When most people hear the word “feedback” they probably think of the ear-piercing squeal that comes from a PA (public address) system when the microphone is too close to the speaker. But feedback is an essential part of electrical, software, and system design — as long as it’s intentional and working how you want it.
WHAT IS FEEDBACK?
Feedback is what occurs when the output of a signal or system is fed back to an input, thereby affecting the output. Feedback comes in two basic varieties, positive and negative. Positive feedback is what hurts your ears in the aforementioned PA system squeal. With the exception of some rock bands, PA system feedback is usually something you want to avoid. Positive feedback occurs when the output is fed back to the input in-phase, reinforcing the signal.
POSITIVE FEEDBACK
Figure 1 is a schematic of a simple single-transistor phase-shift oscillator. This oscillator produces a sine wave at about 1.4KHz (depending on component tolerances) at the collector.
Phase shift oscillator schematic
A phase-shift oscillator works because the resistor/capacitor ladder (R3, R4, R5, C2, C3, C4) produces 180° phase shift at one frequency and the inverting transistor produces another 180° phase shift, for a total of 360° phase shift. Provided there is enough gain in the entire loop, the circuit will oscillate. This circuit could also be built with an opamp. I won’t go into oscillator theory here. I want to use this example to make a few points.
Figure 2 shows the startup characteristics of the oscillator. The lower trace is the 5V supply ramping up after power is applied (note the different voltage scale), the upper trace is the collector of Q1. Ignore the frequency display, the powerup ramp confuses the oscilloscope. You can see that the oscillation starts as the supply voltage approaches 5V, and then the amplitude slowly grows until it is oscillating between the supply rails. This is usually the limiting factor for this type of oscillator. It takes about 20 cycles for this oscillator to reach full amplitude.
Oscillator startup waveform.
The oscillator is started by electrical noise. In the PA system squeal, if you had the speaker and microphone in a very quiet room and slowly raised the volume, you could get it past the oscillation point before it started to squeal; the PA system needs some slight noise, maybe just hum in a speaker, to get the oscillation started.
All linear oscillators work essentially this way, whether the frequency is determined by a crystal, inductor/capacitor circuit, or by a resistor/capacitor network. Digital oscillators that operate by having three or more inverting stages with the output fed back to the input also need phase shift, but the phase shift is provided by the three inverters and is controlled by an RC network or simply by the propagation delay of the gates. I knew an engineer many years ago who said “if you want to build an oscillator, start by trying to build an amplifier”. Which is not exactly true but illustrates the point that if there is enough gain and phase shift at a specific frequency, an amplifier will oscillate, even if it’s unintentional. The circuit shown in Figure 1 is an amplifier, if you take out the feedback network.
A hysteresis switch
Figure 3 shows a simple hysteresis switch built with two transistors. The output is high when the input is high, and the output is low when the input is low. The hysteresis switch is an example of useful positive feedback. Say the input is driven by a 0-1V sine wave, but we want to make it digital so we can connect it to a microcontroller (MCU) input. When the input is 0V, the output is also low, so the junction of R5 and the output is very close to zero. The voltage needed at the base of Q2 to cause the output to switch is about 0.6V. But R6 and R8 make a voltage divider, so the input has to be a bit over 0.6V, in fact about 0.62V to switch the output high. Now here’s where the hysteresis magic comes in. Once the input goes high enough to drive the output high, R6 and R8 still make a voltage divider, only the junction of R8 and the output is now about 5V, so the input has to go lower than 0.6V to turn off Q2, in fact it has to go down to 0.4V.
Hysteresis circuit.
The difference between the high and low switching states is 220mv, so if our sine wave was a little bit noisy, as long as the noise did not exceed 220mv, the switch would filter that out. The positive feedback alters the high and low switching points to convert the sine input into a digital output.
This isn’t a very good hysteresis circuit, it’s just to illustrate how hysteresis works. A comparator, with high impedance inputs, would make a better solution. But positive feedback in the form of hysteresis can clean up a noisy signal, up to a point. It will also speed up the switching time, although this transistor circuit is never going to be very fast.
Bad positive feedback
Of course, as the squealing PA amplifier proves, positive feedback can also be a very bad thing. If allowed to run unchecked, and if the amplifier has enough power, the speakers can be destroyed. Another example of destructive feedback is thermal runaway. This term ordinarily applies to transistors, where transistor heating causes more power to be dissipated, causing more heat, and so on until the transistor fails. But thermal runaway can also apply to a circuit such as an embedded MCU controller. Say a system has a cooling fan that is controlled by the MCU, but the fan is stuck. As the heat builds up, the MCU tries to apply more and more power to the fan in an attempt to cool the system, but the added power just raises the heat more until something breaks. That’s a contrived example, but it illustrates the point.
Positive feedback, both good and bad, applies to other things outside the world of electronics. For a dramatic example, search the Internet for the 1940 Tacoma Narrows bridge collapse.
NEGATIVE FEEDBACK
Positive feedback reinforces the output by feeding back the output to the input in-phase. Negative feedback does the opposite; the output is fed back to the input out of phase, which dampens the output. The phase-shift oscillator in Figure 1 has both positive and negative feedback: the positive feedback makes the circuit oscillate, while the negative feedback is how the transistor is biased.
Resistor R2 sets the bias point of Q1. A 2N3904 has a current gain (ß) of 100 to 300, meaning the collector current Ic is 100 to 300 times the base current Ib (I’m ignoring emitter current here). Ideally Q1 would be biased so that the collector voltage is around half the supply voltage when the feedback network is not connected, so we want the voltage at the collector of Q1 to be about 2.5V, which means 2.5mA through R1. But the key thing is that the bias point not put the transistor into cutoff or saturation. Ib is a function of the collector voltage (Vc), which is a function of Ic as follows:
Ic ≈ ß × Ib
Ib = (Vc – 0.6)/R2 = (Vc – 0.6)/150K
Vc = 5 – Ic × R1 = 5 – (Ic × 1K)
If you solve the simultaneous equations:
Vc = (750K + 600 ß)/(150K + 1000 ß)
So Vc varies from 2V to 3.2v over the range of ß from 100 to 300. Since Ib is a function of Vc, and Vc is a function of Ib, a lower gain transistor, near 100, will have a higher collector voltage, pushing more current into the base and bringing the collector voltage down. A higher gain transistor will have a lower collector voltage, providing less base current, so although the output is dependent on ß, using negative feedback compensates (partly) for ß variations and allows it to stabilize at a useful bias point through the range of possible ß values. Not necessarily a precise bias point, but one that is within an acceptable range. I measured the transistor I used in the example circuit, ß was just over 300, and with C1 removed (disabling the oscillator) the collector voltage was just over 2V. In this case, the negative feedback isn’t compensating for variations in an input signal, but for device-to-device variations in transistor gain.
This is hardly the best way to bias a transistor for most applications. I chose this circuit to demonstrate that it’s entirely possible to have both positive and negative feedback even in a simple circuit or system. In this case, the positive feedback enables oscillation through an AC path that operates at the oscillation frequency, and the negative feedback keeps the DC bias in a reasonable range so the oscillator will work. The positive and negative feedback don’t interact in this circuit, although it would be possible to select DC bias component values that keep the oscillator from starting.
Opamp Example
Figure 4 shows a simple opamp circuit. The output of an opamp, assuming it is operating in a linear region (power supplies within range, output is not at either voltage rail), OUT = Av(V+ – V-). Av is the gain of the opamp, which is usually very high. In the figure, R9 and R11 provide negative feedback to control the gain. They are also a voltage divider between OUT and V-. So working through the math:
OUT = Av(V+-V-)
V- = (OUT x 1K)/11K = OUT/11
OUT = Av V+ – AV OUT /11
OUT/Av = V+ – OUT/11
Since Av is very large, the OUT/Av term is very small and can be discarded. So the resulting formula is OUT = 11 × V+.
Opamp feedback
If you’ve looked at a table of opamp configurations, you’ll recognize this as a noninverting amplifier where the output voltage is R9/R11 + 1. Most opamp feedback calculations can be solved starting with these basic equations. In some cases, such as audio filters, you may have to take frequency into account, and if there is more than one voltage input (such as a voltage instead of ground at the lower end of R11) then the equations can get more complicated. But this is not an opamp tutorial, so I’ll leave it at that.
In an opamp, if the V- input were simply connected to ground, the output would be Av V+. The LM2904 opamp, for example, has Av as high as 140V/mv, meaning each millivolt on V+ tries to move the output 140V. I say “tries to” because the opamp output won’t go that high. Using negative feedback on the V- pin allows the gain to be precisely controlled.
This is the basic principle of any negative feedback system; the output is sampled and used to adjust the output value; if the output gets too high (whether that’s voltage, current, speed of a fan, or any controllable value), the system adjusts the output to bring it back in line. The “system” can be a transistor, as in the phase-shift oscillator, an opamp circuit, or a MCU control circuit for a heater, fan, pump, motor, manufacturing process, or cruise control on an automobile. The basic concept is the same; on a cruise control, if the speed goes too low, the system applies more throttle to tell the engine to apply more power to the wheels. If the speed goes too high, the opposite happens. Of course, a cruise control system has many additional complexities and features, but the basic negative feedback is exactly the same as the opamp and transistor bias circuit; if the output is too high, make it lower. If it’s too low, make it higher. That’s negative feedback in a nutshell.
Control Methods: The actual process of applying negative feedback, especially for something like an industrial process, often involves “tuning” the system for maximum output or minimum variation or fastest correction. There are various schemes for doing this such as PID (Proportional-integral-derivative), PI (proportional-integral), proportional only, bang-bang control, predictive functional control, and others. This won’t be a tutorial on control systems, that’s a topic for another issue, and I looked at PID in the June 2019 Circuit Cellar issue. What I want to address here is the characteristics that affect the complexity and type of negative feedback to be used.
Cost/simplicity: A bang-bang control is the simplest, both in terms of control and the complexity of the controlled element. Most furnaces and air conditioners use bang-bang control. If you set the temperature in your house to 72°F, the heater or air conditioner doesn’t turn partway on. It’s either on or off. The negative feedback system senses the temperature, and when it gets to 72°F, it turns off. When the temperature moves away, the system comes back on. Bang-bang control is only suitable where there is some hysteresis in the system; when the temperature gets to 72°F, whether heating or cooling, it takes a while to ramp the other direction and turn the heat or air conditioning back on. Systems with no hysteresis or lag are unsuitable for bang-bang control because the controlled element will be constantly switching on and off. But the negative feedback principle is still applicable: when it gets too hot, make it cooler, and when it gets too cold, make it warmer.
Lag: Real-world negative feedback control systems have some lag. Even the opamp and transistor examples have some lag, but the input and output changes are too fast for the effect to be noticeable. I developed medical laboratory equipment many years ago. Let’s use as an example a temperature control system in a medical device that is doing some processing on biological samples such as blood. The system has an MCU circuit that controls a heater to heat the sample cabinet to a specific temperature (also called a setpoint).
When the temperature goes low, the MCU will turn on the heater. When the heater reaches the setpoint, it is turned off. But any heater will take time to heat up. If it takes too long, the samples might get too cold, so the amount of power applied to the heater has to bring it up to temperature quickly enough to prevent that. Lag is the time it takes for the heater to actually do something when power is applied, or the time for liquid to flow through a pipe in an industrial control system, or the time for the engine to respond to a command from the cruise control in a car.
Overshoot: At the other end of the cycle, when the setpoint is reached, the heater is turned off. But it will remain hot for a while after the power is removed. This will continue to heat the cabinet, whether it’s for seconds or minutes. This will cause the temperature to overshoot the target value, which may cook the samples or affect the process, so to avoid this overheating, the system might use a proportional-only control, where the drive to the heater is proportional to the difference between the setpoint and the actual temperature. The further the temperature is from the setpoint, the more drive is applied to the heater. As the temperature approaches the setpoint, the drive is reduced. You might do this manually when cooking: turn a stove burner very high to heat the water fast, and then as it is about to boil, turn down the heat so it doesn’t splatter hot water everywhere.
Proportional control has two potential problems: the first is that if the proportional gain is too high, the temperature will overshoot the setpoint. A lower gain can prevent that, but it also causes slower response to changes. In addition, proportional control can cause the temperature to settle a little below setpoint because the difference isn’t enough to activate the heater.
To fix this problem, an integral term might be added, making the system proportional-integral control. The integral term will activate the heater if it stays too long close-but-not-quite-at the setpoint, eliminating the offset. But the integral term also causes overshoot, which may have the same effect as the simple on-off control in overheating and damaging the specimens.
The point of all this is not to do a PID tutorial but to indicate what factors and considerations may be needed in a negative feedback control system. The negative feedback concept of feeding back the output to the input to adjust the setpoint to a fixed value is still valid. But how complicated that adjustment is varies from one application to another. Accuracy of the setpoint, speed of reaching the setpoint, amount of allowable overshoot or oscillation, and even the power efficiency are factors that may impact how the curve between current output and desired setpoint output is shaped. A poorly designed or adjusted control system can even result in positive feedback, causing oscillation.
SOFTWARE EXAMPLE
Figure 5 shows the schematic of a simple controller. This MCU PWM output drives an inductor to provide a boosted voltage of 10V, as you might use to power a sensor or opamp. If you saw my article in the February 2025 Circuit Cellar about switcher efficiency, you’ll recognize this circuit. In this case, the output voltage is fed back to an analog-to-digital-converter (ADC) input on the MCU. This circuit was wired into a development board.
MCU controller schematic.
Figure 6 shows the result using proportional control, where there is some overshoot and then some oscillation until the output settles. This isn’t optimized in any way, but it illustrates the principle. The waveform can be changed in the software by altering the amount of proportional feedback, altering the sampling/update interval, by adding integral or derivative terms, or even by using a different control method. All of these provide negative feedback through the software, but with different characteristics.
Proportional control waveform.
The example here is a single-loop control system. There are multiple-loop systems with multiple feedback points, and you can do a lot of math to model and simulate feedback systems, but that’s beyond the scope of this article.
Conclusion
Both positive and negative feedback are important in circuits and systems. Control systems of all kinds are based on negative feedback. The difference between a simple transistor or opamp circuit and a sophisticated controller is the complexity of the negative feedback requirements and resulting control output waveforms. Designing a feedback system is like most of the hard decisions in life: you have to decide which set of problems you want to manage.
PUBLISHED IN CIRCUIT CELLAR MAGAZINE • APRIL 2025 #417 – Get a PDF of the issue
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Stuart Ball recently retired from a 40+ year career as an electrical engineer and engineering manager. His most recent position was as a Principal Engineer at Seagate Technologies.
