Feedback and Stability
The previous lesson introduced the idea that an oscillator uses positive feedback — where part of the output is returned to the input to reinforce the signal. This lesson goes deeper into how feedback actually works in a real circuit, why oscillations build up from nothing, what limits them to a steady amplitude, and what determines whether the frequency of oscillation is stable or drifts with time, temperature and vibration.
Positive vs Negative Feedback — Contrasting Effects
Feedback in electronics means taking a sample of the output signal and returning it to the input. The crucial question is: does the returned sample add to or subtract from the input?
In negative feedback, the returned sample subtracts from the input. If the output rises, the input is reduced, which drives the output back down. The system resists change and seeks an equilibrium. Negative feedback is the principle behind op-amp circuits, servo motors, thermostats and cruise control. It produces stable, predictable behaviour and reduces distortion, but it always reduces gain.
In positive feedback, the returned sample adds to the input. If the output rises, the input increases, which drives the output up further. The system reinforces change. In most electronic circuits, positive feedback is unwanted — it causes instability, oscillation, and latch-up. But in an oscillator circuit, this instability is exactly what you want and deliberately engineer.
Negative feedback (left) subtracts the fed-back signal, creating stability and reducing gain. Positive feedback (right) adds the fed-back signal, creating regeneration and, if the Barkhausen conditions are met, sustained oscillation.
View LargerIt is worth noting that the same amplifier circuit can be used for either type of feedback depending on which terminal the feedback is applied to. A transistor amplifier has an inverting output. If you apply negative feedback using a non-inverting path, the 180° inversion of the amplifier combines with 0° from the feedback path to give 180° net — that is negative feedback. Apply positive feedback using an inverting path, and the two 180° shifts cancel to give 360° (= 0°) — that is positive feedback.
The Startup Transient in Detail
When power is first applied to an oscillator, there is no signal present. So how does oscillation begin? The answer, as introduced in the previous lesson, is thermal noise — but the mechanism deserves a more careful look.
Thermal noise is a white noise source: it contains all frequencies simultaneously, each at a tiny random amplitude. When power is applied, this noise enters the amplifier and is amplified. The output is a slightly louder version of the noise. The feedback network then samples this output and returns a portion of it to the input. Crucially, the feedback network is frequency-selective — it is a resonant circuit with a peak response at its resonant frequency. Noise components near the resonant frequency pass through the feedback network efficiently; noise at other frequencies is attenuated.
The result is that only the noise components near the resonant frequency keep circulating around the loop. On each pass they are amplified by A and the feedback fraction β returns Aβ of them back to the input. Since Aβ > 1 at design time, each pass produces a slightly larger signal than the previous one. The amplitude grows exponentially.
How fast does it grow? The time constant of the startup depends on the excess gain (Aβ - 1) and the time it takes for a signal to traverse the loop — related to the resonant frequency and the Q factor of the tank. For a simple LC oscillator at 7 MHz with a Q of 100 and an excess gain of 0.5, the amplitude builds to 95% of its final value within roughly 50 microseconds. Higher excess gain means faster startup but also more distortion. Lower excess gain means slower, cleaner startup.
The startup transient of an oscillator: amplitude builds exponentially from the noise floor as the loop gain (Aβ > 1) reinforces the circulating signal, then stabilises once limiting reduces the effective gain to exactly 1.
View LargerHard Limiting — Clipping and Distortion
As the oscillator's amplitude grows, something must eventually stop it. In most simple oscillators, that something is transistor saturation and cutoff — collectively called hard limiting or clipping. Here is what happens:
A bipolar transistor operated in its active region provides a relatively constant current gain. As the signal drives the base voltage more and more positive, a point is reached where the collector-emitter voltage drops to nearly zero and the transistor saturates — the collector current cannot increase further. On the negative swing, the base voltage may drop below the cutoff threshold and the transistor stops conducting entirely. In either case, the transistor is no longer a linear amplifier — it is acting like a switch, clipping the peaks of the waveform.
Clipping is effective at limiting amplitude, but it has a consequence: the output waveform becomes rich in harmonics. A clipped sine wave is no longer a pure sine wave — it contains the fundamental frequency plus significant amounts of the second harmonic (2f), third harmonic (3f) and higher. In a transmitter this is a serious problem because harmonics are unwanted radio emissions. The LC tank circuit at the output provides some filtering, suppressing harmonics because its impedance is high only near the resonant frequency, but hard clipping still produces a noisier, less pure signal than soft limiting.
An oscillator at 3.5 MHz clips its output waveform to about 60% of a full sine. This produces:
Fundamental (3.5 MHz): −0 dB (full amplitude)
3rd harmonic (10.5 MHz): approximately −13 dB below fundamental
5th harmonic (17.5 MHz): approximately −20 dB below fundamental
7th harmonic (24.5 MHz): approximately −27 dB below fundamental
These harmonics fall on other amateur bands. The transmit chain must include band-pass or low-pass filtering after the oscillator and power amplifier stages to meet the spurious emission limits specified by the FCC (generally −43 dBc for amateur stations).
Soft Limiting — AGC and Gentle Amplitude Control
For applications requiring a clean sine wave output — such as signal generators, test equipment, SSB exciters and high-performance reference oscillators — hard limiting is unacceptable. Instead, soft limiting techniques are used that gently reduce gain as amplitude rises, without ever allowing the amplifier to clip.
Diode Limiters
A pair of small-signal diodes connected back-to-back (anode to anode, or cathode to cathode) across part of the feedback network begins to conduct when the signal amplitude exceeds their forward voltage threshold (typically 0.3 V for germanium, 0.6 V for silicon). As the diodes conduct, they shunt part of the feedback network and reduce the effective feedback fraction β. The onset of conduction is gradual, not abrupt, so amplitude control is smoother than transistor clipping. This technique is used in Colpitts and Hartley oscillators intended for relatively clean output.
FET as Variable Resistor
A JFET operating in its ohmic (triode) region below pinch-off acts as a voltage-controlled resistor. The channel resistance decreases as the gate voltage becomes more negative (for n-channel JFETs). In an oscillator using this technique, the JFET is placed in series with the feedback resistor. The gate is connected to a rectified sample of the output amplitude. As amplitude rises, the rectified voltage drives the gate more negative, increasing the FET channel resistance and reducing the feedback. The result is very low distortion, typically well below 0.1%.
Thermistor or Incandescent Lamp (Wien Bridge Oscillators)
The Wien bridge oscillator — widely used in audio test equipment — uses a thermistor or a small incandescent lamp as the gain-setting resistor. As oscillation amplitude increases, the lamp filament heats up and its resistance increases (all metals increase in resistance with temperature). This increases the negative feedback in the bridge, reducing gain exactly enough to maintain Aβ = 1. The lamp's thermal time constant (tens to hundreds of milliseconds) acts as a natural low-pass filter on the AGC control loop, preventing rapid gain changes that would cause amplitude modulation of the output.
Electronic AGC
Modern precision oscillators use electronic AGC circuits. A peak detector or RMS detector measures the output amplitude. This is compared to a reference voltage in an error amplifier. The error amplifier's output controls a variable attenuator or variable-gain amplifier in the oscillator loop. With careful design, the AGC maintains amplitude stability to better than 0.1% and the output contains less than 0.01% total harmonic distortion.
| Limiting Method | Distortion Level | Circuit Complexity | Typical Application |
|---|---|---|---|
| Transistor clipping (hard) | High (many harmonics) | Simple | Basic LC oscillators, homebrew VFOs |
| Diode limiter (soft) | Moderate (<2%) | Low (2 diodes) | Improved LC oscillators |
| FET as variable resistor | Low (<0.1%) | Moderate | Precision sine wave oscillators |
| Lamp/thermistor (Wien bridge) | Very low (<0.01%) | Moderate | Audio oscillators, function generators |
| Electronic AGC | Very low (<0.01%) | High | Reference oscillators, signal generators |
The Limit Cycle — Steady-State Oscillation
Once the amplitude-limiting mechanism has stabilised the oscillation, the oscillator is in its steady state. In control theory this is called a limit cycle — a stable, self-sustaining periodic orbit in the circuit's state space. The amplitude is constant (or varies only very slowly with temperature), the frequency is constant (or nearly so), and the waveform repeats indefinitely.
The frequency at which the limit cycle occurs is not necessarily exactly the resonant frequency of the tank circuit. The amplifier itself introduces a phase shift that varies slightly with operating point, and the amplitude-limiting mechanism also introduces some phase shift. The oscillation frequency adjusts slightly from the open-loop resonant frequency so that the total loop phase is exactly 0°. This is why loading the oscillator output with a reactive impedance can shift the frequency — it adds phase shift to the loop, pulling the frequency.
In a well-designed oscillator, a buffer amplifier isolates the oscillator tank from the load. The buffer has high input impedance (so it does not load the tank) and low output impedance (so it can drive the load without reflecting it back into the tank). This is one of the most important design details in practical oscillator work — a poor buffer allows the load impedance to modulate the oscillator frequency, destroying stability.
Frequency Stability and Q Factor
Why do some oscillators hold their frequency extremely well while others drift noticeably? The key parameter is the Q factor (quality factor) of the frequency-determining resonant element.
Q measures how sharply peaked the resonator's impedance is at resonance. A high-Q resonator has a very narrow peak — the impedance falls off steeply on either side of resonance. When used in an oscillator, this steep slope means that even small changes in component values produce very little change in the frequency where the phase condition is satisfied. The resonator "fights back" against perturbations that would shift the frequency.
A practical LC tank circuit using discrete components might have a Q of 50 to 200. A quartz crystal used as a resonator has a Q of 10,000 to 100,000 or more. This is why crystal oscillators are so much more stable than LC oscillators — the crystal's extremely high Q means the frequency is defined far more precisely by the crystal than by any stray capacitances, supply voltage changes, or temperature effects.
- Discrete LC tank circuit: Q ≈ 50–200, frequency stability ±100 ppm or worse
- Ceramic resonator: Q ≈ 500–2000, frequency stability ±500 ppm typical
- Quartz crystal (AT-cut): Q ≈ 10,000–100,000, stability ±10 to ±100 ppm
- Quartz crystal in OCXO: Q ≈ 100,000+, stability ±0.001 ppm or better
Phase noise — rapid random fluctuation of the oscillation phase — is also governed by Q. The higher the Q, the lower the phase noise. This is expressed by Leeson's equation, which shows that the phase noise power spectral density falls as 1/Q². For radio reception, low phase noise in the local oscillator is essential for receiving weak signals alongside strong ones, because LO phase noise mixes into the IF and raises the noise floor around strong signals.
Practical Observations with an Oscilloscope
If you have access to an oscilloscope and a simple LC or crystal oscillator (even a clock oscillator module from a microcontroller project), you can observe oscillator behaviour directly.
⚖ Experiment: Observing Oscillator Startup and Stability
This experiment uses a readily available 10 MHz or 20 MHz crystal oscillator module and an oscilloscope to observe the startup transient and long-term frequency stability. Most hobbyists own or can borrow a used digital oscilloscope with at least 50 MHz bandwidth, which is sufficient for this experiment.
- Crystal oscillator module (HC-49, 10 MHz or 20 MHz, available for under $2)
- Oscilloscope with at least 50 MHz bandwidth and trigger capability
- 5 V power supply or 9 V battery with a 5 V regulator
- Breadboard and connecting wires
- 100 Ω resistor (to protect the oscilloscope probe from the oscillator output)
- Wire the crystal oscillator module to the 5 V supply. Most 4-pin oscillator modules have: pin 1 = output enable (leave unconnected or tie to +5 V), pin 7 = GND, pin 8 = output, pin 14 = +5 V. Check your module's datasheet.
- Connect the oscilloscope probe (with the 100 Ω in series) to the output pin. Set the scope to 50 ns/div time base and 2 V/div vertical, with trigger on rising edge.
- Power the oscilloscope first, then apply power to the oscillator module. Observe the output waveform. For a 10 MHz oscillator you should see a clean square wave (oscillator modules usually include internal output buffering) at 100 ns period.
- To observe the startup transient, use the oscilloscope's trigger delay or one-shot capture feature. Trigger on the rising edge of the power supply line (using a second probe). The stored capture will show the oscillation amplitude building from zero to full amplitude. On most crystal oscillators this takes 0.1 to 10 milliseconds.
- Measure the frequency using the oscilloscope's frequency measurement function. Record the reading.
- Leave the oscillator running for 10 minutes while it warms to thermal equilibrium. Record the frequency again. Compare the two readings to observe warm-up drift.
The oscillator should be within the manufacturer's frequency tolerance (typically ±50 to ±100 ppm for standard crystal oscillators). The startup takes a short but measurable time — typically less than 1 millisecond for a crystal oscillator at 10 MHz. The warm-up drift is usually small — a few parts per million over 10 minutes — confirming that the crystal's high Q stabilises the frequency effectively. If you substitute an LC oscillator (such as the internal RC oscillator of an Arduino microcontroller), you will observe noticeably larger initial inaccuracy and greater drift, directly illustrating the difference that Q factor makes.
Frequently Asked Questions
Why does my oscillator take a while to settle on frequency after switch-on?
This is warm-up drift. When first powered, the oscillator's transistor, capacitors, and inductor (or crystal) are at room temperature. As the circuit draws current, components warm slightly — typically 5–15°C above ambient. This changes their electrical values (capacitors and inductors have temperature coefficients), which shifts the resonant frequency. After 5 to 15 minutes the temperature stabilises and so does the frequency. This is why transmitters and frequency-sensitive test equipment should be allowed to warm up for 10–30 minutes before critical frequency measurements.
What causes an oscillator to suddenly jump to a different frequency?
This is called a mode jump or spurious oscillation, and it means the circuit has found a different frequency at which the Barkhausen conditions are also satisfied — perhaps a harmonic or an unwanted parasitic resonance in the circuit layout. Common causes include: a transistor with gain at harmonic frequencies, parasitic inductance in circuit wiring, inadequate bypassing of the supply rail, or feedback through the power supply to another stage. Adding ferrite beads on supply leads, improving bypassing with ceramic capacitors, and ensuring the circuit layout has no unintended resonances usually cures this problem.
How does supply voltage affect oscillator frequency?
In a transistor LC oscillator, the transistor's junction capacitances vary slightly with the voltage across them. As supply voltage changes, the collector voltage changes, changing the collector-base junction capacitance (the Miller capacitance), which shifts the frequency. Good oscillator design uses a well-regulated supply voltage and makes the frequency-determining LC tank large enough that the transistor's relatively small junction capacitances are a minor fraction of the total capacitance. Crystal oscillators are less sensitive to supply variation because the crystal's extremely high Q keeps the frequency tightly defined.
Can an oscillator stop oscillating if conditions change?
Yes. If the loop gain falls below 1 — due to transistor aging, component degradation, supply voltage dropping, or excessive loading on the output — the oscillation will die away. This is called oscillator stoppage or stalling. Crystals that have been overdriven can crack internally, permanently changing their characteristics. Electrolytic capacitors in LC tanks can lose capacitance as they age, shifting the resonant frequency beyond the transistor's gain bandwidth. Regular testing of oscillator-critical equipment with a frequency counter is good maintenance practice.
Test Your Knowledge
Answer the questions below to check your understanding. Every answer can be found in the lesson above.