. • The ideal amplifier has zero output impedance VOUT RL Operational Amplifier • Integrated circuit containing ~20 transistors, multiple amplifier stages Operational Amplifier • An op amp is a high voltage gain, DC amplifier with high input impedance, low output impedance, and differential inputs. • Positive input at the non-inverting input produces positive output, positive input at the inverting input produces negative output. Operational Amplifier • An op amp is a high voltage gain, DC amplifier with high input impedance, low output impedance, and differential inputs. • Positive input at the non-inverting input produces positive output, positive input at the inverting input produces negative output. • Can model any amplifier as a "black-box" with a parallel input impedance Rin, and a voltage source with gain Av in series with an output impedance Rout. Ideal op-amp • Place a source and a load on the model RS + vout RL - • Infinite internal resistance Rin (so vin=vs). • Zero output resistance Rout (so vout=Avvin). • "A" very large • iin=0; no current flow into op-amp So the equivalent circuit of an ideal op-amp looks like this: Many Applications e.g. • • • • • • Amplifiers Adders and subtractors Integrators and differentiators Clock generators Active Filters Digital-to-analog converters Applications Originally developed for use in analog computers: http://www.youtube.com/watch?v=PBILL8UypHA Applications Originally developed for use in analog computers: http://www.youtube.com/watch?v=PBILL8UypHA Using op-amps • Power the op-amp and apply a voltage • Works as an amplifier, but: • No flexibility (A~105-6) • Exact gain is unreliable (depends on chip, frequency and temp) • Saturates at very low input voltages (Max vout=power supply voltage) • To operate as an amp, v+-v-<VS/A=12/105 so v+≈v• In the ideal case, when an op-amp is functioning properly in the active region, the voltage difference between the inverting and noninverting inputs≈0 Noninverting Amplifier vO A(v v ) R2 vO A vIN vO R1 R2 AR2 AvIN vO 1 R1 R2 AvIN vO AR2 1 R1 R2 When A is very large: Take A=106, R1=9R, R2=R AvIN vO AR2 1 R1 R2 AvIN vO R2 A R1 R2 vO vIN R1 R2 R2 >>1 10 6 vIN vO 6 10 R 1 9R R 10 6 vIN vO 6 1 1 10 10 vO vIN 10 • Gain now determined only by resistance ratio • Doesn’t depend on A, (or temperature, frequency, variations in fabrication) Negative feedback: • How did we get to stable operation in the linear amplification region??? • Feed a portion of the output signal back into the input (feeding it back into the inverting input = negative feedback) • This cancels most of the input • Maintains (very) small differential signal at input • Reduces the gain, but if the open loop gain is ~, who cares? • Good discussion of negative feedback here: http://www.allaboutcircuits.com/vol_3/chpt_8/4.html Why use Negative feedback?: • Helps to overcome distortion and non-linearity • Improves the frequency response • Makes properties predictable - independent of temperature, manufacturing differences or other properties of the opamp • Circuit properties only depend upon the external feedback network and so can be easily controlled • Simplifies circuit design - can concentrate on circuit function (as opposed to details of operating points, biasing etc.) More insight • Under negative feedback: R1 R2 vIN vO R1 v v 0 A A v v • We also know • i+ ≈ 0 • i- ≈ 0 • Helpful for analysis (under negative feedback) • Two "Golden Rules" 1) No current flows into the op-amp 2) v+ ≈ v- More insight • Allows us to label almost every point in circuit terms of vIN! 1) No current flows into the op-amp 2) v+ ≈ v- Op amp circuit 1: Voltage follower • So vO=vIN •or, using equations vO vIN R1 0 R2 • What's the gain of this circuit? R1 R2 R2 Op amp circuit 1: Voltage follower • So vO=vIN •or, using equations vO vIN R1 R2 R2 R1 0 R2 • What's the application of this circuit? •Buffer Useful interface between different circuits: voltage gain = 1 Has minimum effect on previous and next input impedance=∞ circuit in signal chain output impedance=0 RS VS ROUT VIN RIN AVIN VOUT RL Op amp circuit 2: Inverting Amplifier • Signal and feedback resistor, connected to inverting (-) input. • v+=v- connected to ground iS iF iin 0 i S i F vout v vS v v+ grounded, so: RF RS v v 0 v 0 vS 0 out RF RS vout RF vS RS vout RF Gain vS RS Op amp circuit 3: Summing Amplifier • Same as previous, but add more voltage sources i1 i2 ..... iN iF vS 1 vS 2 vSN vout ..... RS1 RS 2 RSN RF vout RF RF RF vS 1 vS 2 ..... vSN RS 2 RSN RS1 If RS1 RS 2 ... RSN RS vout RF (vS 1 vS 2 ... vSN ) RS Summing Amplifier Applications • Applications - audio mixer • Adds signals from a number of waveforms • http://wiredworld.tripod.com/tronics/mixer.html • Can use unequal resistors to get a weighted sum • For example - could make a 4 bit binary - decimal converter • 4 inputs, each of which is +1V or zero • Using input resistors of 10k (ones), 5k (twos), 2.5k (fours) and 1.25k (eights) Op amp circuit 4: Another non-inverting amplifier • Feedback resistor still to inverting input, but no voltage source on inverting input (note change of current flow) • Input voltage to non-inverting input iS iF v v since iin 0 and v v vS vout v 0 vout v RS RF RF v 1 RS RF vS vout 1 RS vout RF Gain 1 vS RS Op amp circuit 5: Differential Amplifier (subtractor) i1 i2 0 vout v v1 v R1 R2 v v R2 v v2 v R1 R2 vout R2 (v2 v1 ) R1 Useful terms: • if both inputs change together, this is a common-mode input change • if they change independently, this is a normal-mode change • A good differential amp has a high common-mode rejection ratio (CMMR) Differential Amplifier applications • Very useful if you have two inputs corrupted with the same noise • Subtract one from the other to remove noise, remainder is signal • Many Applications : e.g. an electrocardiagram measures the potential difference between two points on the body http://www.picotech.com/applications/ecg.html The AD624AD is an instrumentation amplifier - this is a high gain, dc coupled differential amplifier with a high input impedance and high CMRR (the chip actually contains a few opamps)