To Get a Perfect “A”… An Engr. 311 Project by Corrin Meyer

Project Statement The tuner should generate a pure and perfect A. The tuner should generate a pure and perfect A. The sine wave should oscillate to with in 5% of 440 Hz (which is a perfect tuning A). The sine wave should oscillate to with in 5% of 440 Hz (which is a perfect tuning A). The sine wave should have as little distortion as possible. The sine wave should have as little distortion as possible. The tuner should be able to drive a speaker. The tuner should be able to drive a speaker. The tuner should be portable (in concept). The tuner should be portable (in concept).

Design Process Research sinusoidal oscillators. Research sinusoidal oscillators. Understand benefits and pitfalls of different oscillator designs. Understand benefits and pitfalls of different oscillator designs. Choose an appropriate oscillator. Choose an appropriate oscillator. Improve basic circuit design. Improve basic circuit design.

Basic Theory of Oscillators Oscillators are by definition unstable. Oscillators are by definition unstable. The basic oscillator is depicted to the right. (The response is also shown) The basic oscillator is depicted to the right. (The response is also shown) For oscillations to occur For oscillations to occur Negative Feedback: A*B = -1 Negative Feedback: A*B = -1 Positive Feedback: A*B = 1 Positive Feedback: A*B = 1

Meet the Wein Bridge Basics Basics Uses an Op-Amp for amplification Uses an Op-Amp for amplification Uses positive feedback through a RC band-pass filter Uses positive feedback through a RC band-pass filter Advantages Advantages Few parts Few parts Able to generate very accurate sine waves (Used in audio equipment) Able to generate very accurate sine waves (Used in audio equipment) Disadvantages Disadvantages Not easily tuned to the desired frequency Not easily tuned to the desired frequency May introduce significant distortions into the resulting wave without proper amplitude control. May introduce significant distortions into the resulting wave without proper amplitude control. Positive RC band-pass feedback filter Op-Amp amplifier

Wein Bridge Continued… Derivation of the Loop Gain (A*B) Derivation of the Loop Gain (A*B) Positive feedback: A*B=1 Positive feedback: A*B=1 B is a real number when w=1/RC B is a real number when w=1/RC B=1/3 when w=1/RC B=1/3 when w=1/RC A=3 for the loop gain to equal 1 A=3 for the loop gain to equal 1 The oscillator will oscillate at the frequency w, where w=1/RC and has units rad/s The oscillator will oscillate at the frequency w, where w=1/RC and has units rad/s

The Wein Bridge Problem For oscillations to start, A must be slightly greater than 3. For oscillations to start, A must be slightly greater than 3. If A is greater than 3, then the loop gain is greater than 1. If A is greater than 3, then the loop gain is greater than 1. If the loop gain is greater than 1, then the sine wave amplitude will tend towards infinity. If the loop gain is greater than 1, then the sine wave amplitude will tend towards infinity. Circuit does not infinite power, so the output sine wave becomes severely distorted. Circuit does not infinite power, so the output sine wave becomes severely distorted.

…Solution… Design amplitude limiting circuitry. Design amplitude limiting circuitry. There are 3 general solutions. There are 3 general solutions. Passive devices (diodes) Passive devices (diodes) Resistive lamp Resistive lamp Automatic Gain Control (AGC) Automatic Gain Control (AGC) A diode limited Wein Bridge is depicted to the right. A diode limited Wein Bridge is depicted to the right. Amplitude Limiter

Not So Perfect… The diode limited Wein Bridge does NOT produce a perfect sine wave. The diode limited Wein Bridge does NOT produce a perfect sine wave. The amplifier gain is different when the diodes conduct and when they do not conduct. The amplifier gain is different when the diodes conduct and when they do not conduct. Result: Distorted sine wave. Result: Distorted sine wave. Solution: AGC Solution: AGC

The All Mighty AGC AGC stands for Automatic Gain Control. AGC stands for Automatic Gain Control. Controls the gain of the amplifier based on the output sine wave amplitude. Controls the gain of the amplifier based 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 Rectifier Depicted below is the precision rectifier used in the final oscillator circuit. Depicted below is the precision rectifier used in the final oscillator circuit. The rectifier is designed to invert the positive peaks of the sine so that the wave is always negative. The rectifier is designed to invert the positive peaks of the sine so that the wave is always negative. Signal smoothing is not included here. Signal smoothing is not included here.

Rectifier Stimulus Response

The VCR VCR stands for Voltage Controlled Resistor. VCR stands for Voltage Controlled Resistor. A JFET transistor is used as the basis for the VCR. A JFET transistor is used as the basis for the VCR. Feedback is utilized to linearize the voltage to resistance conversion. Feedback is utilized to linearize the voltage to resistance conversion. Response equations are given at right. Response equations are given at right. For better AC response, a capacitor is added between R1 and R2 For better AC response, a capacitor is added between R1 and R2 i1 i2iD

VCR Response

Frequency Selection An output frequency of 440 Hz is desired. An output frequency of 440 Hz is desired. Capacitors have 5% to 20% tolerances so keep capacitor values low. Capacitors have 5% to 20% tolerances so keep capacitor values low. Use 1% tolerance resistors. Use 1% tolerance resistors. The 10.96k resistors can be rounded up to 11k (use a 10k and 1k in resistor in series). The 10.96k resistors can be rounded up to 11k (use a 10k and 1k in resistor in series).

Putting It All Together… The final oscillator circuit is depicted at right. The final oscillator circuit is depicted at right. In addition to the discussed sections, R12, R14, and C3 were added to smooth the rectified output. In addition to the discussed sections, R12, R14, and C3 were added to smooth the rectified output.

Additional Improvements Run on batteries. Run on batteries. Volume control could be added. Volume control could be added. The 741 Op-Amp can only source about 50mA of current so an output stage to drive a speaker could be implemented. The 741 Op-Amp can only source about 50mA of current so an output stage to drive a speaker could be implemented.

Final Circuit – With Improvements

Final Circuit Continued Rectifier VCR Wein Bridge Volume Control Output Stage

Operation of Circuit in Real Life The output sine wave is much smaller than predicted. The output sine wave is much smaller than predicted. Predicted amplitude: 3V Predicted amplitude: 3V Actual amplitude: 25mV Actual amplitude: 25mV This is due to extreme dependence on Wein Bridge amplifier gain setting resistors. This is due to extreme dependence on Wein Bridge amplifier gain setting resistors. Volume control can make up for the smaller amplitude without introducing distortion. Volume control can make up for the smaller amplitude 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 ideal frequency that was designed for. (plus or minus 5Hz) The output frequency is surprisingly close to the ideal frequency that was designed for. (plus or minus 5Hz)

Final Comments Accomplishments Accomplishments Generates a near perfect sine wave (when taken directly from the oscillator circuit) at around 440Hz. Generates a near perfect sine wave (when taken directly from the oscillator circuit) at around 440Hz. Runs of batteries. Runs of batteries. Areas needing further development/improvement. Areas needing further development/improvement. Output stage introduces some distortion. Output stage introduces some distortion. Make the oscillator easier to tune. (plus or minus 10Hz) Make the oscillator easier to tune. (plus or minus 10Hz) Improve the AGC amplitude detection. Improve the AGC amplitude detection.