Assignment Op Amp Circuit Collection Read Appendix D Answer

Assignmentop Amp Circuit Collectionread Appendix Danswer The Following

Answer The Following questions: For a simulated inductor application, to yield L = 50mH, R1 = 2kohm, and C1 = 100uF, determine required value of R2. For a constant current generator, with a saturation voltage of 15V and a current reference of 18mA, calculate RLmin. For a precision rectifier application, given E IRMS = 5V, determine E Opeak. For an AC to DC converter, given E IPeak = 6V, determine EI. Include all calculations in a Word document with the title: “HW8_StudentID,” with your student ID substituted in the file name.

Read Appendix D.10 Curve Fitting Filters from the textbook (Op Amps for Everyone Fourth Edition). Review the curve fitting equalization application discussed (RIAA – Recording Industry Association of America). Design the equalization preamplifier in Figure D.12 by understanding the circuit design requirements on page 269. Perform AC analysis to plot the response of the preamplifier. Take screenshots of the response and show the approximation of the RIAA equalization curve. Answer the following questions: Describe the operation of this preamplifier circuit and explain how these preamplifier circuits work with single-supply circuits in limiting low-frequency resonating components from the signal. Discuss what parameters can independently be adjusted to enhance sound quality. Discuss the advantages of using this equalization preamplifier for sound reproduction. Create a new Word document called “Lab8_StudentID.docx” with your GID substituted into the file name. Verify all measurements from the simulation. Save results and include screenshots in the Word document. Ensure to answer all questions.

Design a 16-bit DAC circuit. Calculate the resistor values, include calculations, and capture schematic and input/output settings. For a Wien-bridge oscillator with R = 50kΩ and C = 100nF, determine the frequency of oscillation. Given a required frequency of 10kHz and R = 8kΩ, calculate the needed capacitance C. Calculate the signal-to-noise ratio given RMS Noise Voltage = 20mV and RMS Signal Voltage = 2.5V. Calculate E Total RMS given e1RMS = 5V and e2RMS = 7V. Calculate SNR (dB) given a noise specification of 680nV. Calculate the noise specification with SNR (dB) = 350dB. For a simulated inductor application for L = 75mH, R1 = 3kΩ, and C1 = 200uF, determine the required R2. For a constant current generator with saturation voltage 20V and current reference 30mA, compute RLmin. For a precision rectifier with E IRMS = 5V, find E Opeak. For an AC to DC converter, with E IPeak = 10V, determine EI.

Paper For Above instruction

The collection of assignments outlined integrates fundamental and advanced applications of operational amplifiers (op-amps) in various electronic circuits. This comprehensive overview explores simulated inductors, current sources, rectifiers, AC/DC converters, equalization preamplifiers, digital-to-analog converters (DACs), oscillators, and noise analysis, emphasizing both design and analytical considerations crucial for modern electronics engineering.

Simulated Inductor Design and Calculations

In implementing a simulated inductor with an inductance (L) of 50mH, the classic op-amp-based simulated inductance circuit employs a synthetic gyrator approach. The design hinges on using resistors and capacitors to emulate the inductor's behavior. For this application, the relationship is given by:

L = R2 * C1

Given R1 = 2kΩ, C1 = 100μF, and L = 50mH, the value of R2 can be derived considering the specific configuration used. Typically, in a gyrator circuit, the equivalent inductance (L) is given by:

L = R2  R1  C1

Rearranged to find R2:

R2 = L / (R1 * C1)

Inserting the known values (with unit conversions):

L = 50mH = 0.05H


R1 = 2000Ω


C1 = 100μF = 100 x 10^-6 F

Thus:

R2 = 0.05 / (2000 * 100 x 10^-6) = 0.05 / (0.2) = 0.25Ω

Therefore, R2 ≈ 0.25Ω is required for the simulated inductor application.

Constant Current Generator - RLmin Calculation

For a constant current generator, the minimum load resistance (RLmin) relates to the saturation voltage (V_sat) and the reference current (I_ref):

V_sat = I_ref * RLmin

Rearranged to:

RLmin = V_sat / I_ref

Substituting given values—V_sat = 15V, I_ref = 18mA (0.018A):

RLmin = 15 / 0.018 ≈ 833.33Ω

Hence, RLmin ≈ 833Ω.

Precision Rectifier Output Peak Voltage

Given E_IRMS = 5V, the peak voltage (E_Opeak) for a sinusoidal signal is calculated by:

E_Opeak = E_IRMS  √2 ≈ 5  1.4142 ≈ 7.07V

This is based on the RMS-to-peak conversion of sinusoidal signals.

AC to DC Converter Input Peak Voltage

Given E_IPeak = 6V, the input voltage E_I remains at 6V assuming the circuit allows for this peak value directly.

Curve Fitting Equalization and Preamplifier Design

The RIAA equalization curve involves a complex network that compensates for the frequency-dependent response of vinyl records. The preamplifier design in Figure D.12 aims to implement this equalization in a compact form. It operates by integrating multiple RC sections that attenuate or boost certain frequency bands. This is achieved via feedback networks designed for specific frequency response, critical for accurate playback of records.

The circuit's operation hinges on AC feedback to invoke frequency-dependent impedance variations. The preamplifier with single-supply operation uses biasing and decoupling strategies—such as coupling capacitors and bias voltages—to reduce low-frequency resonance effects, preventing excessive bass boost or oscillations.

Adjustable parameters such as resistor values and capacitor values allow independent fine-tuning of frequency response, thereby enhancing sound quality. Components' tolerances primarily influence the precision of frequency compensation, while feedback configurations impact linearity and distortion.

The advantages of employing such a specialized preamplifier include improved signal fidelity, better noise management, and accurate reproduction of the original sound. Its design ensures minimal coloration and distortion, making it suitable for high-fidelity audio systems.

Designing a 16-bit DAC Circuit and Oscillator Calculations

The 16-bit DAC calculation involves selecting resistor values that form a binary-weighted network. For example, with a reference voltage (V_ref) of 5V, the resistors can be assigned as powers of two, with R-weights corresponding to their binary significance. Calculations include setting base resistor R, then deriving subsequent resistors:

R0 = R


R1 = 2 * R


R2 = 4 * R ... and so forth, up to R15

Schematic capture and input/output verification are crucial for implementation accuracy.

For a Wien-bridge oscillator, the frequency of oscillation (f) is given by:

f = 1 / (2π R C)

Given R = 50kΩ and C = 100nF:

f = 1 / (2π  50,000  100 x 10^-9) ≈ 1 / (2π * 0.005) ≈ 31.83Hz

Similarly, to achieve a 10kHz oscillation with R = 8kΩ, solve for C:

C = 1 / (2π R f) = 1 / (2π  8000  10,000) ≈ 1.99nF

Signal-to-Noise Ratio and Noise Calculations

The SNR in decibels (dB) is obtained by:

SNR(dB) = 20 * log10 (V_signal / V_noise)

Given RMS noise voltage of 20mV and signal voltage of 2.5V:

SNR = 20  log10 (2.5 / 0.02) ≈ 20  log10 (125) ≈ 20 * 2.0969 ≈ 41.94dB

For total RMS voltage derived from two noise sources:

E_Total_RMS = √(e1^2_RMS + e2^2_RMS) = √(5^2 + 7^2) = √(25 + 49) = √74 ≈ 8.60V

With SNR(dB) = 350dB, the noise specification (V_noise) can be back-calculated:

V_noise = V_signal / (10^(SNR/20)) = 2.5 / (10^(350/20)) ≈ 2.5 / 10^(17.5) ≈ negligible, indicating very high signal fidelity.

Additional Calculations for Inductor, Current, and Rectifier Applications

For the simulated inductor with L = 75mH, R1 = 3kΩ, and C1 = 200μF, R2 is found via the relation:

L = R2  R1  C1


R2 = L / (R1  C1) = 0.075 / (3000  200 x 10^-6) = 0.075 / 0.6 = 0.125Ω

In a constant current source with V_sat = 20V and I_ref = 30mA:

RLmin = 20 / 0.030 ≈ 666.67Ω

The precision rectifier's output peak voltage with E_IRMS = 5V is:

E_Opeak ≈ 5 * √2 ≈ 7.07V

For an AC to DC converter with E_IPeak = 10V, EI remains at 10V in ideal conditions.

These calculations underpin the design and analysis of complex analog circuits utilizing op-amps, ranging from simulated inductors to high-fidelity audio preamplifiers, showcasing the versatility and precision achievable with modern electronics.

References

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  • Gray, P. R., Hurst, P. J., Lewis, S. H., & Meyer, R. G. (2009). Analysis and Design of Analog Integrated Circuits (5th ed.). Wiley.
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