CURRENT ISSUE Contests
Feature Article
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Issue #209 December 2007
THE DARKER SIDE
Are You Locked?
A PLL Primer
by Robert Lacoste
Start | VCO Basics | PLL Basics | Integer or Fractional? | PLL Design | Silicon Trends | It's Your Turn! | Sources & PDF
VCO BASICS
As we will see, one of the main components of a PLL is a voltage-controlled oscillator (VCO, one more acronym). You will usually not be obliged to build your VCOs yourself, but understanding how things work doesn’t hurt, so let’s spend some time on this interesting subject.
A VCO is a special kind of oscillator. Building an oscillator is not a difficult task; a badly designed amplifier will naturally oscillate, especially if it is not the designer’s intention. Building a good oscillator is of course a little more complex, but any amplifying circuit, meaning with a gain greater than one, will oscillate when its output is fed back on its input, intentionally or not. However, there is an additional condition. There must be a given frequency where the amplifier phase shift is zero. At that frequency, the output signal will be in phase with the input signal. The frequency will be the oscillation frequency.
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| Figure 2—This simple transistor-based amplifier has a positive gain from 250 kHz to 20 MHz. The phase response, shown on the bottom, indicates that its phase response crosses the 0 line at a frequency of 13 MHz. |
Figure 2 shows a basic common emitter amplifier stage preceded by a filtering stage (as well as its simulated gain and phase response). I did this simulation with the Proteus CAD tool suite from Labcenter Electronics (UK), which provides a user-friendly front end for the well-known Spice simulation engine. The simulation shows that the gain of the amplifier is greater than 1 (above 0 dB) from roughly 250 kHz to 20 MHz. Its phase response is zero only at a given frequency, 13 MHz.
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| Figure 3—This simulation shows you that if you take the schematic in Figure 2 and connect its output to its input, you have an oscillator. The oscillation frequency is 14.6 MHz, close to the frequency where we got a null phase response in the open-loop configuration. |
What happens if you connect its output to its input? You bet it will oscillate around 13 MHz (see Figure 3). The simulated oscillation frequency is 14.6 MHz. This is due to a change in the amplifier response because we are now loading its output and capacitively loading its input differently than in the open-loop case. A word of caution here: simulating an oscillator is not always easy with Spice (or whatever tool you are using) because an oscillator needs some noise to start. This is easy in real life but more difficult in the memory of a computer. The usual tricks are to force a short time step in the Spice parameters (1 ns) and declare that one of the capacitors must be precharged at the start of the simulation. You must also visualize the simulation result some time after the origin in order to let the oscillator stabilize (from 500 µs to 500.2 µs in the examples). Labcenter Electronics’s support was a great help in pinpointing the tricks.
Converting an oscillator into a voltage-controlled oscillator is not difficult. Because the oscillation frequency is dependent on the frequency-response curve of the underlying amplifier, you have to make the response voltage dependent. This is usually done with a varicap diode because a diode presents a variable capacitance depending on the inverse DC voltage applied to its pins. Figure 4 shows the phase response of a slightly modified version of our amplifier design, with a varicap diode polarized by a DC voltage from 0 to 25 V generated thanks to the R/R5 divider and applied through the L2 inductance, which behaves as an open circuit in high frequencies. The zero phase response is moved from 11.4 to 12.3 MHz when the voltage is modified. If we loop back the circuit, we will have a VCO.
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| Figure 4—To transform an oscillator into a voltage-controlled oscillator, you just need to add a varicap diode, because its capacitance will change depending on the applied DC voltage, which is simulated here by a variation of the R5 resistor value. The design will give a VCO with a 1-MHz tuning range around 13 MHz. |
The schematics are simplified and designed to illustrate the concept, but typical VCOs built around Pierce or Colpitts oscillator topologies are not very different. You can find good prebuilt VCOs from suppliers like Mini-Circuits, Synergy Microwave, Sirenza Microdevices, and Z-Communications. However, knowing how a VCO is built is always useful. The output frequency of a VCO is driven by a DC voltage so you will easily deduce that any noise on the DC input voltage or any thermal noise in the VCO components themselves will produce a “frequency noise” on the output signal. This means that its frequency will not stay exactly the same from cycle to cycle. This kind of noise is usually called phase noise and it is specified in an exotic unit, the dBc/Hz (see Figure 5). The noise can also be understood as jitter in the time domain, even if the phase noise to jitter relationship is not straightforward mathematically speaking. If you are interested in this mathematical relationship, you can find good information in Brad Brannon’s application notes on the Analog Devices web site.
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| Figure 5—The short-term frequency variations of an oscillator or VCO are measured in dBc/Hz. This strange unit is just a convenient and normalized way to measure how quickly the noise power is reducing when you examine frequencies farther from the carrier. On this spectrum analyzer plot, the power of the signal is 17 dBm or 50 mW (i.e., 1 mW × 1017/10 ) because a “dBm” is a decibel relative to 1 mW by definition. Due to noise, the power measured 100 kHz away through a hypothetical 1-Hz wide band-pass filter is not null but –37 dBm. This is 50 dB (i.e., 17 – 37) lower than the carrier. Because we are comparing the carrier power, the unit is “dBc,” meaning “dB relative to the carrier,” and “dBc/Hz” as we normalize to a 1-Hz-wide noise window. If we measure with a 10-Hz-wide filter, then the noise power will be simply 10 times higher. |
Phase noise is often the main difficulty that a VCO user must fight against. For example, if you design a transmitter, then a high level of noise will give you a noisy transmitter. And if you design a receiver, you will end up with a poorly selective device. Phase noise could be a great concern even in digital applications. For example, if the VCO is used as the clock source for a high-speed ADC, its phase noise (i.e., its jitter) must be strictly controlled in order to achieve a good signal-to-noise ratio. I’m afraid this topic will need another column by itself. However, if you have followed me this far, you will understand that selecting a VCO with a smaller frequency-tuning range will usually provide a lower phase noise. That is because a given noise on the DC VCO input, say 1 mV, will give a lower frequency change on the output. For example, if your application needs a signal tunable from 610 to 620 MHz, you should use an ROS-630+ from Mini-Circuits (595 to 630 MHz) rather than a JTOS-850VW (400 to 850 MHz).
