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In many applications of electronics, we need to create a new signal where none existed before. Audio frequency signals can be used for testing other circuits, to produce warning sounds, or as the starting point for various functions. One example is the common touch-tone telephone, which generates two specific signals each time you press one of the buttons. You can hear the two tones, and so can the telephone switching circuitry which uses those tones to identify what number you are trying to call. For that matter, even the dial tone you hear before you start dialing your number is made up of a pair of distinctive audio tones. The signal you hear to tell you the distant phone is ringing is another generated signal, as is the signal that causes that remote phone to actually ring. All of this in just part of the telephone system — the part that connects to the users. There are more internal parts to the telephone network that also use audio signals to control the behavior of the system.
New signals are also needed in many capacities at radio frequencies. These are sometimes used for testing purposes, or for adjusting the settings of tuned circuits to exactly the right frequency. Such signals are also used as the base carrier signals for radio and television broadcast transmitters. Yet another application is in radio and TV receivers, to change the original carrier frequency to something much lower, so the signal can be properly amplified and filtered before the actual information is separated from the carrier.
There are many ways to generate such signals, and the specific method chosen usually is determined according to the characteristics of the required signal and the application that requires it. However, the basis of the generating circuit is always the same. The canonical form of that circuit is shown to the right.
In this circuit, we have some arbitrary input signal (VIN), some kind of amplifier with a gain of A, and an output signal (VOUT). We have also added a passive network which feeds a fraction (β) of VOUT back to be combined with the original VIN. The Greek letter Σ (Sigma) indicates that the two signals are added together, and the "-" sign specifies that the signal being fed back is subtracted from the original VIN. Thus, we can say that the signal being fed back is βVOUT and the signal being amplified is actually VIN - βVOUT. We can write the equation for this circuit as:
VOUT = A × (VIN - βVOUT)
The gain of this circuit is VOUT/VIN. Solving the above equation to determine the gain, we get:
Most of the time, this expression is perfectly good, and can be used to define the gain of the overall circuit. But what happens if we arrange the component values in the feedback circuit in such a way that Aβ = -1 (called the Barkhausen Criterion)? When that happens, the expression gives us division by zero, which implies infinite gain. In reality, the output voltage shifts towards one of the power supply rails. At that extreme of output voltage, the active devices in the amplifier no longer operate in a linear fashion. The value of A changes (usually being significantly reduced), and the circuit behavior changes. At this point, one of three things can happen, depending on the details of circuit design:
When the feedback circuit is arranged to meet the Barkhausen Criterion, we no longer need VIN. The signal fed back to the input is sufficient to maintain the output signal. The result is an oscillator. When the feedback circuit is designed so that the Barkhausen Criterion is only met at one frequency, that is the frequency at which oscillation will occur. Note that if you don't take care to design the feedback circuit to accomplish this, oscillation will take place at a frequency determined by component parameters, parasitic capacitances, etc., and not at the frequency you had in mind. The results can be entertaining, but not generally useful.
On these pages, we will examine a number of different oscillator circuits, and see just how each of them is designed to properly meet the Barkhausen Criterion.
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