Practical feedback oscillators: required gain behavior For a feedback oscillator to be practically useful and produce a stable waveform, the loop gain must be controlled so that the overall gain is:

Introduction / Context:
Feedback oscillators (e.g., Wien bridge, Colpitts, Hartley, phase-shift) rely on positive feedback and gain to sustain sinusoidal output without an external input. The Barkhausen criteria specify the conditions at the oscillation frequency, but practical circuits must also control amplitude and gain to avoid distortion or dying out.

Given Data / Assumptions:

• Linear sinusoidal oscillator using positive feedback.
• Goal is a steady, low-distortion sinusoid.
• Amplifier gain can be adjusted by automatic or designed mechanisms.

Concept / Approach:
At startup, loop gain slightly above unity allows oscillations to build from noise. For steady operation, the loop gain should settle to exactly unity in magnitude with the correct phase shift. This requires some form of gain stabilization (automatic level control, AGC element, lamp, thermistor, diodes, or nonlinear resistance) so the amplitude neither grows into clipping nor decays to zero.

Step-by-Step Solution:
Design the amplifier such that initial loop gain > 1 to start oscillation.Introduce an amplitude control mechanism (e.g., lamp in Wien bridge or FET/diodes as variable resistors).As amplitude grows, the control element reduces gain until the loop gain magnitude ≈ 1.Oscillation amplitude stabilizes with low distortion.

Verification / Alternative check:
Observe on an oscilloscope: with proper stabilization the waveform becomes a clean sinusoid and remains constant. Without stabilization the output either clips (gain too high) or decays (gain too low).

Why Other Options Are Wrong:
< 1: loop gain less than unity cannot sustain oscillation.Self-adjusting: too vague; what is required is explicit gain stabilization around unity.Nonlinear: although nonlinear elements may be used to stabilize, the target is a linear, low-distortion sinusoid with stabilized gain.

Common Pitfalls:
Misreading Barkhausen as “loop gain must always be greater than one.” That is only for startup; steady state needs unity magnitude with precise phase.

Final Answer:
stabilized