To Get a Perfect To Get a Perfect “A”…“A”…

An Engr. 311 Project by Corrin Meyer

Project StatementProject Statement The tuner should generate a pure and The tuner should generate a pure and

perfect A. perfect A. The sine wave should oscillate to with in 5% The sine wave should oscillate to with in 5%

of 440 Hz (which is a perfect tuning A).of 440 Hz (which is a perfect tuning A). The sine wave should have as little distortion The sine wave should have as little distortion

as possible.as possible. The tuner should be able to drive a The tuner should be able to drive a

speaker.speaker. The tuner should be portable (in concept).The tuner should be portable (in concept).

Design ProcessDesign Process Research sinusoidal oscillators.Research sinusoidal oscillators. Understand benefits and pitfalls of Understand benefits and pitfalls of

different oscillator designs.different oscillator designs. Choose an appropriate oscillator.Choose an appropriate oscillator. Improve basic circuit design.Improve basic circuit design.

Basic Theory of Basic Theory of OscillatorsOscillators

Oscillators are by Oscillators are by definition unstable.definition unstable.

The basic oscillator is The basic oscillator is depicted to the right. depicted to the right. (The response is also (The response is also shown)shown)

For oscillations to occurFor oscillations to occur Negative Feedback: A*B = Negative Feedback: A*B =

-1-1 Positive Feedback: A*B = 1Positive Feedback: A*B = 1

A Vin Vout Vout

A Vin A Vout Vout

A Vin Vout A Vout

A Vin Vout 1 A

VoutVin

A

1 A

Meet the Wein BridgeMeet the Wein Bridge BasicsBasics

Uses an Op-Amp for Uses an Op-Amp for amplificationamplification

Uses positive feedback Uses positive feedback through a RC band-pass filterthrough a RC band-pass filter

AdvantagesAdvantages Few partsFew parts Able to generate very Able to generate very

accurate sine waves (Used in accurate sine waves (Used in audio equipment)audio equipment)

DisadvantagesDisadvantages Not easily tuned to the Not easily tuned to the

desired frequencydesired frequency May introduce significant May introduce significant

distortions into the resulting distortions into the resulting wave without proper wave without proper amplitude control.amplitude control.

R2

R4R3

R1

C2C1

0

0

+

-

OUT Vout

Positive RC band-pass feedback filter

Op-Amp amplifier

Wein Bridge Continued…Wein Bridge Continued… Derivation of the Loop Derivation of the Loop

Gain (A*B)Gain (A*B) Positive feedback: A*B=1Positive feedback: A*B=1 B is a real number when B is a real number when

w=1/RCw=1/RC B=1/3 when w=1/RCB=1/3 when w=1/RC A=3 for the loop gain to A=3 for the loop gain to

equal 1equal 1 The oscillator will The oscillator will

oscillate at the frequency oscillate at the frequency w, where w=1/RC and w, where w=1/RC and has units rad/shas units rad/s

A 1R4R3

If R1 = R2 and C1 = C2...

R

RCs 1

R1

Cs

RRCs 1

1

3 RCs1

RCs

1

3 j RC1

RC

Gainloop A 1

R3R4

3 j RC1

RC

The Wein Bridge The Wein Bridge ProblemProblem

For oscillations to start, A must be slightly For oscillations to start, A must be slightly greater than 3.greater than 3.

If A is greater than 3 , then the loop gain is If A is greater than 3 , then the loop gain is greater than 1.greater than 1.

If the loop gain is greater than 1, then the If the loop gain is greater than 1, then the sine wave amplitude will tend towards sine wave amplitude will tend towards infinity.infinity.

Circuit does not infinite power, so the output Circuit does not infinite power, so the output sine wave becomes severely distorted.sine wave becomes severely distorted.

……Solution…Solution… Design amplitude Design amplitude

limiting circuitry.limiting circuitry. There are 3 general There are 3 general

solutions.solutions. Passive devices Passive devices

(diodes)(diodes) Resistive lampResistive lamp Automatic Gain Control Automatic Gain Control

(AGC)(AGC) A diode limited Wein A diode limited Wein

Bridge is depicted to Bridge is depicted to the right.the right.

R2

20.3k

R4

10k

R5

10.96k

R710.96k

R83k

R61.2k

R31.2k

R13k

C1

33n

C233n

D1

D1N4148

D2

D1N4148

0 0

0

U1LM741

+3

-2

V+7

V-4

OUT6

OS11

OS25

VCC

VDD

VCC

VDD

Vout

Amplitude Limiter

Not So Perfect…Not So Perfect… The diode limited Wein Bridge does The diode limited Wein Bridge does

NOT produce a perfect sine wave.NOT produce a perfect sine wave. The amplifier gain is different when The amplifier gain is different when

the diodes conduct and when they the diodes conduct and when they do not conduct.do not conduct.

Result: Distorted sine wave.Result: Distorted sine wave. Solution: AGCSolution: AGC

The All Mighty AGCThe All Mighty AGC AGC stands for Automatic Gain AGC stands for Automatic Gain

Control.Control. Controls the gain of the amplifier based Controls the gain of the amplifier based

on the output sine wave amplitude.on the output sine wave amplitude. The AGC requires two parts…The AGC requires two parts…

An AC rectifier with signal smoothing.An AC rectifier with signal smoothing. A VCR (Voltage Controlled Resistor).A VCR (Voltage Controlled Resistor).

The RectifierThe Rectifier Depicted below is the precision rectifier used in the Depicted below is the precision rectifier used in the

final oscillator circuit.final oscillator circuit. The rectifier is designed to invert the positive peaks The rectifier is designed to invert the positive peaks

of the sine so that the wave is always negative.of the sine so that the wave is always negative. Signal smoothing is not included here.Signal smoothing is not included here.

R3

R1 R2

D2

D1

0

Vin

Vout

+

-

OUT +

-

OUT

Rectifier Stimulus Rectifier Stimulus ResponseResponse

Time

250ms 251ms 252ms 253ms 254ms 255ms 256ms 257ms 258ms 259ms 260msV(U4:OUT) V(U1:OUT)

-3.0V

-2.0V

-1.0V

-0.0V

1.0V

2.0V

3.0V

Rectifier Output

Rectifier Input

The VCRThe VCR VCR stands for Voltage VCR stands for Voltage

Controlled Resistor.Controlled Resistor. A JFET transistor is A JFET transistor is

used as the basis for used as the basis for the VCR.the VCR.

Feedback is utilized to Feedback is utilized to linearize the voltage to linearize the voltage to resistance conversion.resistance conversion.

Response equations are Response equations are given at right.given at right.

For better AC response, For better AC response, a capacitor is added a capacitor is added between R1 and R2between R1 and R2

J1

R2

0

R1

Rd

VCC

Vin

i1

i2 iD

id12

knWL

vGS Vt vDS12

vDS2

Need to remove the 12

vDS2 term to linearize iD

vin vGS

R1

vGS vDS

R2

R2R1

vin vGS vGS vD

R2R1

vin vDS vGS 1R2R1

Setting R2 = R1, we get a 12

vDS

vGS12

vin12

vDS

Placing this result in the equation removes the 12

vDS2

VCR ResponseVCR Response

V_V1

-10V -9V -8V -7V -6V -5V -4V -3V -2V -1V -0VV(J1:d)/ I(J1:d)

-0.4K

0

0.4K

0.8K

1.2K

1.6K

2.0K

Frequency SelectionFrequency Selection An output frequency of An output frequency of

440 Hz is desired.440 Hz is desired. Capacitors have 5% to Capacitors have 5% to

20% tolerances so keep 20% tolerances so keep capacitor values low.capacitor values low.

Use 1% tolerance Use 1% tolerance resistors.resistors.

The 10.96k resistors The 10.96k resistors can be rounded up to can be rounded up to 11k (use a 10k and 1k 11k (use a 10k and 1k in resistor in series).in resistor in series).

0

0

+

-

OUT Vout

R3

4.7k

R4

10k

R1

10.96k

R2

10.96k

C1

0.033u

C2

0.033u

Putting It All Together…Putting It All Together… The final oscillator The final oscillator

circuit is depicted circuit is depicted at right.at right.

In addition to the In addition to the discussed sections, discussed sections, R12, R14, and C3 R12, R14, and C3 were added to were added to smooth the smooth the rectified output.rectified output.

J12N5486/PLP

U4LM741

+3

-2

V+7

V-4

OUT6

OS11

OS25

R16

10.96k

R10

10k

R9

4.7k

R15

10.96k

R8

4.7k

R5

10k

R2

10k

R1

10k

R14470k

C5

0.033u

C4

0.033u

C20.033u

C310u

U2LM741

+3

-2

V+7

V-4

OUT6

OS11

OS25

U1LM741

+3

-2

V+7

V-4

OUT6

OS11

OS25

D2

D1N4148

D1

D1N4148

R13

4.7k

VDD

VDD

VCC

VDD

VCC

VCC

0

0

0

0

R121k

Additional ImprovementsAdditional Improvements Run on batteries.Run on batteries. Volume control could be added.Volume control could be added. The 741 Op-Amp can only source The 741 Op-Amp can only source

about 50mA of current so an output about 50mA of current so an output stage to drive a speaker could be stage to drive a speaker could be implemented.implemented.

Final Circuit – With Final Circuit – With ImprovementsImprovements

Wein Bridge Oscillator

Precision Rectifier

AGC

Output StageVolume Control

Q4Q2N2907

Q2Q2N2907 Q1

Q2N2222

Q3

Q2N2222

VDD

VDD

VCC

VDD

VCC

R310k

R1110k

VCCSpeaker

U3LM741

+3

-2

V+7

V-4

OUT6

OS11

OS25

R6

47k

R4100k

SET = 1

VDD

VCC0J12N5486/PLP

U4LM741

+3

-2

V+7

V-4

OUT6

OS11

OS25

R16

10.96k

R10

10k

R9

4.7k

R15

10.96k

R8

4.7k

R5

10k

R2

10k

R1

10k

R14470k

C5

0.033u

C4

0.033u

C20.033u

C310u

U2LM741

+3

-2

V+7

V-4

OUT6

OS11

OS25

U1LM741

+3

-2

V+7

V-4

OUT6

OS11

OS25

D2

D1N4148

D1

D1N4148

R13

4.7k

VDD

VDD

VCC

VDD

VCC

VCC

0

0

0

0

OSC

R121k

Final Circuit ContinuedFinal Circuit Continued

Rectifier

VCR

Wein Bridge

Volume Control

Output Stage

Operation of Circuit in Operation of Circuit in Real LifeReal Life

The output sine wave is much smaller than The output sine wave is much smaller than predicted.predicted. Predicted amplitude: 3VPredicted amplitude: 3V Actual amplitude: 25mVActual amplitude: 25mV This is due to extreme dependence on Wein Bridge This is due to extreme dependence on Wein Bridge

amplifier gain setting resistors.amplifier gain setting resistors. Volume control can make up for the smaller amplitude Volume control can make up for the smaller amplitude

without introducing distortion.without introducing distortion. The output sine wave is very clean and precise.The output sine wave is very clean and precise. The output frequency is surprisingly close to the The output frequency is surprisingly close to the

ideal frequency that was designed for. (plus or ideal frequency that was designed for. (plus or minus 5Hz)minus 5Hz)

Final CommentsFinal Comments AccomplishmentsAccomplishments

Generates a near perfect sine wave (when taken Generates a near perfect sine wave (when taken directly from the oscillator circuit) at around directly from the oscillator circuit) at around 440Hz.440Hz.

Runs of batteries.Runs of batteries. Areas needing further Areas needing further

development/improvement.development/improvement. Output stage introduces some distortion.Output stage introduces some distortion. Make the oscillator easier to tune. (plus or minus Make the oscillator easier to tune. (plus or minus

10Hz)10Hz) Improve the AGC amplitude detection.Improve the AGC amplitude detection.