Feedback Principle
Part of Vacuum Tubes
Feedback — coupling a portion of an amplifier’s output back to its input — is the most powerful technique in electronic design, reducing distortion, stabilizing gain, and controlling impedance.
Why This Matters
Harold Black’s 1927 invention of negative feedback transformed amplifier design from an art requiring carefully selected, matched tubes into a reliable engineering discipline. A tube amplifier without feedback produces gain that varies with tube age, temperature, and supply voltage, and distortion that increases with signal level. The same amplifier with negative feedback has stable, predictable gain, dramatically reduced distortion, and well-defined input and output impedances.
For community communication systems, feedback matters because tubes are irreplaceable resources that age and vary. Without feedback, every tube replacement requires rebalancing and readjusting the circuit to compensate for the new tube’s slightly different parameters. With enough negative feedback, these variations become irrelevant — the circuit performance is set by the feedback network components (resistors and capacitors) which can be made or salvaged with good precision, rather than by the tube parameters which vary widely.
Understanding feedback also helps in diagnosing oscillating amplifiers and other instability problems. Positive feedback — feedback with the wrong phase — causes oscillation. Many troublesome behaviors in tube circuits, including motorboating (low-frequency oscillation) and parasitic oscillation at RF frequencies, are forms of unintended positive feedback that understanding the feedback principle lets you identify and eliminate.
Negative Feedback Basics
Negative feedback means taking a sample of the output signal, inverting it (making it negative), and adding it to the input. The result is that the amplifier responds to the difference between the desired input and its actual output, correcting any errors.
If the open-loop gain (gain without feedback) is A, and the fraction of the output fed back to the input is β, then the closed-loop gain (gain with negative feedback) is:
Af = A / (1 + Aβ)
The term (1 + Aβ) is called the feedback factor. For large Aβ (strong feedback), the closed-loop gain approaches 1/β, which is determined entirely by the feedback network components. A resistor ratio can be made much more precisely and stably than a tube gain can be, so strong negative feedback makes amplifier gain stable and predictable.
If an amplifier has a gain of 100 and a feedback fraction of 0.09 (β = 0.09):
- Aβ = 100 × 0.09 = 9
- Feedback factor = 1 + 9 = 10
- Closed-loop gain = 100 / 10 = 10
The gain dropped by a factor of 10. But all the beneficial effects of feedback also increase by the same factor of 10. Distortion generated within the amplifier is reduced by a factor of 10. Output impedance is reduced by a factor of 10 (for series feedback configurations). Gain variation with tube aging or temperature is reduced by a factor of 10.
Types of Feedback Topology
Feedback comes in four topologies depending on how the output sample is taken and how it is returned to the input.
Series-voltage feedback (most common in tube audio amplifiers): the output is sampled in parallel with the load (measuring output voltage), and the feedback is returned in series with the input. This increases input impedance and decreases output impedance. The classic cathode-degeneration effect — leaving the cathode bypass capacitor off — is a local example of series-voltage feedback.
Shunt-current feedback: the output current is sampled and fed back in parallel with the input. This decreases both input and output impedance. Used in specialized applications such as current amplifiers.
Global feedback from output transformer secondary to first stage: a resistor from the speaker output terminal feeds a fraction of the output voltage back to the cathode or grid of the input stage. This is the global negative feedback used in most high-fidelity audio amplifiers. It reduces distortion produced by the output stage (the largest source in a well-designed amplifier) and reduces output impedance, improving speaker damping.
Phase response and stability: negative feedback works at the design frequency, but every amplifier introduces phase shift at frequencies far above and below the intended operating range. If the phase shift through the amplifier reaches 180 degrees at some frequency, the negative feedback becomes positive feedback at that frequency. If the loop gain is greater than 1 at that frequency, the amplifier oscillates at that frequency regardless of the input signal.
Applying Global Feedback in Practice
For an audio power amplifier with a feedback loop from the speaker output to the first stage input:
The feedback resistor (Rf) connects from the speaker output terminal to the cathode of the first tube (or to the grid through a series resistor). The cathode resistor (Rk) of the first tube remains unbypassed and serves as the summing element. The feedback signal appears across Rk and subtracts from the input signal.
The feedback fraction β = Rk / (Rk + Rf). For Rk = 1000 ohms and Rf = 22,000 ohms, β = 1000/23000 = 0.043. With a nominal open-loop gain of 200:
- Aβ = 200 × 0.043 = 8.7
- Closed-loop gain = 200 / 9.7 = 20.6
- Distortion reduction factor: 9.7
For stability, the feedback loop must have adequate phase margin — the phase of the loop gain at the frequency where its magnitude drops to 1 must be less than 180 degrees. Ensure this by rolling off the high-frequency gain of the amplifier with a small capacitor across the feedback resistor or the plate resistor of the first stage. This prevents the phase shift from accumulating to 180 degrees before the gain has dropped below unity.
Test for stability by applying a square wave input and observing the output on an oscilloscope. A well-damped, stable amplifier shows square wave reproduction without ringing (oscillation on the transitions). Ringing indicates insufficient phase margin. Reduce it by adding more high-frequency rolloff before the feedback loop is closed.
Local vs. Global Feedback
Local feedback acts on a single stage. Examples include the unbypassed cathode resistor (degeneration), the cathode follower configuration (100% series feedback), and a plate-to-grid feedback resistor.
Global feedback encompasses multiple stages or the entire amplifier. It is more effective at reducing distortion because it corrects errors from all stages in the loop, not just one. But it is harder to stabilize because the phase shift accumulates from all the stages in the loop.
A practical approach: apply local feedback first to each stage individually (particularly the output stage, where distortion is largest), then apply moderate global feedback over the entire amplifier. This produces a well-behaved system that is stable and provides substantial distortion reduction without the marginal stability problems that come with high-gain global feedback around many stages.
Cathode degeneration — leaving the cathode bypass capacitor off the output stage tubes — is a particularly effective and simple local feedback technique. It adds a series resistance between the cathode and ground equal to the cathode resistor value, which the tube’s internal transconductance multiplies to an effective plate resistance increase by the factor (1 + gm × Rk). This linearizes the output stage characteristic markedly and is always worth considering before applying global feedback.