# How does an active device work as an oscillator when its output is fed back to the input?

In the book The Art of Electronics by Paul Horowitz and Winfield Hill, it is mentioned that "Device with power gain are distinguishable by their ability to make oscillators, by feeding some output signal back into the input". I have two question regarding this statement.

1. Is this statement complete in itself? Is there no need of another circuitry(let's say a filter)? If yes, what causes the oscillation in such a feedback circuit which contains only an active device?
2. Is it true for all device which can produce a power gain (that is active devices)?
• It's Winfield Hill. Jul 6, 2017 at 17:55
• @ElectricalArchitect I think you mean Wineld Hill
– pipe
Jul 6, 2017 at 18:00
• @pipe Of course. Jul 6, 2017 at 18:05
• It's semantics - "some" output is the clincher for me that means the statement is true. Anything else is playing with words so go look up barkhausen criteria. Jul 6, 2017 at 18:19
• @EletricalArchitect Sorry about that, too much GoT Jul 7, 2017 at 14:17

The statement is not complete on its own. Overall, you need a gain greater than +1. Over-unity power gain is a necessity, but it also has to be of the right phase, and the oscillator must NOT have over-unity gain at DC.

Less than unity gain means the signal is diminished each pass thru the amplifier, so any oscillation will die out.

Gain but inverted causes negative feedback when the output is fed back to the input. This causes the system to stabilize and not oscillate.

Gain and in phase but DC coupled results in two stable states, each with the output driven to the two extremes.

It takes gain greater than 1, in phase, but DC gain less than 1 to make a oscillator.

• Thanks, @Olin for the answer. From what I understand from your answer is that gain greater than 1 and the correct phase are important to sustain an oscillation. What I am actually interested in is the transient behavior. How does a DC voltage gets converted to an oscillation considering the conditions that you have mentioned are satisfied? Is it because of the noise in the input DC signal? This article suggests so. Jul 7, 2017 at 14:24

Pretty much any active circuit can oscillate (especially when you don't want it to). All it requires is that you have positive one feedback at the frequency of oscillation. Another way of looking at it is that the feedback has 360 degrees phase shift. There is always "other circuitry" required to provide this phase shift, but some of this "circuitry" often is the internal capacitance of the device or the inductance of leads and traces. You do need a device capable of providing gain, and some combination of external components and internal reactance that will provide the correct phase for the feedback.

I can't think of a component that has gain that you would not be able to cause to oscillate with the correct circuitry around it.

• "way of looking at it is that the feedback has 360 degrees phase shift" Or you can look at it as having 0 phase shift, or that it is "in phase". Jul 6, 2017 at 18:23
• Agreed Olin. Just trying to make the point that in most oscillators there are multiple parts contributing to phase shift in the feedback path, and the contributions from all of the components have to add up to get you back in phase. Jul 6, 2017 at 18:27
• Thank you @John for the answer. Would you please refer to the comment I made in Olin's answer regarding a doubt I have? Jul 7, 2017 at 14:26
• I think you are correct in that you need some initial perturbation to start an oscillation, and that it is theoretically possible that a device with positive one feedback and the right initial condition would not start until there is a difference between input and output. In the real world there is always noise. Jul 7, 2017 at 14:42

1) Power gain for Oscillation means the transistor draws DC power to amplify the AC signal to boost its output power with some sort of 2nd order effect such as discrete or parasitic or distributed conductor LC values. THe LC values provide the impedance ratio and thus voltage or current filtering and phase shift to cause oscillations.

The "Barkhausen" criteria for oscillation is positive AC feedback and gain =>1. AC Analysis of all circuit, cable and component LC values are necessary to determine if the impedance ratio and voltage gain leads to ringing or steady oscillation or a growing oscillation to saturation ( square wave).

Note that there are also RC oscillators which are 1st order filters but with hysteresis on negative feedback which will create a "relaxation oscillator" . This uses negative DC feedback ( to become self DC-biased) with hysteresis causes a time delay with a shunt capacitance and thus a 90 deg phase shift with each half cycle netting an equivalent positive AC feedback of 360 deg. In this case the input appears as a triangle wave and the output a square wave, yet the same principles apply drawing DC power gain with filtering to produce AC oscillations with more output power than the input. In THIS case the input is a DC offset which causes a slew rate which contains enough signal of the frequency of oscillation to grow to a steady saturated oscillation very quickly, often symmetrical about V+/2.

When unity gain with 0 or 360 deg feedback (positive) the output is sinusoidal. We know emitter followers provide unity voltage gain and power gain from current amplification. But when driving a series inductive thin wire with a very low driving impedance a high Q ringing on square edge signals will cause ringing from impedance mismatch and in some cases degenerative feedback will sustain the oscillation at very high frequency due to the emitter LC cable loading effects.

Other examples are feedback with gain with LC parallel resonance are Colpitts Hartley and Crystal oscillators which are emulated by LC components to net a 0 or 360 deg. etc. phase shift at resonant frequency.

THe startup time is by the dampening factor or Q or real/reactive impedance ratios of the circuit. ( where I will stop here ,as I fear I have said too much already). Crystals often have Q=10k while LC circuits ~100 max from physical constraints and RC hysteresis Oscillators limited only by the Gain-BW of the amplifier.

2) All transistors and diodes are call Active devices due to the semiconductive slope of I/V which gives rise to gain of voltage or current depending on the load with a DC source. Passive devices (RLC) may also have an AC voltage gain or current gain from a DC power step voltage from impedance ratios of a tuned circuit but are not able to sustain the oscillations because there is NO ACTIVE SEMICONDUCTOR device to provide POWER GAIN. So V or I gain is always at the expense of a rise in output resistance for passive only circuits. THus an Active device is necessary for Power gain. THe power gain is limited by the size of the device, where efficiency of AC power gain and DC consumption depends greatly on the circuit design with tradeoffs for linearity, distortion etc.

THe Reactive impedance is used to determine if there is gain relative to the the resistive loading. Dampening factor is derived from this impedance ratio.

Is it true for all device which can produce a power gain (that is active devices)?

No. For example a device with a 10x current gain and 0.5x voltage gain can never oscillate, in voltage feedback mode.

What it states is a necessary but not sufficient condition.