department of information engineering357 operation amplifier the tail, large impedance gives high...

1Department of Information Engineering

Operation amplifier

The tail,large impedancegives high CMRR

Mirror asactive load.High gain

Follower as buffer

amplifier

Push-pullclass B amp


Operational amplifier

• Op-amp

– Differential amp + non-linear amp + output driver

• Op-amp has very high gain (A)

– But the gain is non-linear (because IC vs VBE is not linear)

• Use global feedback to build linear amplifier

– Exact value of the gain of the op amp is not important, as long as it is very large


Feedback Op amp golden rules

Approximations:

1. Voltage difference between the two inputs is zero

2. Input draws no current

Why?

– VOUT = A VIN

– If VOUT is around 10V, A=10,000, then VIN ~ 1mV, voltage difference ~ 1mV (close to zero)

– FET draws virtually zero input current

VIN VOUT


Gain of this amplifier?

V

1 2

2

1 1 2

2

1

( ) ( )

(assume opamp draws no input current)

( )

~ (assume A is very large)

OUT

OUT

IN OUT

IN

V A V V AV V V V

V V V V

R R

V AR

V AR R R

R

R


An easier method

• Because A is so large that V ~ 0 (known as virtual earth)

V ~ 0

1 2

2

1

00 OUTIN

OUT

IN

VV

R R

V R

V R


Inverting amplifier

• Input impedance (RIN)?

– V~ 0, so RIN = R1

• Important

– gain is determined by external parameters that we can control (the resistors)

– gain (A) of the op amp can be non-linear, its exact value is not important, as long as it is very large


Negative feedback

• Feedback MUST be applied to the –ve terminal (–ve feedback), so that V~ 0 (IMPORTANT)

A) Works B) Doesn’t Work


Positive feedback

• +ve VIN produces large +ve VOUT

– +ve VOUT produces +ve V

• which produces an even larger +ve output.

– output reaches max +ve supply voltage very quickly

• useless as an amplifier (but good as a switch, small +ve signal produces large maximum output)


Non-inverting amplifier

• RIN?

– infinite !

• V-?

– V- ~ VIN (V ~ 0)

• Current through R1?

– I=VIN / R1

• Output voltage?

–

V-

IN1

2121OUT V

RRR

)RR(IV

V


Voltage follower

• Left side circuit (work)

– If output is too large, then feedback to the –ve terminal will reduce output to a equilibrium level until V ~ 0

• Right side circuit (doesn’t work)

– If output is too large, then feedback to the +ve terminal will make the output even larger until saturation


Power booster

• The output current of an op amp is usually small

• If you want larger output current, add an external push-pull follower made of discrete power transistors


Power booster

• Normally push-pull follower has cross-over distortion

– Not this one !

• The gain of the amplifier depends on the external feedback circuit

• The forward gain of the internal circuit can be non-linear but must be large


Power of feedback

• Can put in anything in the forward loop, still get good result


Funny circuits

• What is the function of this circuit?


Funny circuits

• Does this circuit work?


Practical circuits

• Design an inverting amplifier with a gain of -100, to be driven by a source whose output impedance is 1M– What is the value of R? How about 100R?


Practical circuits

• A better solution


Practical circuits

• Summing circuit (an adder)

VIN

VOUT


•

•

3213

32

21

1 IIII,k4

VI,

k2V

I,k1

VI

)4/V2/VV(

k1k4

V

k2V

k1V

k1IV

321

321OUT

V1

V2

V3

I


Practical circuits (a simple digital-to-analog converter)

• VOUT = A+2B-3C


Practical circuits

• Perfect current source using imperfect FET

V+-VIN


Active rectifier

• The simple passive rectifier has 0.6V drop between input and output


Active rectifier without the diode drop (optional)

• The active rectifier does not have the 0.6V drop !!

– VIN >0, VOUT is +ve, diode is short-circuit

• Feedback => VOUT = VIN (no 0.6V DC offset)


Problem

• –ve input to V+, VOUT , diode is open circuit

• VOUT pushes to –ve extreme

• When input becomes +ve, takes a long time for the output to move from –ve to +ve (limited by the slew rate)


Active rectifier (optional)

• This improved circuit prevents the rectifier from saturation


Negative-impedance converter (NIC)

• An interesting two-terminals active device

– apply a +ve voltage, you see a current flowing OUT

– a negative impedance (!!)

– i.e. ZIN = - Z !!

– (leave the proof as exercise)


Gyrator

• The following circuit is a gyrator

– (leave the proof as exercise)ZR

Z2

in


Gyrator

• Use of gyrator

– can turn a capacitor into inductor !!

• How?

–

– ZIN behaves as an inductor with L = CR2

• The use– replace bulky inductors by small gyrated capacitors

– useful in integrated circuit design and small devices

22

in jwCRZ

RZ

jwC1

Z


Positive feedback

• Apply feedback to the non-inverting (+ve) terminal

– small +ve input produces a larger +ve output

– output is feedback to the non-inverting input

– produces an even larger output

– quickly push the output to saturation

• Uses

– Comparators

– Oscillators


Comparator – a simple switch

• Output = +15V if VIN < 0

• Output = -15V if VIN > 0

VIN -

+

VOUT

+15V

-15V


• A poor comparator because

– if the input is noisy, the output makes several transitions (switching noise)


311 op amp

• The output stage (emitter follower) is connected to external power supply

• User can choose the output voltage they like


Schmitt trigger (an inverter switch, high VIN, low VOUT)

• Hysteresis (circuit has memory)

– the output switches at two separate threshold


Analysis

• If VOUT = high (~5V)

– VOUT ~= 5V,

– Switching threshold V+ = 5V

• When VIN > 5V

– VOUT =0V

– Switching threshold V+=4.76V

• Now if VIN drops slightly below 5V

– VOUT won’t change state

– Eliminate noisy switching

10V 5V

10K

10K100K

1K

V+


Analysis

• VIN > 5V, VOUT=0V, V+ =4.76V

• If VIN < 4.76V, VOUT=5V,

– V+ =5V (the new threshold)

10V

10K

10K100K

V+ 0V


Positive feedback

• if phase shift = 180o in box ‘X’ at certain frequency, then the feedback becomes +ve (unstable) !!

• This high frequency has sustained itself even there is no input

– oscillation


Nasty oscillators

• A follower driving a long cable (a common problem)

– phase shift through the op amp = 180o

– cable’s capacitance adds another 90o

– The internal capacitance at high frequency adds another 90o

• The follower oscillates !

(cable capacitance)


Ways to break the oscillation

• Op amp oscillates at high frequency because of the additional phase shift introduced by its internal capacitor

• Solution

– Reduce the loop gain AB at high frequency

• At the frequency that may cause oscillation, make A ~ 0, so that the loop gain (AB) < 1

– Op am that does this is called frequency compensated op amp

• Disadvantage is that the max bandwidth is reduced


• One oscillates, the other not

– 411 is frequency compensated, never oscillates

411 311

Never oscillates May oscillates

|A|

f

|A|

ffocc


Slew rate

• The rate that output can change

• Wider bandwidth higher frequency faster slew rate

• 311 has faster slew rate, good as a switch


• What is the use of these two resistors?

department of information engineering357 operation amplifier the tail, large impedance gives high...

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