Oscillator is a kind of heart in all RF system and the performance of this component would influence almost every other components in the system and will have crucial effect on the final data accuracy.

The function of Oscillator is very simple (at least in theory). It is just to create a pure sinosoidal wave as shown below.

This page starts with the output of an ideal oscillator, and then explains the condition that makes a circuit oscillate at all. After that it compares ideal and real oscillators in the spectrum and over temperature, and it closes with the common types of oscillators and where each one is used.

• Ideal Oscillator Output
• Oscillation Condition
• Ideal vs Real Oscillator
• Types of Oscillators

Ideal Oscillator Output

Let's first fix what a perfect oscillator would deliver, because every imperfection later on the page is measured against it. An ideal oscillator produces one sine wave with a constant amplitude and a constant frequency. We can look at that wave in the frequency domain or in the time domain, and each view shows a different property.

• The upper plot shows amplitude against frequency. The whole output sits in one narrow line at the frequency f, with nothing on either side.
• The lower plot shows amplitude against time. The sine wave repeats with a constant amplitude and a constant spacing between peaks.
• The arrow under the time plot marks the length of one cycle and labels it λ = 1/f. On a time axis this length is the period, T = 1/f. The wavelength λ is a distance, and it equals c/f for a wave in free space.

The two plots describe the same signal. A single line in the spectrum means that the time signal is a pure sine wave that never changes its frequency or its phase. Any spreading of that line, or any extra line next to it, means that the time signal carries some unwanted variation. That is why the spectrum is the usual way to judge an oscillator.

• An ideal oscillator has one spectral line : all of its power sits at the frequency f.
• Period and wavelength are different quantities : the period T = 1/f is a time, and the wavelength λ = c/f is a distance.
• The spectrum shows the imperfections most clearly : small variations of frequency or phase appear as spreading or extra lines around f.

Oscillation Condition

How does a circuit produce a sine wave with no input signal at all? The answer is positive feedback. An amplifier drives a frequency selective network, and the network feeds part of the output back to the amplifier input. Figure 1 shows this loop.

Figure 1. Oscillator as a feedback loop. The resonator passes the fed back signal with the right phase at one frequency only, so the loop sustains oscillation at that frequency.

The loop oscillates at a frequency where two conditions hold together. This pair is known as the Barkhausen criterion. The first condition is on the magnitude: the loop gain |A β| equals 1, so the signal returns to the amplifier input with the same amplitude. The second condition is on the phase: the total phase shift around the loop is 0 deg or a multiple of 360 deg, so the returning signal adds to the signal already there.

A real oscillator does not start with a sine wave. It starts from noise. At power on, the loop gain is set a little above 1, so the noise component at the resonant frequency grows with every round trip. As the amplitude grows, the amplifier begins to compress. Its gain falls until the loop gain is exactly 1, and the amplitude then stays constant. So the nonlinearity of the amplifier sets the output level.

The resonator sets the frequency. An LC tank resonates at f = 1/(2π sqrt(LC)). For example, L = 10 nH and C = 1 pF give about 1.59 GHz. A quartz crystal replaces the LC tank when the frequency must be accurate and stable. Its quality factor Q is much higher than that of an LC tank, so its phase changes very steeply with frequency near resonance. A steep phase slope means that a disturbance in the amplifier can move the frequency only a little. This is the same property that gives a crystal oscillator low phase noise.

• An oscillator is an amplifier with positive feedback : a frequency selective network returns part of the output to the input.
• The Barkhausen criterion has two parts : the loop gain is 1 and the loop phase is 0 or n x 360 deg at the oscillation frequency.
• Start up needs a loop gain above 1 : the oscillation grows from noise, and amplifier compression then limits the amplitude.
• A higher resonator Q gives a more stable frequency : this is why crystals are used as frequency references.

Ideal vs Real Oscillator

Now let's compare real oscillators with the ideal one. Two kinds of imperfection matter most in practice. The first is the shape of the spectrum around the carrier. The second is how far the frequency moves when the temperature changes.

As any other components, there is pretty big gap between the ideal performance and realistic performance in oscillator as shown below.

On the right side, you see three different frequency responses of realistic oscillators.

The first (top) plot shows the most common non-ideal (undesired) issues. The highest center peak is the one that we want to get from the oscillator, but all the other smaller peaks around the center peak is the one that we don't want. In this case, the gap between those small peak seems to be pretty constant which would give us at least some clue for troubleshooting. (I would not go any deeper on this type of small peaks here).

The second (middle) plot shows a lot of small peaks around the center peak, some of the peaks seems to be in similar gaps and some of them are now. Overall.. the frequency response around the center peak is not so symetric.

The third (bottom) plot shows the center peak magnified along frequency axis (horizontal axis). The center peak of ideal oscillator should show very sharp beak however much you magnify it, but this one shows a kind of widening skirt as it goes down to the bottom of the peak. This is caused by phase noise of the oscillator and this is what everybody wants to avoid, but impossible to remove completely.

• The Ideal plot on the left shows one line. The three Real/Practical plots on the right are measured spectra with their own axes.
• The top plot shows discrete spurious lines on both sides of the carrier, with a fairly regular spacing.
• The middle plot shows many lines and a raised floor around the carrier, and the pattern is not symmetric.
• The bottom plot shows the carrier close up, in dBm against frequency in MHz. The skirt falls gradually on both sides of the carrier instead of dropping at once.

There is another important characteristics which makes a big difference between ideal and realistic oscillators. It is about frequency changes of oscillator over temperature. Everybody wants to have an oscillator in which the frequency does not change at all with temperature as shown on the plot to the left. But this kind of oscillator exists only in our idea, not in reality. The oscillators in reality shows the frequency response over temperature as shown on the right plots. it shows the frequency changes over temperature and this kind of frequency change can influence greatly on the performance of a communication system. There are several techniques to compensate this kind of frequency changes (e.g, PLL, Oven Control etc) but it is almost impossible to completely remove these frequency changes.

• The Ideal plot is a flat line. The frequency is the same at every temperature.
• The upper Real/Practical plot rises to a maximum and then falls. This parabolic shape is typical of a tuning fork crystal, such as a 32.768 kHz watch crystal.
• The lower Real/Practical plot rises, falls and rises again. This cubic shape is typical of an AT-cut crystal, the common cut for MHz range references.

Frequency errors of this kind are given in ppm, parts per million of the nominal frequency. The error in Hz is the ppm value times the frequency. A useful point follows from this. A PLL multiplies the reference frequency, and it multiplies the error by the same factor. So the error in ppm stays the same. Let's take a 26 MHz reference with an error of 20 ppm. The reference is off by 520 Hz. After a PLL multiplies it to a 2 GHz carrier, the carrier is off by 40 kHz, which is more than two LTE subcarriers of 15 kHz.

Mobile standards set tight limits on this error. 36.101 clause 6.5.1 requires the LTE UE modulated carrier frequency to be accurate to within +/-0.1 PPM. The error is observed over one time slot of 0.5 ms, and it is compared with the carrier frequency received from the E-UTRA Node B. At 2 GHz this is +/-200 Hz. The requirement is relative to the received downlink, so a UE does not need an absolute reference that good. Instead, it measures the downlink frequency and corrects its own oscillator to follow it.

• Real oscillators show spurious lines and a phase noise skirt : the carrier is never a single line.
• Crystal frequency drifts with temperature in a known shape : parabolic for a tuning fork crystal and cubic for an AT-cut crystal.
• A ppm error scales with the carrier frequency : 20 ppm is 520 Hz at 26 MHz and 40 kHz at 2 GHz.
• The LTE UE must stay within +/-0.1 PPM of the received carrier : this is 200 Hz at 2 GHz, and the UE meets it by tracking the downlink.

Types of Oscillators

Oscillators come in many packages, and the package tells you a lot about the stability class. The main difference between the classes is how each one deals with the temperature drift described in the previous section. The picture below collects typical examples, from small crystal cans to magnetrons.

There are many different types of oscillator. you would see the oscillators like (a)~(d) if you break any of your electronic product. If you break some electronic equipment which requires high frequency accuracy, you would see the oscillators like (f)~(g) which is called OCXO(Oven Controled Crystal Oscillator).

If you see the product like (j)~(l), it would not look like an oscillator, but I categorized these into an oscillator since the function of these is basically same as those oscillators that we commonly see. These are called 'Magnetron' which is usually used in Microwave oven or very high power transmitter like radar system.

• Items (a) to (e) are small parts: crystal cans in metal housings, a surface mount package, and a DIP package.
• Items (f) to (i) are larger metal modules of the kind used for high stability references.
• Items (j) to (l) are magnetrons, the microwave tubes used in microwave ovens and radar transmitters.

The common classes differ in how they handle the temperature curve. A plain crystal oscillator, XO, leaves the drift uncorrected. A TCXO, a temperature compensated crystal oscillator, measures the temperature and applies a correction that follows the curve of the crystal. A VCXO lets a control voltage pull the crystal frequency slightly, so a loop can steer it, for example to track a received carrier. An OCXO keeps the crystal in a small oven at a constant temperature, near a turning point of the curve where the slope is zero. It is the most stable class, but it is also the largest and needs the most power.

At RF, the carrier itself usually comes from a VCO, a voltage controlled oscillator built around an LC tank. A VCO tunes over a wide range, but on its own its frequency is not stable. So a PLL locks the VCO to a crystal reference. The result combines the tuning range of the VCO with the long term stability of the crystal.

If you want to know more about oscillators in more commercial context, I would recommend Rakon (http://www.rakon.com). You will get not only the information on diverse commercial product but also many application notes which will be very helpful.

• XO, TCXO and OCXO differ in temperature handling : no correction, a correction that follows the crystal curve, and a constant temperature oven.
• A VCXO can be steered by a control voltage : a loop can use it to follow a reference or a received carrier.
• RF carriers come from a VCO locked by a PLL : the VCO gives the tuning range and the crystal reference gives the stability.