To Get a Perfect “A”… An Engr. 311 Project by Corrin Meyer
Project Statement • 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 have as little distortion as possible. • The tuner should be able to drive a speaker. • The tuner should be portable (in concept).
Design Process • Research sinusoidal oscillators. • Understand benefits and pitfalls of different oscillator designs. • Choose an appropriate oscillator. • Improve basic circuit design.
Basic Theory of Oscillators • Oscillators are by definition unstable. • The basic oscillator is depicted to the right. (The response is also shown) • For oscillations to occur • Negative Feedback: A*B = -1 • Positive Feedback: A*B = 1
Meet the Wein Bridge Op-Amp amplifier • Basics • Uses an Op-Amp for amplification • Uses positive feedback through a RC band-pass filter • Advantages • Few parts • Able to generate very accurate sine waves (Used in audio equipment) • Disadvantages • Not easily tuned to the desired frequency • May introduce significant distortions into the resulting wave without proper amplitude control. PositiveRC band-pass feedback filter
Wein Bridge Continued… • Derivation of the Loop Gain (A*B) • Positive feedback: A*B=1 • B is a real number when w=1/RC • B=1/3 when w=1/RC • 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 Wein Bridge Problem • 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 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.
…Solution… • Design amplitude limiting circuitry. • There are 3 general solutions. • Passive devices (diodes) • Resistive lamp • Automatic Gain Control (AGC) • 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 amplifier gain is different when the diodes conduct and when they do not conduct. • Result: Distorted sine wave. • Solution: AGC
The All Mighty AGC • AGC stands for Automatic Gain Control. • Controls the gain of the amplifier based on the output sine wave amplitude. • The AGC requires two parts… • An AC rectifier with signal smoothing. • A VCR (Voltage Controlled Resistor).
The Rectifier • 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. • Signal smoothing is not included here.
The VCR • VCR stands for Voltage Controlled Resistor. • A JFET transistor is used as the basis for the VCR. • Feedback is utilized to linearize the voltage to resistance conversion. • Response equations are given at right. • For better AC response, a capacitor is added between R1 and R2 i2 iD i1
Frequency Selection • An output frequency of 440 Hz is desired. • Capacitors have 5% to 20% tolerances so keep capacitor values low. • Use 1% tolerance resistors. • 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. • In addition to the discussed sections, R12, R14, and C3 were added to smooth the rectified output.
Additional Improvements • Run on batteries. • 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.
Final Circuit Continued Rectifier Volume Control VCR Output Stage Wein Bridge
Operation of Circuit in Real Life • The output sine wave is much smaller than predicted. • Predicted amplitude: 3V • Actual amplitude: 25mV • 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. • 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)
Final Comments • Accomplishments • Generates a near perfect sine wave (when taken directly from the oscillator circuit) at around 440Hz. • Runs of batteries. • Areas needing further development/improvement. • Output stage introduces some distortion. • Make the oscillator easier to tune. (plus or minus 10Hz) • Improve the AGC amplitude detection.