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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 Vout A Vin A Vout Vout A Vin Vout A Vin Vout A Vout A Vin Vout 1 A Vout A Vin 1 A Meet the Wein Bridge Basics Uses an Op-Amp for amplification Uses positive feedback through a RC band-pass filter R3 - Few parts Able to generate very accurate sine waves (Used in audio equipment) Not easily tuned to the desired frequency May introduce significant distortions into the resulting wave without proper amplitude control. Vout OUT R1 + C1 Disadvantages R4 0 Advantages Op-Amp amplifier C2 R2 0 Positive RC 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 A 1 R4 R3 If R1 = R2 and C1 = C2... R RCs 1 R 1 Cs 1 R 3 RCs RCs 1 1 Gain loop A 1 R3 R4 3 j RC 1 RC 1 RCs 3 j RC RC 1 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) VCC R1 3k D1 D1N4148 R2 20.3k VDD R4 4 2 - VOS1 10k OUT 0 3 A diode limited Wein Bridge is depicted to the right. + 7 OS2 V+ R3 1.2k U1 LM741 1 6 Vout 5 VCC C2 33n 0 C1 R5 33n 10.96k R6 1.2k R7 10.96k 0 D2 D1N4148 R8 3k Amplitude Limiter VDD 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. R1 R2 Vi n D1 OUT + 0 OUT D2 R3 + Vout Rectifier Stimulus Response 3.0V 2.0V Rectifier Input 1.0V -0.0V -1.0V Rectifier Output -2.0V -3.0V 250ms 251ms V(U4:OUT) V(U1:OUT) 252ms 253ms 254ms 255ms Time 256ms 257ms 258ms 259ms 260ms The VCR VCC 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 Rd R2 i2 iD R1 J1 Vi n i1 W 1 id k 2 n L 1 Need to remove the 2 v in v GS v GS v DS R1 R2 R2 R1 vin vGS 2 v DS v GS 1 v v DS R1 in 2 v in term to linearize iD R2 R1 Setting R2 = R1, we get a 1 0 v GS v D R2 v GS 2 v GS Vt v DS 2 v DS 1 1 v 2 DS 1 v 2 DS Placing this result in the equation removes the 1 2 2 v DS VCR Response 2.0K 1.6K 1.2K 0.8K 0.4K 0 -0.4K -10V -9V V(J1:d)/ I(J1:d) -8V -7V -6V -5V V_V1 -4V -3V -2V -1V -0V 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). R3 R4 4.7k 10k 0 Vout OUT R1 + 10.96k 0 C1 C2 R2 0.033u 0.033u 10.96k Putting It All Together… R1 R2 D1 10k 6 D1N4148 - OUT 5 OS2 VCC + VCC 4.7k R14 470k R9 4.7k 4.7k 0 10k R10 10k C2 0.033u VDD 4 R13 R8 R5 J1 2N5486/PLP 2 - C3 10u 3 0 OS1 OUT R15 + 7 R12 1k 3 V- + U2 LM741 2 4 OS1 D2 3 V- 1 OUT OS2 VDD 10.96k OS2 U4 LM741 1 6 5 V+ 5 - 10k D1N4148 U1 LM741 2 7 6 OS1 7 1 V- 4 VDD V+ 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. V+ VCC 0 0 C4 C5 R16 0.033u 0.033u 10.96k 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 – With Improvements Precision Rectifier R2 R1 D1 10k 4 1 OS1 D2 OS2 R5 VCC 4.7k 0 4 2 J1 2N5486/PLP - OUT 3 0 + 7 R15 C3 10u OS1 10.96k OS2 U4 LM741 1 - OS1 + OS2 0 1 VDD 6 Speaker VCC 5 Q3 VCC Q4 Q2N2907 Q2N2222 R11 10k 6 5 VDD V+ R14 470k 3 Q1 Q2N2222 VDD OUT 10k VDD C2 0.033u V- R13 U3 LM741 2 47k R10 4.7k 4.7k R6 0 10k R9 R8 R12 1k SET = 1 3 V+ VCC + 4 5 R3 10k Q2 Q2N2907 OUT V- D1N4148 - VCC VCC R4 100k 7 + 6 3 Output Stage Volume Control U2 LM741 2 V+ OUT OS2 VDD V- - V+ 5 OS1 10k D1N4148 U1 LM741 2 7 6 7 1 V- 4 VDD VDD VCC AGC C4 C5 R16 0.033u 0.033u 10.96k 0 Wein Bridge Oscillator OSC 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.