Questions

1. Design a phase-shift oscillator using three \(\text{RC}\) sections with \(\text{R} = 10\,\text{k}\Omega\), \(\text{C} = 0.01 \,\mu \text{F}\) and Find the frequency of oscillation.
2. Determine the minimum amplifier gain required for sustained oscillations for the above oscillator.
3. Find frequency of a Hartley oscillator has inductors \(L_1 = 10 \mu \text{H}\), \(L_2 = 40 \mu \text{H}\), capacitor \(\text{C} = 100 \,\text{pF}\).
4. Find frequency a Colpitts oscillator has \(C_1 = 100 \,\text{pF}\), \(C_2 = 200 \,\text{pF}\), \(\text{L} = 10 \mu \text{H}\).
5. Find frequency of a Wien bridge oscillator with \(\text{R} = 10\,\text{k}\Omega\), \(\text{C} = 0.01 \,\mu \text{F}\).
6. What gain must the amplifier provide in a Wien bridge oscillator for sustained oscillations?
7. Calculate frequency drift an \(\text{LC}\) oscillator has \(\text{L} = 100 \mu \text{H}\), \(\text{C} = 100 \,\text{pF}\) and the capacitor tolerance is \(\pm 5 \,\%\).

Answers

1. \(f = \frac{1}{2\pi \text{RC} \sqrt{6}} \approx 651 \, \text{Hz}\)
2. \(\text{Attenuation of RC network} = 1/29\); \(\text{Required amplifier gain} \geq 29\).
3. \(f = \frac{1}{2\pi \sqrt{(L_1 + L_2)C}} \approx 2.25 \, \text{MHz}\)
4. \(C_{eq} = \frac{C_1 C_2}{C_1 + C_2} = 66.7 \,\text{pF}\); \(f = \frac{1}{2\pi \sqrt{LC_{eq}}} \approx 6.16 \, \text{MHz}\)
5. \(f = \frac{1}{2\pi RC} = 1591 \, \text{Hz}\)
6. \(\text{Bridge attenuation} = 1/3\); \(\text{Required amplifier gain} = 3\).
7. \(f = \frac{1}{2\pi \sqrt{LC}} = \approx 1.59 \, \text{MHz}\); \(With \pm 5 \,\% C:\) \(C_{min} = 95 \,\text{pF}\), \(f_{max} \approx 1.63 \,\text{MHz}\); \(C_{max} = 105 \,\text{pF}\), \(f_{min} \approx 1.55 \,\text{MHz}\)

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